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  • 101.
    Dmytryshyn, Andrii
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Structure preserving stratification of skew-symmetric matrix polynomials2017Ingår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 532, s. 266-286Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study how elementary divisors and minimal indices of a skew-symmetric matrix polynomial of odd degree may change under small perturbations of the matrix coefficients. We investigate these changes qualitatively by constructing the stratifications (closure hierarchy graphs) of orbits and bundles for skew-symmetric linearizations. We also derive the necessary and sufficient conditions for the existence of a skew-symmetric matrix polynomial with prescribed degree, elementary divisors, and minimal indices.

  • 102.
    Dmytryshyn, Andrii
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Johansson, Stefan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Codimension computations of congruence orbits of matrices, symmetric and skew-symmetric matrix pencils using Matlab2013Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Matlab functions to work with the canonical structures for congru-ence and *congruence of matrices, and for congruence of symmetricand skew-symmetric matrix pencils are presented. A user can providethe canonical structure objects or create (random) matrix examplesetups with a desired canonical information, and compute the codi-mensions of the corresponding orbits: if the structural information(the canonical form) of a matrix or a matrix pencil is known it isused for the codimension computations, otherwise they are computednumerically. Some auxiliary functions are provided too. All thesefunctions extend the Matrix Canonical Structure Toolbox.

  • 103.
    Dmytryshyn, Andrii
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. School of Science and Technology, Örebro University, Örebro, Sweden.
    Johansson, Stefan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Van Dooren, Paul
    Department of Mathematical Engineering, Université catholique de Louvain, Louvain-la-Neuve, Belgium.
    Geometry of Matrix Polynomial Spaces2019Ingår i: Foundations of Computational Mathematics, ISSN 1615-3375, E-ISSN 1615-3383Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study how small perturbations of general matrix polynomials may change their elementary divisors and minimal indices by constructing the closure hierarchy (stratification) graphs of matrix polynomials' orbits and bundles. To solve this problem, we construct the stratification graphs for the first companion Fiedler linearization of matrix polynomials. Recall that the first companion Fiedler linearization as well as all the Fiedler linearizations is matrix pencils with particular block structures. Moreover, we show that the stratification graphs do not depend on the choice of Fiedler linearization which means that all the spaces of the matrix polynomial Fiedler linearizations have the same geometry (topology). This geometry coincides with the geometry of the space of matrix polynomials. The novel results are illustrated by examples using the software tool StratiGraph extended with associated new functionality.

  • 104.
    Dmytryshyn, Andrii
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Orbit closure hierarchies of skew-symmetric matrix pencils2014Rapport (Övrigt vetenskapligt)
    Abstract [en]

    We study how small perturbations of a skew-symmetric matrix pencil may change its canonical form under congruence. This problem is also known as the stratification problem of skew-symmetric matrix pencil orbits and bundles. In other words, we investigate when the closure of the congruence orbit (or bundle) of a skew-symmetric matrix pencil contains the congruence orbit (or bundle) of another skew-symmetric matrix pencil. This theory relies on our main theorem stating that a skew-symmetric matrix pencil A-λB can be approximated by pencils strictly equivalent to a skew-symmetric matrix pencil C-λD if and only if A-λB can be approximated by pencils congruent to C-λD.

  • 105.
    Edlund, Jeanette
    et al.
    Sveriges lantbruksuniversitet.
    Servin, Martin
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Keramati, Ehsan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    A long-tracked bogie design for forestry machines on soft and rough terrain2013Ingår i: Journal of terramechanics, ISSN 0022-4898, E-ISSN 1879-1204, Vol. 50, nr 2, s. 73-83Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A new design for a tracked forestry machine bogie (long track bogie; LTB) on soft and rough terrain is investigated using nonsmooth multibody dynamics simulation. The new bogie has a big wheel that is connected to and aligned with the chassis main axis. A bogie frame is mounted on the wheel axis but left to rotate freely up to a maximum angle and smaller wheels that also rotate freely are mounted on the frame legs with axes plane parallel to the driving wheel. The wheels are covered by a single conventional forestry machine metal track. The new bogie is shown to have higher mobility and cause less ground damage than a conventional tracked bogie but requires larger torque to create the same traction force as a conventional bogie. The new bogie also gives less acceleration when passing obstacles than the conventional bogie. Additionally, due to the shape and size of the new bogie concept, it can pass wider ditches.

  • 106. Effenberger, Cedric
    et al.
    Kressner, Daniel
    Engström, Christian
    ETH Zurich, Seminar for Applied Mathematics.
    Linearization techniques for band structure calculations in absorbing photonic crystals2012Ingår i: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 89, nr 2, s. 180-191Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Band structure calculations for photonic crystals require the numerical solution of eigenvalue problems. In this paper, we consider crystals composed of lossy materials with frequency-dependent permittivities. Often, these frequency dependencies are modeled by rational functions, such as the Lorentz model, in which case the eigenvalue problems are rational in the eigenvalue parameter. After spatial discretization using an interior penalty discontinuous Galerkin method, we employ a recently developed linearization technique to deal with the resulting rational matrix eigenvalue problems. In particular, the efficient implementation of Krylov subspace methods for solving the linearized eigenvalue problems is investigated in detail. Numerical experiments demonstrate that our new approach is considerably cheaper in terms of memory and computing time requirements compared with the naive approach of turning the rational eigenvalue problem into a polynomial eigenvalue problem and applying standard linearization techniques. Copyright © 2011 John Wiley & Sons, Ltd.

  • 107.
    Elfverson, Daniel
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Larson, Mats G.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Larsson, Karl
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    A new least squares stabilized Nitsche method for cut isogeometric analysis2019Ingår i: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 349, s. 1-16Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We derive a new stabilized symmetric Nitsche method for enforcement of Dirichlet boundary conditions for elliptic problems of second order in cut isogeometric analysis (CutIGA). We consider C1 splines and stabilize the standard Nitsche method by adding a certain elementwise least squares terms in the vicinity of the Dirichlet boundary and an additional term on the boundary which involves the tangential gradient. We show coercivity with respect to the energy norm for functions in H2(Ω) and optimal order a priori error estimates in the energy and L2 norms. To obtain a well posed linear system of equations we combine our formulation with basis function removal which essentially eliminates basis functions with sufficiently small intersection with Ω. The upshot of the formulation is that only elementwise stabilization is added in contrast to standard procedures based on ghost penalty and related techniques and that the stabilization is consistent. In our numerical experiments we see that the method works remarkably well in even extreme cut situations using a Nitsche parameter of moderate size.

