4 citations · 9 across the 7 of their papers we have counts for
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Latent Inversion of Material Coefficients from Boundary Data via Finite Tests and Neural Surrogates
Erik Burman, Mats G. Larson, Karl Larsson +1
We reconstruct a spatially varying material coefficient in a scalar elliptic equation from finitely many boundary excitations, each producing a full Dirichlet trace. To mitigate th…
Tangent-Space Multiscale Manifold Methods for Nonlinear Elliptic Problems
Mats G. Larson, Anna Persson
We introduce a tangent-space multiscale manifold method for nonlinear heterogeneous elliptic problems. The method represents the fine-scale solution by a nonlinear reconstruction o…
Cut Finite Element Methods for Convection-Diffusion in Mixed-Dimensional Domains
Erik Burman, Peter Hansbo, Mats G. Larson +2
We develop a cut finite element method (CutFEM) for convection--diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in…
Solving Inverse Parametrized Problems via Finite Elements and Extreme Learning Networks
Erik Burman, Mats G. Larson, Karl Larsson +1
We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. Th…
An optimal Petrov-Galerkin framework for operator networks
Philip Charles, Deep Ray, Yue Yu +7
The optimal Petrov-Galerkin formulation to solve partial differential equations (PDEs) recovers the best approximation in a specified finite-dimensional (trial) space with respect…
Robust Trimmed Multipatch IGA with Singular Maps
Tobias Jonsson, Mats G. Larson, Karl Larsson
We consider elliptic problems in multipatch isogeometric analysis (IGA) where the patch parameterizations may be singular. Specifically, we address cases where certain dimensions o…
Stabilizing and Solving Unique Continuation Problems by Parameterizing Data and Learning Finite Element Solution Operators
Erik Burman, Mats G. Larson, Karl Larsson +1
We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct b…