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  • 1.
    Bengzon, Fredrik
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Larson, Mats G
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Adaptive finite element approximation of multiphysics problems: a fluid structure interaction model problem2010In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 84, no 12, p. 1451-1465Article in journal (Refereed)
    Abstract [en]

    We consider computation of the displacement of an elastic object immersed into a viscous incompressible flow. For simplicity, we assume that the mechanics of the solid is governed by linear elasticity and the motion of the fluid by the Stokes equation. We derive an a posteriori error estimate for this one way coupled problem using duality techniques. Based on these estimates we develop an adaptive algorithm that automatically constructs a suitable adapted mesh for the fluid and solid domains given goal quantities specified on the solid problem.

  • 2.
    Bernland, Anders
    et al.
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Wadbro, Eddie
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Berggren, Martin
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Acoustic shape optimization using cut finite elements2018In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 113, no 3, p. 432-449Article in journal (Refereed)
    Abstract [en]

    Fictitious domain methods are attractive for shape optimization applications, since they do not require deformed or regenerated meshes. A recently developed such method is the CutFEM approach, which allows crisp boundary representations and for which uniformly well-conditioned system matrices can be guaranteed. Here, we investigate the use of the CutFEM approach for acoustic shape optimization, using as test problem the design of an acoustic horn for favorable impedance-matching properties. The CutFEM approach is used to solve the Helmholtz equation, and the geometry of the horn is implicitly described by a level-set function. To promote smooth algorithmic updates of the geometry, we propose to use the nodal values of the Laplacian of the level-set function as design variables. This strategy also improves the algorithm's convergence rate, counteracts mesh dependence, and, in combination with Tikhonov regularization, controls small details in the optimized designs. An advantage with the proposed method is that the exact derivatives of the discrete objective function can be expressed as boundary integrals, as opposed to when using a traditional method that uses mesh deformations. The resulting horns possess excellent impedance-matching properties and exhibit surprising subwavelength structures, not previously seen, which are possible to capture due to the fixed mesh approach.

  • 3. Burman, Erik
    et al.
    Claus, Susanne
    Hansbo, Peter
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Massing, Andre
    Center for Biomedical Computing, Simula Research Laboratory, PO Box 134, NO-1325 Lysaker, Norway.
    CutFEM: Discretizing geometry and partial differential equations2015In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 104, no 7, p. 472-501Article in journal (Refereed)
    Abstract [en]

    We discuss recent advances on robust unfitted finite element methods on cut meshes. These methods are designed to facilitate computations on complex geometries obtained, for example, from computer-aided design or image data from applied sciences. Both the treatment of boundaries and interfaces and the discretization of PDEs on surfaces are discussed and illustrated numerically.

  • 4. Burman, Erik
    et al.
    Hansbo, Peter
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Augmented Lagrangian and Galerkin least-squares methods for membrane contact2018In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 114, no 11, p. 1179-1191Article in journal (Refereed)
    Abstract [en]

    In this paper, we propose a stabilized finite element method for the numerical solution of contact between a small deformation elastic membrane and a rigid obstacle. We limit ourselves to friction-free contact, but the formulation is readily extendable to more complex situations.

  • 5. Cenanovic, Mirza
    et al.
    Hansbo, Peter
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Minimal surface computation using a finite element method on an embedded surface2015In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 104, no 7, p. 502-512Article in journal (Refereed)
    Abstract [en]

    We suggest a finite element method for finding minimal surfaces based on computing a discrete Laplace-Beltrami operator operating on the coordinates of the surface. The surface is a discrete representation of the zero level set of a distance function using linear tetrahedral finite elements, and the finite element discretization is carried out on the piecewise planar isosurface using the shape functions from the background three-dimensional mesh used to represent the distance function. A recently suggested stabilized scheme for finite element approximation of the mean curvature vector is a crucial component of the method.

  • 6. Effenberger, Cedric
    et al.
    Kressner, Daniel
    Engström, Christian
    ETH Zurich, Seminar for Applied Mathematics.
    Linearization techniques for band structure calculations in absorbing photonic crystals2012In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 89, no 2, p. 180-191Article in journal (Refereed)
    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.

  • 7.
    Engström, Christian
    et al.
    ETH Zurich, Seminar for Applied Mathematics.
    Wang, Mengyu
    Complex dispersion relation calculations with the applications to absorptive photonic crystals2010In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 84, p. 849-863Article in journal (Refereed)
  • 8.
    Hansbo, Peter
    et al.
    Göteborg, Sweden.
    Heintz, David
    Göteborg, Sweden.
    Larson, Mats G
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    An adaptive finite element method for second-order plate theory2010In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 81, no 5, p. 584-603Article in journal (Refereed)
    Abstract [en]

    We present a discontinuous finite element method for the Kirchhoff plate model with membrane stresses. The method is based on P(2)-approximations on simplices for the out-of-plane deformations, using C(0)-continuous approximations. We derive a posteriori error estimates for linear functionals of the error and give some numerical examples. Copyright (C) 2009 John Wiley & Sons, Ltd.