  • 108.
    Elfverson, Daniel
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Larson, Mats G.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Larsson, Karl
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    CutIGA with basis function removal2018Ingår i: Advanced Modeling and Simulation in Engineering Sciences, ISSN 2213-7467, Vol. 5, nr 6Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider a cut isogeometric method, where the boundary of the domain is allowed to cut through the background mesh in an arbitrary fashion for a second order elliptic model problem. In order to stabilize the method on the cut boundary we remove basis functions which have small intersection with the computational domain. We determine criteria on the intersection which guarantee that the order of convergence in the energy norm is not affected by the removal. The higher order regularity of the B-spline basis functions leads to improved bounds compared to standard Lagrange elements.

  • 109.
    Elfverson, Daniel
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Larson, Mats G.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Målqvist, Axel
    Multiscale methods for problems with complex geometry2017Ingår i: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 321, s. 103-123Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We construct corrected coarse test and trail spaces which takes the fine scale features of the computational domain into account. The corrections only need to be computed in regions surrounding fine scale geometric features. We achieve linear convergence rate in the energy norm for the multiscale solution. Moreover, the conditioning of the resulting matrices is not affected by the way the domain boundary cuts the coarse elements in the background mesh. The analytical findings are verified in a series of numerical experiments.

  • 110.
    Eljammaly, Mahmoud
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Karlsson, Lars
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    On the Tunability of a New Hessenberg Reduction Algorithm Using Parallel Cache Assignment2018Ingår i: Parallel Processing and Applied Mathematics. PPAM 2017: Part 1 / [ed] Wyrzykowski R., Dongarra J., Deelman E., Karczewski K., Springer, 2018, s. 579-589Konferensbidrag (Refereegranskat)
    Abstract [en]

    The reduction of a general dense square matrix to Hessenberg form is a well known first step in many standard eigenvalue solvers. Although parallel algorithms exist, the Hessenberg reduction is one of the bottlenecks in AED, a main part in state-of-the-art software for the distributed multishift QR algorithm. We propose a new NUMA-aware algorithm that fits the context of the QR algorithm and evaluate the sensitivity of its algorithmic parameters. The proposed algorithm is faster than LAPACK for all problem sizes and faster than ScaLAPACK for the relatively small problem sizes typical for AED.

  • 111.
    Engström, Christian
    ETH Zurich, Electromagnetic Fields and Microwave Electronics Laboratory.
    On a high-order discontinuous Galerkin method applied to canonical scattering problems2010Ingår i: International Symposium on Electromagnetic Theory: EMTS, 2010 URSI, 2010, s. 752-755Konferensbidrag (Refereegranskat)
    Abstract [en]

    A high-order interior penalty method for scattering problems in two-dimensions is presented. Results for perfectly conducting objects illustrate the high accuracy of the method at low computational cost.

  • 112.
    Engström, Christian
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Spectral approximation of quadratic operator polynomials arising in photonic band structure calculations2014Ingår i: Numerische Mathematik, ISSN 0029-599X, E-ISSN 0945-3245, Vol. 126, nr 3, s. 413-440Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Galerkin spectral approximation theory for non-self-adjoint quadratic operator polynomials with periodic coefficients is considered. The main applications are complex band structure calculations in metallic photonic crystals, periodic waveguides, and metamaterials. We show that the spectrum of the considered operator polynomials consists of isolated eigenvalues of finite multiplicity with a nonzero imaginary part. The spectral problem is equivalent to a non-compact block operator matrix and norm convergence is shown for a block operator matrix having the same generalized eigenvectors as the original operator. Convergence rates of finite element discretizations are considered and numerical experiments with the p -version and the h -version of the finite element method confirm the theoretical convergence rates.

  • 113.
    Engström, Christian
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Giani, Stefano
    Grubisic, Luka
    Efficient and reliable hp-FEM estimates for quadratic eigenvalue problems and photonic crystal applications2016Ingår i: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 72, nr 4, s. 952-973Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present a-posteriori analysis of higher order finite element approximations (hp-FEM) for quadratic Fredholm-valued operator functions. Residual estimates for approximations of the algebraic eigenspaces are derived and we reduce the analysis of the estimator to the analysis of an associated boundary value problem. For the reasons of robustness we also consider approximations of the associated invariant pairs. We show that our estimator inherits the efficiency and reliability properties of the underlying boundary value estimator. As a model problem we consider spectral problems arising in analysis of photonic crystals. In particular, we present an example where a targeted family of eigenvalues cannot be guaranteed to be semisimple. Numerical experiments with hp-FEM show the predicted convergence rates. The measured effectivities of the estimator compare favorably with the performance of the same estimator on the associated boundary value problem. We also present a benchmark estimator, based on the dual weighted residual (DWR) approach, which is more expensive to compute but whose measured effectivities are close to one. 

  • 114.
    Engström, Christian
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Grubisic, Luka
    University of Zagreb.
    A Subspace Iteration Algorithm for Fredholm Valued Functions2015Ingår i: Mathematical problems in engineering (Print), ISSN 1024-123X, E-ISSN 1563-5147, Vol. 2015, artikel-id 459895Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present an algorithm for approximating an eigensubspace of a spectral component of an analytic Fredholm valued function. Our approach is based on numerical contour integration and the analytic Fredholm theorem. The presented method can be seen as a variant of the FEAST algorithm for infinite dimensional nonlinear eigenvalue problems. Numerical experiments illustrate the performance of the algorithm for polynomial and rational eigenvalue problems.

  • 115.
    Engström, Christian
    et al.
    Lund University, Department of Electrical and Information Technology.
    Sjöberg, Daniel
    Lund University, Department of Electrical and Information Technology.
    A Comparison of two numerical methods for homogenization of Maxwell's equations2004Konferensbidrag (Refereegranskat)
  • 116.
    Engström, Christian
    et al.
    Lund University, Department of Electrical and Information Technology.
    Sjöberg, Daniel
    Lund University, Department of Electrical and Information Technology.
    On two numerical methods for homogenization of Maxwell's equations2007Ingår i: Journal of Electromagnetic Waves and Applications, ISSN 0920-5071, Vol. 21, nr 13, s. 1845-1856Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    When the wavelength is much larger than the typical scale of the microstructure in a material, it is possible to define effective or homogenized material coefficients. The classical way of determination of the homogenized coefficients consists of solving an elliptic problem in a unit cell. This method and the Floquet-Bloch method, where an eigenvalue problem is solved, are numerically compared with respect to accuracy and contrast sensitivity. Moreover, we provide numerical bounds on the effective permittivity. The Floquet-Bloch method is shown to be a good alternative to the classical homogenization method, when the contrast is modest.

