3 papers
math.NA2026
A nonoverlapping spectral additive Schwarz method for interior penalty discontinuous Galerkin discretizations of Anisotropic Elliptic Problems
Maurice S. Fabien, Sijing Liu, Marcus Sarkis
We design and analyze a nonoverlapping additive Schwarz preconditioner for interior penalty discontinuous Galerkin discretizations of anisotropic elliptic problems. The preconditio…
math.NA2026
Two-scale neural networks for optimal control of linear convection-dominated equations
Sijing Liu, Marcus Sarkis, Yi Zhang +1
We propose a two-scale neural network method for optimal control problems governed by convection-dominated convection-diffusion-reaction equations. Building on two-scale architectu…
math.NA2025
Adaptive Nonoverlapping Preconditioners for the Helmholtz Equation
Yi Yu, Marcus Sarkis, Guanglian Li +1
The Helmholtz equation poses significant computational challenges due to its oscillatory solutions, particularly for large wavenumbers. Inspired by the Schur complement system for…