  • 9.
    Jakobsson, Håkan
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Bengzon, Fredrik
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Adaptive component mode synthesis in linear elasticity2011In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 86, no 7, p. 801-934Article in journal (Refereed)
    Abstract [en]

    Component mode synthesis (CMS) is a classical method for the reduction of large-scale finite element models in linear elasticity. In this paper we develop a methodology for adaptive refinement of CMS models. The methodology is based on a posteriori error estimates that determine to what degree each CMS subspace influence the error in the reduced solution. We consider a static model problem and prove a posteriori error estimates for the error in a linear goal quantity as well as in the energy and L2 norms. Automatic control of the error in the reduced solution is accomplished through an adaptive algorithm that determines suitable dimensions of each CMS subspace. The results are demonstrated in numerical examples.

  • 10.
    Jakobsson, Håkan
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Larson, Mats
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Bengzon, Fredrik
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Duality-based adaptive model reduction for one-way coupled thermoelastic problems2012In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 91, no 3, p. 306-318Article in journal (Other academic)
    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.

  • 11.
    Jakobsson, Håkan
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Mode superposition with submodeling2012In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 90, no 6, p. 739-751Article in journal (Refereed)
    Abstract [en]

    We investigate a new approach for local enhancement of mode superpositions, which builds on the concept of submodeling. To this end, we impose a multiscale split on the reduced solution into a global part defined by the mode superposition method and a local part defined by a patch problem solved in a subspace of the finite element space associated with a subdomain around some region of interest. The patch problem yields a local correction on the modal approximation. We describe the basics of this approach and evaluate the accuracy of the approximation in elastostatic numerical examples. We also demonstrate how the submodeling technique may be applied as a post-processing operation on a set of reduced solutions, for example, from dynamics simulation, to enhance accuracy in some domain of interest. Copyright (C) 2012 John Wiley & Sons, Ltd.

  • 12.
    Servin, Martin
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Wang, Da
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Lacoursiere, Claude
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Bodin, Kenneth
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Examining the smooth and nonsmooth discrete element approaches to granular matter2014In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 97, no 12, p. 878-902Article in journal (Refereed)
    Abstract [en]

    The smooth and nonsmooth approaches to the discrete element method (DEM) are examined from a computational perspective. The main difference can be understood as using explicit versus implicit time integration. A formula is obtained for estimating the computational effort depending on error tolerance, system geometric shape and size, and on the dynamic state. For the nonsmooth DEM (NDEM), a regularized version mapping to the Hertz contact law is presented. This method has the conventional nonsmooth and smooth DEM as special cases depending on size of time step and value of regularization. The use of the projected Gauss-Seidel solver for NDEM simulation is studied on a range of test systems. The following characteristics are found. First, the smooth DEM is computationally more efficient for soft materials, wide and tall systems, and with increasing flow rate. Secondly, the NDEM is more beneficial for stiff materials, shallow systems, static or slow flow, and with increasing error tolerance. Furthermore, it is found that just as pressure saturates with depth in a granular column, due to force arching, also the required number of iterations saturates and become independent of system size. This effect make the projected Gauss-Seidel solver scale much better than previously thought.

  • 13.
    Udawalpola, Rajitha
    et al.
    Department of Information Technology, Uppsala University.
    Berggren, Martin
    Department of Information Technology, Uppsala University.
    Optimization of an acoustic horn with respect to efficiency and directivity2007In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 73, no 11, p. 1571-1606Article in journal (Refereed)
  • 14.
    Udawalpola, Rajitha
    et al.
    Department of Information Technology, Uppsala University.
    Wadbro, Eddie
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Berggren, Martin
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Optimization of a variable mouth acoustic horn2011In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 85, no 5, p. 591-606Article in journal (Refereed)
    Abstract [en]

    By using boundary shape optimization on the end part of a semi-infinite waveguide for acoustic waves, we design transmission-efficient interfacial devices without imposing an upper bound on the mouth diameter. The boundary element method solves the Helmholtz equation modeling the exterior wave propagation problem. A gradient-based optimization algorithm solves the resulting least-squares problem and the adjoint method provides the necessary gradients. The results demonstrate that there appears to be a natural limit on the optimal mouth diameter.

1 - 14 of 14
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