  • 117.
    Engström, Christian
    et al.
    ETH Zurich, Seminar for Applied Mathematics.
    Wang, Mengyu
    Complex dispersion relation calculations with the applications to absorptive photonic crystals2010Ingår i: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 84, s. 849-863Artikel i tidskrift (Refereegranskat)
  • 118.
    Eriksson, Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    A Mass Conserving Wind Model Evaluation With Finite Element2013Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Detta arbete testar och utvärderar en metod for att approximera ett

    stationärt vind fält i en urban miljö i syfte att användas for spridnings

    beräkningar. Istället for att använda Navier Stokes ekvation används en

    massbevarande modell. Denna modell använder empirisk information for

    att approximera vind fältet. Fältet görs sedan massbevarande. Detta arbete

    visar att det ar möjligt att lösa modellen med Finita Element och

    Comsol Multiphysics för stora urbana miljöer på kort tid. Jämförelser med

    vindtunnel experiment visar att de stora virvlarna är synliga men att hastigheterna

    är lägre. Bland de iterativa lösarna som användes presterade

    Multigrid och Conjugat Gradient metoden bäst. En urban miljö med

    2 100 000 frihetsgrader hade en lösningstid på ca 3 minuter.

  • 119.
    Ersson, Back Tomas
    et al.
    Sveriges lantbruksuniversitet.
    Jundén, Linus
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Bergsten, Urban
    Sveriges lantbruksuniversitet.
    Servin, Martin
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Simulated productivity of one- and two-armed tree planting machines2013Ingår i: Silva Fennica, ISSN 0037-5330, E-ISSN 2242-4075, Vol. 47, nr 2, artikel-id 958Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    To increase mechanized planting, planting machine productivity must increase in order to improve cost-efficiency. To determine if excavators with two crane arms could potentially help to increase planting machine productivity under Nordic clearcut conditions, we modelled one- armed and semi-automated two-armed excavators with one- and two-headed planting devices. Using a recently developed tool for discrete-event simulation, these machine models then mounded and planted seedlings on terrain models with moraine soil having various frequencies of obstacles (stumps, roots and stones). Compared to if the two heads were mounted pairwise on only one arm, the results showed that productivity did not increase if two planting heads were attached individually to two separate crane arms. But productivity did increase if the planting machine had four planting heads mounted pairwise on two separate arms. However, despite assuming automated mounding and crane motion between planting spots, the two-armed, four- headed model never achieved high enough productivity levels to make it more cost-efficient than one-armed machines. The simulations illustrate that our terrain models generate realistic root architecture and boulder content distributions in moraine soil, while our machine models functionally describe mechanized planting work. Based on our assumptions, we conclude that further development work on two-armed excavator-based planting machines for Nordic clearcut conditions is not warranted. Our simulations reveal that increasing the number of planting heads per crane arm rather than number of crane arms per base machine offers the greatest potential to raise the productivity of intermittently advancing planting machines.

  • 120.
    Ersson, Back Tomas
    et al.
    Sveriges lantbruksuniversitet.
    Linus, Jundén
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Bergsten, Urban
    Sveriges lantbruksuniversitet.
    Servin, Martin
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Simulations of Mechanized Planting: Modelling Terrain and Crane-Mounted Planting Devices2012Ingår i: OSCAR 2012: The Nordic Baltic conference on forestoperations / [ed] Andis Lazdiņš, Latvian State Forest Research Institute "Silava" , 2012, s. 15-19Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    When reforesting clearcuts in southern Sweden, the Bracke Planter has shown to plant seedlings with better planting quality than operational manual tree planting (Ersson and Petersson 2011). Consequently, there is an increasing demand for intermittently advancing tree planting machines with crane-mounted planting devices in southern Sweden.

    Nevertheless, regardless of using one- (Bracke Planter) or two-headed planting devices (M-Planter), today’s average planting machine productivity is still too low (Rantala and Laine 2010, Ersson et al. 2011) for planting machines to cost-wise compete with manual tree planting in southern Sweden (Ersson 2010). There is, therefore, a need to develop new planting machines concepts that are significantly more productive on Nordic terrain, i.e. clearcuts on moraine soils with varying prevalences of stones and stumps where the slash has been harvested for bioenergy.

    For over 40 years, simulation studies have proven useful for testing prospective forest machine concepts (e.g. (Sjunnesson 1970)), including different types of planting heads (Andersson et al. 1977). In particular, simulations studies can nowadays help to cost-efficiently evaluate new ideas before real world implementation (Jundén 2011). However, previous forest machine simulations simplified terrain characteristics like stumps, roots and stones to the extent that these models are too simplistic for meaningful planting machine simulations. For this reason, we have built several terrain, base machine and planting device models for use during discrete-event simulations to test potential solutions that realistically might increase Nordic planting machine productivity. These simulations were performed using a simulator built with the SimPy discrete-event simulation language (Jundén 2011).

    TERRAIN MODELS

    Presently, our terrain models encompass stumps, roots and underground stones. To delineate the clearcuts, we used Herlitz’s (1975) type stands for clearcutting. These type stands also provided theinput data necessary for sizing and spatially allocating the stumps. To all stumps, we attached a root plate according to the deterministic data from Björkhem et al. (1975) and a stochastic root architecture inspired by Kalliokoski et al.’s (2010) root models.As concluded already during the 1960s (Bäckström 1978), the presence of non-visible, underground stones and boulders is what makes mechanized reforestation on moraine soils so difficult. To model this difficulty, we used parameter values from Andersson et al. (1977) to define incidences of stones and boulders (boulder quota or stoniness) and mean stone sizes. Then, we chose an exponential distribution to link stone frequency to stone diameter. In accordance with Eriksson and Holmgren (1996), our modelled stones are spherical in shape and are spatially allocated in a random manner.

    BASE MACHINE MODELS

    Today’s planting machines use excavators as base machines. If using standard components, it might be techno-economically feasible to add another arm to the excavator; thereby creating two- (Fig. 2) or four-headed planting machines where planting head interdependence is minimized. We hypothesized that the productivity of two-armed planting machines, compared to normal one-armed machines, might especially be higher on obstacle-rich terrain since one arm could be free to move while the other arm is busy working. Moreover, two-armed machines might particularly benefit from additional task automation. Preliminary results, however, show that this productivity increase might not be high enough to warrant further development of our two-armed planting machine concept.

    PLANTING DEVICE MODELS

    We modelled today’s two most common planting devices, the one-headed Bracke Planter and the two-headed M-Planter. During simulation, the planting machine operator searches sequentially for microsites free from visible obstacles (stumps and main lateral roots). However, both devices can be impeded by underground roots or stones during mounding, and by stones during the planting phase. Striking obstacles with the M-Planter can result in delays for one or both heads.

    FURTHER DEVELOPMENT

    We are currently expanding the terrain models to include humus layers and surface boulders, on which new multi-headed planting device concepts (with two to four planting heads) with obstacle-avoiding capabilities are being tested. Those simulation results will provide guidance as to how future crane-mounted planting devices should behave and be designed in order to increase planting machine productivity.

