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Larson, Mats G.
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Publications (10 of 114) Show all publications
Burman, E., Hansbo, P., Larson, M. G. & Samvin, D. (2019). A cut finite element method for elliptic bulk problems with embedded surfaces. GEM - International Journal on Geomathematics, 10(1), Article ID UNSP 10.
Open this publication in new window or tab >>A cut finite element method for elliptic bulk problems with embedded surfaces
2019 (English)In: GEM - International Journal on Geomathematics, ISSN 1869-2672, E-ISSN 1869-2680, Vol. 10, no 1, article id UNSP 10Article in journal (Refereed) Published
Abstract [en]

We propose an unfitted finite element method for flow in fractured porous media. The coupling across the fracture uses a Nitsche type mortaring, allowing for an accurate representation of the jump in the normal component of the gradient of the discrete solution across the fracture. The flow field in the fracture is modelled simultaneously, using the average of traces of the bulk variables on the fractures. In particular the Laplace-Beltrami operator for the transport in the fracture is included using the average of the projection on the tangential plane of the fracture of the trace of the bulk gradient. Optimal order error estimates are proven under suitable regularity assumptions on the domain geometry. The extension to the case of bifurcating fractures is discussed. Finally the theory is illustrated by a series of numerical examples.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2019
Keywords
Finite element, Unfitted, Embedded, Fractures
National Category
Computer Sciences Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-158762 (URN)10.1007/s13137-019-0120-z (DOI)000463142200001 ()30873244 (PubMedID)
Available from: 2019-05-13 Created: 2019-05-13 Last updated: 2019-05-13Bibliographically approved
Elfverson, D., Larson, M. G. & Larsson, K. (2019). A new least squares stabilized Nitsche method for cut isogeometric analysis. Computer Methods in Applied Mechanics and Engineering, 349, 1-16
Open this publication in new window or tab >>A new least squares stabilized Nitsche method for cut isogeometric analysis
2019 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 349, p. 1-16Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
Fictitious domain methods, Nitsche’s method, Least squares stabilization, Isogeometric analysis
National Category
Computational Mathematics
Identifiers
urn:nbn:se:umu:diva-156840 (URN)10.1016/j.cma.2019.02.011 (DOI)2-s2.0-85062154279 (Scopus ID)
Funder
Swedish Research Council, 2013-4708Swedish Research Council, 2017-03911Swedish Foundation for Strategic Research , AM13-0029eSSENCE - An eScience Collaboration
Available from: 2019-03-01 Created: 2019-03-01 Last updated: 2019-06-13Bibliographically approved
Odsæter, L. H., Kvamsdal, T. & Larson, M. G. (2019). A simple embedded discrete fracture-matrix model for a coupled flow and transport problem in porous media. Computer Methods in Applied Mechanics and Engineering, 343, 572-601
Open this publication in new window or tab >>A simple embedded discrete fracture-matrix model for a coupled flow and transport problem in porous media
2019 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 343, p. 572-601Article in journal (Refereed) Published
Abstract [en]

Accurate simulation of fluid flow and transport in fractured porous media is a key challenge in subsurface reservoir engineering. Due to the high ratio between its length and width, fractures can be modeled as lower dimensional interfaces embedded in the porous rock. We apply a recently developed embedded finite element method (EFEM) for the Darcy problem. This method allows for general fracture geometry, and the fractures may cut the finite element mesh arbitrarily. We present here a velocity model for EFEM and couple the Darcy problem to a transport problem for a passive solute. The main novelties of this work are a locally conservative velocity approximation derived from the EFEM solution, and the development of a lowest order upwind finite volume method for the transport problem. This numerical model is compatible with EFEM in the sense that the same computational mesh may be applied, so that we retain the same flexibility with respect to fracture geometry and meshing. Hence, our coupled solution strategy represents a simple approach in terms of formulation, implementation and meshing. We demonstrate our model by some numerical examples on both synthetic and realistic problems, including a benchmark study for single-phase flow. Despite the simplicity of the method, the results are promising.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
Discrete fracture-matrix model, Embedded interface, Finite element method, Finite volume method, Porous media flow
National Category
Computational Mathematics
Identifiers
urn:nbn:se:umu:diva-153110 (URN)10.1016/j.cma.2018.09.003 (DOI)000447411100026 ()
Available from: 2018-11-12 Created: 2018-11-12 Last updated: 2018-11-12Bibliographically approved
Burman, E., Hansbo, P. & Larson, M. G. (2019). A simple finite element method for elliptic bulk problems with embedded surfaces. Computational Geosciences, 23(1), 189-199
Open this publication in new window or tab >>A simple finite element method for elliptic bulk problems with embedded surfaces
2019 (English)In: Computational Geosciences, ISSN 1420-0597, E-ISSN 1573-1499, Vol. 23, no 1, p. 189-199Article in journal (Refereed) Published
Abstract [en]

In this paper, we develop a simple finite element method for simulation of embedded layers of high permeability in a matrix of lower permeability using a basic model of Darcy flow in embedded cracks. The cracks are allowed to cut through the mesh in arbitrary fashion and we take the flow in the crack into account by superposition. The fact that we use continuous elements leads to suboptimal convergence due to the loss of regularity across the crack. We therefore refine the mesh in the vicinity of the crack in order to recover optimal order convergence in terms of the global mesh parameter. The proper degree of refinement is determined based on an a priori error estimate and can thus be performed before the actual finite element computation is started. Numerical examples showing this effect and confirming the theoretical results are provided. The approach is easy to implement and beneficial for rapid assessment of the effect of crack orientation and may for example be used in an optimization loop.

