The cost-accuracy trade-off in operator learning with neural networks
The termsurrogate modeling'in computational science and engineering refers to the
development of computationally efficient approximations for expensive simulations, such as …
development of computationally efficient approximations for expensive simulations, such as …
Novel design and analysis of generalized finite element methods based on locally optimal spectral approximations
C Ma, R Scheichl, T Dodwell - SIAM Journal on Numerical Analysis, 2022 - SIAM
In this paper, the generalized finite element method (GFEM) for solving second order elliptic
equations with rough coefficients is studied. New optimal local approximation spaces for …
equations with rough coefficients is studied. New optimal local approximation spaces for …
Super-localization of elliptic multiscale problems
M Hauck, D Peterseim - Mathematics of Computation, 2023 - ams.org
Numerical homogenization aims to efficiently and accurately approximate the solution space
of an elliptic partial differential operator with arbitrarily rough coefficients in a $ d …
of an elliptic partial differential operator with arbitrarily rough coefficients in a $ d …
Exponentially convergent multiscale finite element method
We provide a concise review of the exponentially convergent multiscale finite element
method (ExpMsFEM) for efficient model reduction of PDEs in heterogeneous media without …
method (ExpMsFEM) for efficient model reduction of PDEs in heterogeneous media without …
Optimal local approximation spaces for parabolic problems
J Schleuß, K Smetana - Multiscale Modeling & Simulation, 2022 - SIAM
We propose local space-time approximation spaces for parabolic problems that are optimal
in the sense of Kolmogorov and may be employed in multiscale and domain decomposition …
in the sense of Kolmogorov and may be employed in multiscale and domain decomposition …
Exponentially convergent multiscale methods for 2D high frequency heterogeneous Helmholtz equations
In this paper, we present a multiscale framework for solving the Helmholtz equation in
heterogeneous media without scale separation and in the high frequency regime where the …
heterogeneous media without scale separation and in the high frequency regime where the …
A unified framework for multiscale spectral generalized FEMs and low-rank approximations to multiscale PDEs
C Ma - arXiv preprint arXiv:2311.08761, 2023 - arxiv.org
This work presents an abstract framework for the design, implementation, and analysis of the
multiscale spectral generalized finite element method (MS-GFEM), a particular numerical …
multiscale spectral generalized finite element method (MS-GFEM), a particular numerical …
Novel design and analysis of generalized FE methods based on locally optimal spectral approximations
C Ma, R Scheichl, T Dodwell - arXiv preprint arXiv:2103.09545, 2021 - arxiv.org
In this paper, the generalized finite element method (GFEM) for solving second order elliptic
equations with rough coefficients is studied. New optimal local approximation spaces for …
equations with rough coefficients is studied. New optimal local approximation spaces for …
An Edge Multiscale Interior Penalty Discontinuous Galerkin method for heterogeneous Helmholtz problems with large varying wavenumber
Abstract We propose an Edge Multiscale Finite Element Method (EMsFEM) based on an
Interior Penalty Discontinuous Galerkin (IPDG) formulation for the heterogeneous Helmholtz …
Interior Penalty Discontinuous Galerkin (IPDG) formulation for the heterogeneous Helmholtz …
An MsFEM approach enriched using Legendre polynomials
F Legoll, PL Rothé, C Le Bris, U Hetmaniuk - Multiscale Modeling & …, 2022 - SIAM
We consider a variant of the conventional MsFEM approach with enrichments based on
Legendre polynomials, both in the bulk of mesh elements and on their interfaces. A …
Legendre polynomials, both in the bulk of mesh elements and on their interfaces. A …