  • 121.
    Fahlén, Jessica
    et al.
    Umeå universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Landfors, Mattias
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Freyhult, Eva
    Umeå universitet, Medicinska fakulteten, Institutionen för klinisk mikrobiologi, Klinisk bakteriologi. Umeå universitet, Medicinska fakulteten, Molekylär Infektionsmedicin, Sverige (MIMS).
    Bylesjö, Max
    Trygg, Johan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Kemiska institutionen.
    Hvidsten, Torgeir
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysiologisk botanik. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå Plant Science Centre (UPSC).
    Rydén, Patrik
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Bioinformatics strategies for cDNA-microarray data processing2009Ingår i: Batch effects and noise in microarray experiments: sources and solutions / [ed] Scherer, Andreas, Wiley and Sons , 2009, 1, , s. 272s. 61-74Kapitel i bok, del av antologi (Övrigt vetenskapligt)
    Abstract [en]

    

    Pre-processing plays a vital role in cDNA-microarray data analysis. Without proper pre-processing it is likely that the biological conclusions will be misleading. However, there are many alternatives and in order to choose a proper pre-processing procedure it is necessary to understand the effect of different methods. This chapter discusses several pre-processing steps, including image analysis, background correction, normalization, and filtering. Spike-in data are used to illustrate how different procedures affect the analytical ability to detect differentially expressed genes and estimate their regulation. The result shows that pre-processing has a major impact on both the experiment’s sensitivity andits bias. However, general recommendations are hard to give, since pre-processing consists of several actions that are highly dependent on each other. Furthermore, it is likely that pre-processing have a major impact on downstream analysis, such as clustering and classification, and pre-processing methods should be developed and evaluated with this in mind.

  • 122.
    Forsman, Mona
    et al.
    Department of Forest Resource Management, Swedish University of Agricultural Sciences, 90183 Umeå, Sweden.
    Börlin, Niclas
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Olofsson, Kenneth
    Department of Forest Resource Management, Swedish University of Agricultural Sciences, 90183 Umeå, Sweden.
    Reese, Heather
    Department of Forest Resource Management, Swedish University of Agricultural Sciences, 90183 Umeå, Sweden.
    Holmgren, Johan
    Department of Forest Resource Management, Swedish University of Agricultural Sciences, 90183 Umeå, Sweden.
    Bias of cylinder diameter estimation from ground-based laser scanners with different beam widths: a simulation study2018Ingår i: ISPRS journal of photogrammetry and remote sensing (Print), ISSN 0924-2716, E-ISSN 1872-8235, Vol. 135, s. 84-92Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this study we have investigated why diameters of tree stems, which are approximately cylindrical, are often overestimated by mobile laser scanning. This paper analyzes the physical processes when using ground-based laser scanning that may contribute to a bias when estimating cylinder diameters using circle-fit methods. A laser scanner simulator was implemented and used to evaluate various properties, such as distance, cylinder diameter, and beam width of a laser scanner-cylinder system to find critical conditions. The simulation results suggest that a positive bias of the diameter estimation is expected. Furthermore, the bias follows a quadratic function of one parameter - the relative footprint, i.e., the fraction of the cylinder width illuminated by the laser beam. The quadratic signature opens up a possibility to construct a compensation model for the bias.

  • 123.
    Fotios, Kasolis
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Wadbro, Eddie
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Berggren, Martin
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Analysis of fictitious domain approximations of hard scatterers2015Ingår i: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 53, nr 5, s. 2347-2362Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Consider the Helmholtz equation del center dot alpha del p+k(2 alpha)p = 0 in a domain that contains a so-called hard scatterer. The scatterer is represented by the value alpha = epsilon, for 0 < epsilon << 1, whereas alpha = 1 whenever the scatterer is absent. This scatterer model is often used for the purpose of design optimization and constitutes a fictitious domain approximation of a body characterized by homogeneous Neumann conditions on its boundary. However, such an approximation results in spurious resonances inside the scatterer at certain frequencies and causes, after discretization, ill-conditioned system matrices. Here, we present a stabilization strategy that removes these resonances. Furthermore, we prove that, in the limit epsilon -> 0, the stabilized problem provides linearly convergent approximations of the solution to the problem with an exactly modeled scatterer. Numerical experiments indicate that a finite element approximation of the stabilized problem is free from internal resonances, and they also suggest that the convergence rate is indeed linear with respect to epsilon.

  • 124.
    Fransson, Peter
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Optimal thinning: a theoretical investigation on individual-tree level2019Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    Paper I: In paper I, we asked how a tree should optimally allocate its resources to maximize its fitness. We let a subject tree grow in an environment shaded by nearby competing trees. The competitors were assumed to have reached maturity and had stopped growing, thus creating a static light environment for the subject tree to grow in. The light environment was modeled as a logistic function. For the growth model we used the pipe model as a foundation, linking tree width and leaf mass. This allowed us to construct a dynamic tree-growth model where the tree can allocate biomass from photosynthesis (net productivity) to either stem-height growth, crown-size growth, or reproduction (seed production). Using Pontryagin's maximum principle we derived necessary conditions for optimal biomass allocation, and on that built a heuristic allocation model. The heuristic model states that the tree should first invest into crown-size and then switch to tree height-growth, and lastly invest into crown-size before the growth investments stop and all investments are allocated to reproduction. To test our heuristic method, we used it to determine the growth in several different light environments. The results were then compared to the optimal growth trajectories. The optimal growth was determined by applying dynamic programming. Our less computationally demanding heuristic performed very well in comparison. We also found there exist a critical crown-size: if the subject tree possessed a larger crown-size, the tree would be unable to reach up to the canopy height.

    Paper II: One of the most important aspects of modelling forest growth, and modelling growth of individual trees in general, is the competition between trees. A high level of competition pressure has a negative impact on the growth of individual trees. There are many ways of modelling competition, the most common one is by using a competition index. In this paper we tested 16 competition indices, in conjunction with a log-linear growth model, in terms of the mean squared error and the coefficient of determination. 5 competition indices are distance-independent (i.e. distance between the competitors are not taken into consideration) and 11 are distance-dependent. The data we used to fit our growth model, with accompanying competition index, was taken from an experimental site, in northern Sweden, of Norway spruce. The growth data for the Norway spruce comes from stands which were treated with one of two treatments, solid fertilization, liquid fertilization, or no treatment (control stand). We found that the distance-dependent indices perform better than the distance-independent. However, both the best distance-dependent and independent index performed overall well. We also found that the ranking of the indices was unaffected by the stand treatment, i.e. indices that work well for one treatment will work well for the others.