Place, publisher, year, edition, pages
Springer, 2019
Keywords
Darcy equation, Fracture, Embedded layer, Cut finite element methods
National Category
Computer Sciences Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-157594 (URN)10.1007/s10596-018-9792-y (DOI)000459423400010 ()
Available from: 2019-03-28 Created: 2019-03-28 Last updated: 2019-03-28Bibliographically approved
Burman, E., Hansbo, P. & Larson, M. G. (2019). Augmented Lagrangian finite element methods for contact problems. Mathematical Modelling and Numerical Analysis, 53(1), 173-195
Open this publication in new window or tab >>Augmented Lagrangian finite element methods for contact problems
2019 (English)In: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, E-ISSN 1290-3841, Vol. 53, no 1, p. 173-195Article in journal (Refereed) Published
Abstract [en]

We propose two different Lagrange multiplier methods for contact problems derived from the augmented Lagrangian variational formulation. Both the obstacle problem, where a constraint on the solution is imposed in the bulk domain and the Signorini problem, where a lateral contact condition is imposed are considered. We consider both continuous and discontinuous approximation spaces for the Lagrange multiplier. In the latter case the method is unstable and a penalty on the jump of the multiplier must be applied for stability. We prove the existence and uniqueness of discrete solutions, best approximation estimates and convergence estimates that are optimal compared to the regularity of the solution.

Keywords
Signorini problem, obstacle problem, finite element method, Lagrange mutlipliers, augmented grangian, error estimates
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-158369 (URN)10.1051/m2an/2018047 (DOI)000464277200001 ()
Funder
Swedish Research Council, 2011-4992Swedish Research Council, 2013-4708
Available from: 2019-04-26 Created: 2019-04-26 Last updated: 2019-04-26Bibliographically approved
Burman, E., Hansbo, P., Larson, M. G. & Massing, A. (2019). Cut finite element methods for partial differential equations on embedded manifolds of arbitrary codimensions. Mathematical Modelling and Numerical Analysis, 52(6), 2247-2282
Open this publication in new window or tab >>Cut finite element methods for partial differential equations on embedded manifolds of arbitrary codimensions
2019 (English)In: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, E-ISSN 1290-3841, Vol. 52, no 6, p. 2247-2282Article in journal (Refereed) Published
Abstract [en]

We develop a theoretical framework for the analysis of stabilized cut finite element methods for the Laplace-Beltrami operator on a manifold embedded in R-d of arbitrary codimension. The method is based on using continuous piecewise linears on a background mesh in the embedding space for approximation together with a stabilizing form that ensures that the resulting problem is stable. The discrete manifold is represented using a triangulation which does not match the background mesh and does not need to be shape-regular, which includes level set descriptions of codimension one manifolds and the non-matching embedding of independently triangulated manifolds as special cases. We identify abstract key assumptions on the stabilizing form which allow us to prove a bound on the condition number of the stiffness matrix and optimal order a priori estimates. The key assumptions are verified for three different realizations of the stabilizing form including a novel stabilization approach based on penalizing the surface normal gradient on the background mesh. Finally, we present numerical results illustrating our results for a curve and a surface embedded in R-3.

Place, publisher, year, edition, pages
EDP Sciences, 2019
Keywords
Surface PDE, Laplace-Beltrami operator, cut finite element method, stabilization, condition number, a priori error estimates, arbitrary codimension
National Category
Computational Mathematics
Identifiers
urn:nbn:se:umu:diva-162515 (URN)10.1051/m2an/2018038 (DOI)000457984700005 ()
Available from: 2019-08-21 Created: 2019-08-21 Last updated: 2019-08-21Bibliographically approved
Burman, E., Peter, H., Larson, M. G. & Larsson, K. (2019). Cut finite elements for convection in fractured domains. Computers & Fluids, 179, 726-734
Open this publication in new window or tab >>Cut finite elements for convection in fractured domains
2019 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 179, p. 726-734Article in journal (Refereed) Published
Abstract [en]

