The cost-accuracy trade-off in operator learning with neural networks
MV de Hoop, DZ Huang, E Qian, AM Stuart - ar** obstacle, with boundary data coming from plane-wave incidence, by the …
Two-level hybrid Schwarz preconditioners with piecewise-polynomial coarse spaces for the high-frequency Helmholtz equation
We analyse two-level hybrid Schwarz domain-decomposition GMRES preconditioners for
finite-element discretisations of the Helmholtz equation with wavenumber $ k $, where the …
finite-element discretisations of the Helmholtz equation with wavenumber $ k $, 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 …
Generalized multiscale finite element method for language competition modeling I: Offline approach
DA Ammosov, NV Malysheva… - Journal of Computational …, 2024 - Elsevier
This paper develops a multiscale solver for the problem of two languages competing in a
heterogeneous medium. The mathematical model contains terms for language group …
heterogeneous medium. The mathematical model contains terms for language group …
[PDF][PDF] Wavenumber explicit convergence of a multiscale GFEM for heterogeneous Helmholtz problems
C Ma, C Alber, R Scheichl - arxiv preprint arxiv:2112.10544, 2021 - researchgate.net
In this paper, a generalized finite element method (GFEM) with optimal local approximation
spaces for solving high-frequency heterogeneous Helmholtz problems is systematically …
spaces for solving high-frequency heterogeneous Helmholtz problems is systematically …
Fast-convergent two-level restricted additive Schwarz methods based on optimal local approximation spaces
A Strehlow, C Ma, R Scheichl - arxiv preprint arxiv:2408.16282, 2024 - arxiv.org
This paper proposes a two-level restricted additive Schwarz (RAS) method for multiscale
PDEs, built on top of a multiscale spectral generalized finite element method (MS-GFEM) …
PDEs, built on top of a multiscale spectral generalized finite element method (MS-GFEM) …