    Paper III: In this paper we studied how spatial distribution and size selection affect the residual trees, after a thinning operation, in terms of merchantable wood production and stand economy. We constructed a spatially explicit individual-based forest-growth model and fitted and validated the model against empirical data for Norway spruce stands in northern Sweden. To determine the cost for the forest operation we employed empirical cost functions for harvesting and forwarding. The income from the harvested timber is calculated from volume-price lists. The thinnings were determined by three parameters: the spatial evenness of residual trees, the size selection of removed trees, and the basal area reduction. In order to find tree selections fulfilling these constraints we used the metropolis algorithm. We varied these three constrains and applied them for thinning of different initial configurations of Norway spruce stands. The initial configurations for the stands where collected from empirical data. We found that changing the spatial evenness and size selection improved the net wood production and net present value of the stand up to 8%. However, the magnitude of improvement was dependent on the initial configuration (the magnitude of improvement varied between 1.7%—8%).

    Paper IV: With new technology and methods from remote sensing, such as LIDAR, becoming more prevalent in forestry, the ability to assess information on a detailed scale has become more available. Measurements for each individual tree can be more easily gathered on a larger scale. This type of data opens up for using individual-based model for practical precision forestry planning. In paper IV we used the individual-based model constructed in paper III to find the optimal harvesting time for each individual tree, such that the land expectation value is maximized. We employed a genetic algorithm to find a near optimal solution to our optimization. We optimized a number of initial Norway spruce stands (data obtained from field measurements). The optimal management strategy was to apply thinning from above. We also found that increasing the discount rate will decrease the time for final felling and increase basal area reduction for the optimal strategy. Decreasing relocation costs (the cost to bring machines to the stand) led to an increase in the number of optimal thinnings and postponed the first thinning. Our strategy was superior to both the unthinned strategy and a conventional thinning strategy, both in terms of land expectation value (>20% higher) and merchantable wood production.

  • 125.
    Gonoskov, Ivan
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Marklund, Mattias
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik. Department of Physics, Chalmers University of Technology, SE-41296 Gothenburg, Sweden.
    Single-step propagators for calculation of time evolution in quantum systems with arbitrary interactions2016Ingår i: Computer Physics Communications, ISSN 0010-4655, E-ISSN 1879-2944, Vol. 202, s. 211-215Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We propose and develop a general method of numerical calculation of the wave function time evolution in a quantum system which is described by Hamiltonian of an arbitrary dimensionality and with arbitrary interactions. For this, we obtain a general n-order single-step propagator in closed-form, which could be used for the numerical solving of the problem with any prescribed accuracy. We demonstrate the applicability of the proposed approach by considering a quantum problem with non-separable time-dependent Hamiltonian: the propagation of an electron in focused electromagnetic field with vortex electric field component. 

  • 126.
    Gunnars, Johan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Credit Risk Modeling and Implementation2017Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Finanskrisen och Lehman Brothers konkurs 2008 ledde till hårdare regleringar för banksektorn som bland annat innefattade krav på större kapitalreserver för bankerna. En del som bidrog till denna ökning av kapitalreserverna var kreditvärdighetsjusteringens kapitalkrav som kan förklaras som marknadsvärdet av motpartsrisken. Syftet med kreditvärdighetsjusteringens kapitalkrav är att kapitalisera risken för framtida förändringar i marknadsvärdet av motpartsrisken. Ett derivat som hade en nyckelroll under finanskrisen var kreditswappen. En kreditswap innefattar tre parter, en säljare, en köpare och ett referensföretag. Kreditswappen kan ses som en försäkring mot en kredithändelse, till exempel en konkurs på referensföretaget. Detta arbete fokuserar på studier och beräkningar av kreditvärdesjusteringen på kreditswappar. Kreditvärdesjusteringen på en kreditswap kan implementeras med två olika antaganden. I det första fallet antas säljaren (köparen) vara riskfri och då bidrar bara köparen (säljaren) till konkursrisken. I det andra fallet antas både säljaren och köparen bidra till konkursrisken.

  • 127.
    Gürkan, Ceren
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Massing, André
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Department of Mathematical Sciences, Norwegian University of Science and Technology, NO 7491, Trondheim, Norway.
    A stabilized cut discontinuous Galerkin framework for elliptic boundary value and interface problems2019Ingår i: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 348, s. 466-499Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We develop a stabilized cut discontinuous Galerkin framework for the numerical solution of elliptic boundary value and interface problems on complicated domains. The domain of interest is embedded in a structured, unfitted background mesh in R d , so that the boundary or interface can cut through it in an arbitrary fashion. The method is based on an unfitted variant of the classical symmetric interior penalty method using piecewise discontinuous polynomials defined on the background mesh. Instead of the cell agglomeration technique commonly used in previously introduced unfitted discontinuous Galerkin methods, we employ and extend ghost penalty techniques from recently developed continuous cut finite element methods, which allows for a minimal extension of existing fitted discontinuous Galerkin software to handle unfitted geometries. Identifying four abstract assumptions on the ghost penalty, we derive geometrically robust a priori error and condition number estimates for the Poisson boundary value problem which hold irrespective of the particular cut configuration. Possible realizations of suitable ghost penalties are discussed. We also demonstrate how the framework can be elegantly applied to discretize high contrast interface problems. The theoretical results are illustrated by a number of numerical experiments for various approximation orders and for two and three-dimensional test problems. (C) 2018 Published by Elsevier B.V.

  • 128.
    Hansbo, Peter
    et al.
    Jönköping University.
    Jonsson, Tobias
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Larson, Mats G.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Larsson, Karl
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    A Nitsche method for elliptic problems on composite surfaces2017Ingår i: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 326, s. 505-525Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We develop a finite element method for elliptic partial differential equations on so called composite surfaces that are built up out of a finite number of surfaces with boundaries that fit together nicely in the sense that the intersection between any two surfaces in the composite surface is either empty, a point, or a curve segment, called an interface curve. Note that several surfaces can intersect along the same interface curve. On the composite surface we consider a broken finite element space which consists of a continuous finite element space at each subsurface without continuity requirements across the interface curves. We derive a Nitsche type formulation in this general setting and by assuming only that a certain inverse inequality and an approximation property hold we can derive stability and error estimates in the case when the geometry is exactly represented. We discuss several different realizations, including so called cut meshes, of the method. Finally, we present numerical examples.

  • 129. Hansbo, Peter
    et al.
    Larson, Mats G.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    A stabilized finite element method for the Darcy problem on surfaces2017Ingår i: IMA Journal of Numerical Analysis, ISSN 0272-4979, E-ISSN 1464-3642, Vol. 37, nr 3, s. 1274-1299Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider a stabilized finite element method for the Darcy problem on a surface based on the Masud-Hughes formulation. A special feature of the method is that the tangential condition of the velocity field is weakly enforced through the bilinear form, and that standard parametric continuous polynomial spaces on triangulations can be used. We prove optimal order a priori estimates that take the approximation of the geometry and the solution into account.