We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain which is a union of manifolds of different dimensions such that a d dimensional component always resides on the boundary of a d+1 dimensional component. This type of domain can for instance be used to model porous media with embedded fractures that may intersect. The convection problem is formulated in a compact form suitable for analysis using natural abstract directional derivative and divergence operators. The cut finite element method is posed on a fixed background mesh that covers the domain and the manifolds are allowed to cut through a fixed background mesh in an arbitrary way. We consider a simple method based on continuous piecewise linear elements together with weak enforcement of the coupling conditions and stabilization. We prove a priori error estimates and present illustrating numerical examples.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
Convection problems, Fractured domains, Mixed-dimensional domains, Galerkin least squares, A priori error estimates
National Category
Computational Mathematics
Identifiers
urn:nbn:se:umu:diva-158254 (URN)10.1016/j.compfluid.2018.07.022 (DOI)000467514000053 ()2-s2.0-85052134188 (Scopus ID)
Funder
Swedish Research Council, 2013-4708Swedish Research Council, 2017-03911Swedish Research Council, 2018-05262Swedish Foundation for Strategic Research , AM13-0029eSSENCE - An eScience Collaboration, -
Available from: 2019-04-17 Created: 2019-04-17 Last updated: 2019-06-18Bibliographically approved
Burman, E., Elfverson, D., Hansbo, P., Larson, M. G. & Larsson, K. (2019). Cut topology optimization for linear elasticity with coupling to parametric nondesign domain regions. Computer Methods in Applied Mechanics and Engineering, 350, 462-479
Open this publication in new window or tab >>Cut topology optimization for linear elasticity with coupling to parametric nondesign domain regions
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2019 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 350, p. 462-479Article in journal (Refereed) Published
Abstract [en]

We develop a density based topology optimization method for linear elasticity based on the cut finite element method. More precisely, the design domain is discretized using cut finite elements which allow complicated geometry to be represented on a structured fixed background mesh. The geometry of the design domain is allowed to cut through the background mesh in an arbitrary way and certain stabilization terms are added in the vicinity of the cut boundary, which guarantee stability of the method. Furthermore, in addition to standard Dirichlet and Neumann conditions we consider interface conditions enabling coupling of the design domain to parts of the structure for which the design is already given. These given parts of the structure, called the nondesign domain regions, typically represents parts of the geometry provided by the designer. The nondesign domain regions may be discretized independently from the design domains using for example parametric meshed finite elements or isogeometric analysis. The interface and Dirichlet conditions are based on Nitsche's method and are stable for the full range of density parameters. In particular we obtain a traction-free Neumann condition in the limit when the density tends to zero.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
Material distribution topology optimization, Design and nondesign domain regions, Cut finite element method
National Category
Computational Mathematics
Identifiers
urn:nbn:se:umu:diva-157679 (URN)10.1016/j.cma.2019.03.016 (DOI)000468163500019 ()
Funder
Swedish Research Council, 2013-4708Swedish Research Council, 2017-03911Swedish Research Council, 2018-05262Swedish Foundation for Strategic Research , AM13-0029eSSENCE - An eScience Collaboration, -
Available from: 2019-03-29 Created: 2019-03-29 Last updated: 2019-06-11Bibliographically approved
Jonsson, T., Larson, M. G. & Larsson, K. (2019). Graded Parametric CutFEM and CutIGA for Elliptic Boundary Value Problems in Domains with Corners. Computer Methods in Applied Mechanics and Engineering, 354, 331-350
Open this publication in new window or tab >>Graded Parametric CutFEM and CutIGA for Elliptic Boundary Value Problems in Domains with Corners
2019 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 354, p. 331-350Article in journal (Refereed) Published
Abstract [en]

We develop a parametric cut finite element method for elliptic boundary value problems with corner singularities where we have weighted control of higher order derivatives of the solution to a neighborhood of a point at the boundary. Our approach is based on identification of a suitable mapping that grades the mesh towards the singularity. In particular, this mapping may be chosen without identifying the opening angle at the corner. We employ cut finite elements together with Nitsche boundary conditions and stabilization in the vicinity of the boundary. We prove that the method is stable and convergent of optimal order in the energy norm and L2 norm. This is achieved by mapping to the reference domain where we employ a structured mesh.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
Corner singularities, a priori error estimates, Cut finite element method, Cut isogeometric analysis
National Category
Computational Mathematics
Identifiers
urn:nbn:se:umu:diva-159747 (URN)10.1016/j.cma.2019.05.024 (DOI)
Funder
Swedish Foundation for Strategic Research , AM13-0029Swedish Research Council, 2013-4708Swedish Research Council, 2017-03911eSSENCE - An eScience Collaboration, -
Available from: 2019-06-05 Created: 2019-06-05 Last updated: 2019-06-12Bibliographically approved
Johansson, A., Kehlet, B., Larson, M. G. & Logg, A. (2019). Multimesh finite element methods: Solving PDEs on multiple intersecting meshes. Computer Methods in Applied Mechanics and Engineering, 343, 672-689
Open this publication in new window or tab >>Multimesh finite element methods: Solving PDEs on multiple intersecting meshes
2019 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 343, p. 672-689Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
FEM, Unfitted mesh, Non-matching mesh, Multimesh, CutFEM, Nitsche
National Category
Computational Mathematics
Identifiers
urn:nbn:se:umu:diva-153109 (URN)10.1016/j.cma.2018.09.009 (DOI)000447411100029 ()2-s2.0-85054002398 (Scopus ID)
Available from: 2018-11-12 Created: 2018-11-12 Last updated: 2018-11-12Bibliographically approved
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