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math.NA2025
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…
math.NA2025
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…
math.NA2024
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…