  • 130. Hansbo, Peter
    et al.
    Larson, Mats G.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Continuous/discontinuous finite element modelling of Kirchhoff plate structures in R3 using tangential differential calculus2017Ingår i: Computational Mechanics, ISSN 0178-7675, E-ISSN 1432-0924, Vol. 60, nr 4, s. 693-702Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We employ surface differential calculus to derive models for Kirchhoff plates including in-plane membrane deformations. We also extend our formulation to structures of plates. For solving the resulting set of partial differential equations, we employ a finite element method based on elements that are continuous for the displacements and discontinuous for the rotations, using -elements for the discretisation of the plate as well as for the membrane deformations. Key to the formulation of the method is a convenient definition of jumps and averages of forms that are d-linear in terms of the element edge normals.

  • 131. Hansbo, Peter
    et al.
    Larson, Mats G.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Larsson, Fredrik
    Tangential differential calculus and the finite element modeling of a large deformation elastic membrane problem2015Ingår i: Computational Mechanics, ISSN 0178-7675, E-ISSN 1432-0924, Vol. 56, nr 1, s. 87-95Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We develop a finite element method for a large deformation membrane elasticity problem on meshed curved surfaces using a tangential differential calculus approach that avoids the use of classical differential geometric methods. The method is also applied to form finding problems.

  • 132.
    Hansbo, Peter
    et al.
    Jönköping University, School of Engineering, JTH, Product Development.
    Larson, Mats G.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Larsson, Karl
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Cut Finite Element Methods for Linear Elasticity Problems2018Ingår i: Geometrically Unfitted Finite Element Methods and Applications: Proceedings of the UCL Workshop 2016 / [ed] Stéphane P. A. Bordas; Erik Burman; Mats G. Larson; Maxim A. Olshanskii, Springer, 2018, s. 25-63Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    We formulate a cut finite element method for linear elasticity based on higher order elements on a fixed background mesh. Key to the method is a stabilization term which provides control of the jumps in the derivatives of the finite element functions across faces in the vicinity of the boundary. We then develop the basic theoretical results including error estimates and estimates of the condition number of the mass and stiffness matrices. We apply the method to the standard displacement problem, the frequency response problem, and the eigenvalue problem. We present several numerical examples including studies of thin bending dominated structures relevant for engineering applications. Finally, we develop a cut finite element method for fibre reinforced materials where the fibres are modeled as a superposition of a truss and a Euler-Bernoulli beam. The beam model leads to a fourth order problem which we discretize using the restriction of the bulk finite element space to the fibre together with a continuous/discontinuous finite element formulation. Here the bulk material stabilizes the problem and it is not necessary to add additional stabilization terms.

  • 133.
    Hansbo, Peter
    et al.
    Tekniska Högskolan i Jönköping.
    Larson, Mats G
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Larsson, Karl
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Intrinsic finite element modeling of curved beamsManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    In the mid '90s Delfour and Zolesio [4-6] established elasticity models on surfaces described using the signed distance function, an approach they called intrinsic modeling. For problems in codimension-two, e.g. one-dimensional geometries embedded in R3, an analogous description can be done using a vector distance function. In this paper we investigate the intrinsic approach for the modeling of codimension-two problems by deriving a weak formulation for a linear curved beam expressed in three dimensions from the equilibrium equations of linear elasticity. Based on this formulation we implement a finite element model using global degrees of freedom and discuss upon the effects of curvature and locking. Comparisons with classical solutions for both straight and curved cantilever beams under a tip load are given.

  • 134.
    Hansbo, Peter
    et al.
    Högskolan i Jönköping, Tekniska Högskolan, JTH.
    Larson, Mats G.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Larsson, Karl
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Variational formulation of curved beams in global coordinates2014Ingår i: Computational Mechanics, ISSN 0178-7675, E-ISSN 1432-0924, Vol. 53, nr 4, s. 611-623Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we derive a variational formulation for the static analysis of a linear curved beam natively expressed in global Cartesian coordinates. Using an implicit description of the beam midline during derivation we eliminate the need for local coordinates. The only geometrical information appearing in the final expressions for the governing equations is the tangential direction. As a consequence, zero or discontinuous curvature, for example at inflection points, pose no difficulty in this formulation. Kinematic assumptions encompassing both Timoshenko and Euler–Bernoulli beam theories are considered. With the exception of truly three-dimensional formulations, models for curved beams found in the literature are typically derived in the local Frenet frame. We implement finite element methods with global degrees of freedom and discuss curvature coupling effects and locking. Numerical comparisons with classical solutions for straight and curved cantilever beams under tip load are given, as well as numerical examples illustrating curvature coupling effects.

  • 135. Hansbo, Peter
    et al.
    Larson, Mats G.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Massing, André
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    A stabilized cut finite element method for the Darcy problem on surfaces2017Ingår i: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 326, s. 298-318Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We develop a cut finite element method for the Darcy problem on surfaces. The cut finite element method is based on embedding the surface in a three dimensional finite element mesh and using finite element spaces defined on the three dimensional mesh as trial and test functions. Since we consider a partial differential equation on a surface, the resulting discrete weak problem might be severely ill conditioned. We propose a full gradient and a normal gradient based stabilization computed on the background mesh to render the proposed formulation stable and well conditioned irrespective of the surface positioning within the mesh. Our formulation extends and simplifies the Masud-Hughes stabilized primal mixed formulation of the Darcy surface problem proposed in Hansbo and Larson (2016) on fitted triangulated surfaces. The tangential condition on the velocity and the pressure gradient is enforced only weakly, avoiding the need for any tangential projection. The presented numerical analysis accounts for different polynomial orders for the velocity, pressure, and geometry approximation which are corroborated by numerical experiments. In particular, we demonstrate both theoretically and through numerical results that the normal gradient stabilized variant results in a high order scheme.

  • 136. Hansbo, Peter
    et al.
    Larson, Mats G.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Zahedi, Sara
    A cut finite element method for coupled bulk-surface problems on time-dependent domains2016Ingår i: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 307, s. 96-116Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this contribution we present a new computational method for coupled bulk-surface problems on time-dependent domains. The method is based on a space-time formulation using discontinuous piecewise linear elements in time and continuous piecewise linear elements in space on a fixed background mesh. The domain is represented using a piecewise linear level set function on the background mesh and a cut finite element method is used to discretize the bulk and surface problems. In the cut finite element method the bilinear forms associated with the weak formulation of the problem are directly evaluated on the bulk domain and the surface defined by the level set, essentially using the restrictions of the piecewise linear functions to the computational domain. In addition a stabilization term is added to stabilize convection as well as the resulting algebraic system that is solved in each time step. We show in numerical examples that the resulting method is accurate and stable and results in well conditioned algebraic systems independent of the position of the interface relative to the background mesh.

  • 137.
    Holmberg, Carl
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Cut finite element methods for incompressibleflows with unfitted interfaces2018Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [en]

    Problems with time-evolving domains are frequently occurring in computationalfluid dynamics and many other fields of science and engineering.Unfitted methods, where the computational mesh does not conform to thegeometry, are of great interest for handling such problems, since they removethe burden of mesh generation. We work towards the goal of developingan unfitted solver for Navier-Stokes equations on time-evolving domainsby developing and presenting cut finite element (CutFEM) splitting methodsfor solving Navier-Stokes equations. These CutFEM splitting methodsuse Nitsche’s method for incorporating boundary conditions and employpatch-based ghost penalty stabilization of the cut elements to achieve stabilityand optimal order error estimates. Numerical benchmarks are used toverify the methods and implementations. The methods are tested against aproblem with known analytical solution, the Taylor-Green vortex, and alsocompared to the classical Deutsche Forschungsgemeinschaft (DFG) benchmarkproblem with channel flow around a cylinder. For both benchmarks,the methods was shown to be stable when satisfying the parabolic Courant–Friedrichs–Lewy (CFL) condition, and to produce optimal convergencerates.

  • 138.
    Holme, Petter
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik. Sungkyunkwan University, Suwon, Korea and tockholm University, Stockholm, Sweden.
    Extinction Times of Epidemic Outbreaks in Networks2013Ingår i: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 8, nr 12, artikel-id e84429Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In the Susceptible–Infectious–Recovered (SIR) model of disease spreading, the time to extinction of the epidemics happens at an intermediate value of the per-contact transmission probability. Too contagious infections burn out fast in the population. Infections that are not contagious enough die out before they spread to a large fraction of people. We characterize how the maximal extinction time in SIR simulations on networks depend on the network structure. For example we find that the average distances in isolated components, weighted by the component size, is a good predictor of the maximal time to extinction. Furthermore, the transmission probability giving the longest outbreaks is larger than, but otherwise seemingly independent of, the epidemic threshold.

  • 139.
    Hosseini, S. Ahmad
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Faculty of Engineering and Natural Sciences, Sabanci University, Istanbul, Turkey.
    Sahin, Guvenc
    Unluyurt, Tonguc
    A penalty-based scaling algorithm for the multi-period multi-product distribution planning problem2017Ingår i: Engineering optimization (Print), ISSN 0305-215X, E-ISSN 1029-0273, Vol. 49, nr 4, s. 583-596Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Multi-period multi-product distribution planning problems are depicted as multi-commodity network flow problems where parameters may change over time. The corresponding mathematical formulation is presented for a discrete time setting, and it can also be used as an approximation for a continuous time setting. A penalty-based method which employs a cost-scaling approach is developed to solve some auxiliary penalty problems aiming to obtain an optimal solution for the original problem. The experiments on both random instances and case study problems show that the algorithm finds good-quality solutions with reasonable computational effort.

  • 140.
    Hägg, Linus
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Quasi-Arithmetic Filters for Topology Optimization2016Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    Topology optimization is a framework for finding the optimal layout of material within a given region of space. In material distribution topology optimization, a material indicator function determines the material state at each point within the design domain. It is well known that naive formulations of continuous material distribution topology optimization problems often lack solutions. To obtain numerical solutions, the continuous problem is approximated by a finite-dimensional problem. The finite-dimensional approximation is typically obtained by partitioning the design domain into a finite number of elements and assigning to each element a design variable that determines the material state of that element. Although the finite-dimensional problem generally is solvable, a sequence of solutions corresponding to ever finer partitions of the design domain may not converge; that is, the optimized designs may exhibit mesh-dependence. Filtering procedures are amongst the most popular methods used to handle the existence issue related to the continuous problem as well as the mesh-dependence related to the finite-dimensional approximation. Over the years, a variety of filters for topology optimization have been presented.

    To harmonize the use and analysis of filters within the field of topology optimization, we introduce the class of fW-mean filters that is based on the weighted quasi-arithmetic mean, also known as the weighted generalized f-mean, over some neighborhoods. We also define the class of generalized fW-mean filters that contains the vast majority of filters for topology optimization. In particular, the class of generalized fW-mean filters includes the fW-mean filters, as well as the projected fW-mean filters that are formed by adding a projection step to the fW-mean filters.

    If the design variables are located in a regular grid, uniform weights are used within each neighborhood, and equal sized polytope shaped neighborhoods are used, then a cascade of generalized fW-mean filters can be applied with a computational complexity that is linear in the number of design variables. Detailed algorithms for octagonal shaped neighborhoods in 2D and rhombicuboctahedron shaped neighborhoods in 3D are provided. The theoretically obtained computational complexity of the algorithm for octagonal shaped neighborhoods in 2D has been numerically verified. By using the same type of algorithm as for filtering, the additional computational complexity for computing derivatives needed in gradient based optimization is also linear in the number of design variables.

    To exemplify the use of generalized fW-mean filters in topology optimization, we consider minimization of compliance (maximization of global stiffness) of linearly elastic continuum bodies. We establish the existence of solutions to a version of the continuous minimal compliance problem when a cascade of projected continuous fW-mean filters is included in the formulation. Bourdin's classical existence result for the linear density filter is a partial case of this general theorem for projected continuous fW-mean filters. Inspired by the works of Svanberg & Svärd and Sigmund, we introduce the harmonic open-close filter, which is a cascade of four fW-mean filters. We present large-scale numerical experiments indicating that, for minimal compliance problems, the harmonic open-close filter produces almost binary designs, provides independent size control on both material and void regions, and yields mesh-independent designs.

  • 141.
    Hägg, Linus
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Wadbro, Eddie
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Nonlinear filters in topology optimization: existence of solutions and efficient implementation for minimum compliance problems2017Ingår i: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 55, nr 3, s. 1017-1028Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Material distribution topology optimization problems are generally ill-posed if no restriction or regularization method is used. To deal with these issues, filtering procedures are routinely applied. In a recent paper, we presented a framework that encompasses the vast majority of currently available density filters. In this paper, we show that these nonlinear filters ensure existence of solutions to a continuous version of the minimum compliance problem. In addition, we provide a detailed description on how to efficiently compute sensitivities for the case when multiple of these nonlinear filters are applied in sequence. Finally, we present large-scale numerical experiments illustrating some characteristics of these cascaded nonlinear filters.

  • 142.
    Hägg, Linus
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Wadbro, Eddie
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    On minimum length scale control in density based topology optimization2018Ingår i: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 58, nr 3, s. 1015-1032Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The archetypical topology optimization problem concerns designing the layout of material within a given region of space so that some performance measure is extremized. To improve manufacturability and reduce manufacturing costs, restrictions on the possible layouts may be imposed. Among such restrictions, constraining the minimum length scales of different regions of the design has a significant place. Within the density filter based topology optimization framework the most commonly used definition is that a region has a minimum length scale not less than D if any point within that region lies within a sphere with diameter D > 0 that is completely contained in the region. In this paper, we propose a variant of this minimum length scale definition for subsets of a convex (possibly bounded) domain We show that sets with positive minimum length scale are characterized as being morphologically open. As a corollary, we find that sets where both the interior and the exterior have positive minimum length scales are characterized as being simultaneously morphologically open and (essentially) morphologically closed. For binary designs in the discretized setting, the latter translates to that the opening of the design should equal the closing of the design. To demonstrate the capability of the developed theory, we devise a method that heuristically promotes designs that are binary and have positive minimum length scales (possibly measured in different norms) on both phases for minimum compliance problems. The obtained designs are almost binary and possess minimum length scales on both phases.

  • 143.
    Hägg, Linus
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Wadbro, Eddie
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Noreland, Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Berggren, Martin
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    1D-model of the interaction between a stack of wood and an imposed electromagnetic wave2015Manuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    We have developed and investigated a 1D-model for the interaction between a stack of wood and an impinging electromagnetic field. Maxwell's equations are used to model the electromagnetic interaction and each layer in a stack of boards has been modeled as a homogenous lossy dielectric slab. The main reason for developing this model has been to investigate the possibility of measuring the moisture content of wood inside a drying kiln using electromagnetic waves. Our investigations show that it is in principle possible to measure the moisture content, since the electromagnetic field is sensitive to changes in the moisture content of the wood. We also show that it might be possible to measure the average moisture content, without detailed knowledge of the distribution of moisture content between different boards.

  • 144.
    Högberg, Magnus
    et al.
    Department of Mechanics, Royal Institute of Technology, Stockholm.
    Berggren, Martin
    Department of Information Technology, Uppsala University.
    Numerical Approaches to Optimal Control of a Model Equation for Shear Flow Instabilities2000Ingår i: Flow Turbulence and Combustion, ISSN 1386-6184, E-ISSN 1573-1987, Vol. 65, s. 299-320Artikel i tidskrift (Refereegranskat)
  • 145.
    Jakobsson, Håkan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Discontinous Galerkin Methods for Coupled Flow and Transport problems2009Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [en]

    We investigate the use of discontinuous Galerkin finite element methods in a mul- tiphysics setting involving coupled flow and transport in porous media. We solve an elliptic equation for the fluid pressure using Nitsche’s method and an approxima- tion, Σ, of the exact convection field σ will be constructed by interpolation onto the lowest-order Raviart-Thomas space of functions. We sequentially solve the transport equation, with the convection field Σ, for the fluid saturation by use of the lowest order discontinuous Galerkin method. We also supply numerical evidence of the importance of local conservation in this setting, and furthermore propose a line of argument indicating that if Σ is constructed using conservative fluxes, the modeling error σ − Σ may not have a great impact on the total error in certain quantities of interest. 

  • 146. Jakobsson, Håkan
    On generalized proper orthogonal decompositionsManuskript (preprint) (Övrigt vetenskapligt)
  • 147. Jakobsson, Håkan
    et al.
    Larson, Mats
    A posteriori error analysis of component mode synthesis for the frequency response problemManuskript (preprint) (Övrigt vetenskapligt)
  • 148.
    Jakobsson, Håkan
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Larson, Mats
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Bengzon, Fredrik
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Duality-based adaptive model reduction for one-way coupled thermoelastic problems2012Ingår i: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 91, nr 3, s. 306-318Artikel i tidskrift (Övrigt vetenskapligt)
    Abstract [en]

     In this paper, we derive a discrete a posteriori error estimate for a thermoelastic model problem discretized using a reduced finite element method. The problem is one-way coupled in the sense that heat transfer affects elastic deformation but not vice versa. A reduced model is constructed using component mode synthesis in each of the heat transfer and linear elastic finite element solvers. The error estimate bounds the difference between the reduced and the standard finite element solution in terms of discrete residuals and corresponding dual weights. A main feature with the estimate is that it automatically gives a quantitative measure of the propagation of error between the solvers with respect to a certain computational goal. The analytical results are accompanied by a numerical example.

  • 149.
    Janzon, Krister
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Monte Carlo Path Simulation and the Multilevel Monte Carlo Method2018Självständigt arbete på avancerad nivå (yrkesexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [en]

    A standard problem in the field of computational finance is that of pricing derivative securities. This is often accomplished by estimating an expected value of a functional of a stochastic process, defined by a stochastic differential equation (SDE). In such a setting the random sampling algorithm Monte Carlo (MC) is useful, where paths of the process are sampled. However, MC in its standard form (SMC) is inherently slow. Additionally, if the analytical solution to the underlying SDE is not available, a numerical approximation of the process is necessary, adding another layer of computational complexity to the SMC algorithm. Thus, the computational cost of achieving a certain level of accuracy of the estimation using SMC may be relatively high.

    In this thesis we introduce and review the theory of the SMC method, with and without the need of numerical approximation for path simulation. Two numerical methods for path approximation are introduced: the Euler–Maruyama method and Milstein's method. Moreover, we also introduce and review the theory of a relatively new (2008) MC method – the multilevel Monte Carlo (MLMC) method – which is only applicable when paths are approximated. This method boldly claims that it can – under certain conditions – eradicate the additional complexity stemming from the approximation of paths. With this in mind, we wish to see whether this claim holds when pricing a European call option, where the underlying stock process is modelled by geometric Brownian motion. We also want to compare the performance of MLMC in this scenario to that of SMC, with and without path approximation.

    Two numerical experiments are performed. The first to determine the optimal implementation of MLMC, a static or adaptive approach. The second to illustrate the difference in performance of adaptive MLMC and SMC – depending on the used numerical method and whether the analytical solution is available. The results show that SMC is inferior to adaptive MLMC if numerical approximation of paths is needed, and that adaptive MLMC seems to meet the complexity of SMC with an analytical solution. However, while the complexity of adaptive MLMC is impressive, it cannot quite compensate for the additional cost of approximating paths, ending up roughly ten times slower than SMC with an analytical solution.

  • 150. Johansson, August
    et al.
    Kehlet, Benjamin
    Larson, Mats G.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Logg, Anders
    Multimesh finite element methods: Solving PDEs on multiple intersecting meshes2019Ingår i: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 343, s. 672-689Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are naturally separate; such as the components of an engine, the domains of a multiphysics problem, or solid bodies interacting under the influence of forces from surrounding fluids or other physical fields. Such multimesh finite element methods are particularly well suited to problems in which the computational domain undergoes large deformations as a result of the relative motion of the separate components of a multi-body system. In the present paper, we formulate the multimesh finite element method for the Poisson equation. Numerical examples demonstrate the optimal order convergence, the numerical robustness of the formulation and implementation in the face of thin intersections and rounding errors, as well as the applicability of the methodology. In the accompanying paper (Johansson et al., 2018), we analyze the proposed method and prove optimal order convergence and stability.

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