A class of iterative solvers for the Helmholtz equation: Factorizations, sweeping preconditioners, source transfer, single layer potentials, polarized traces, and …
Solving time-harmonic wave propagation problems by iterative methods is a difficult task,
and over the last two decades an important research effort has gone into developing …
and over the last two decades an important research effort has gone into developing …
Theoretical bounds for algebraic multigrid performance: review and analysis
SP MacLachlan, LN Olson - Numerical Linear Algebra with …, 2014 - Wiley Online Library
Algebraic multigrid methods continue to grow in robustness as effective solvers for the large
and sparse linear systems of equations that arise in many applications. Unlike geometric …
and sparse linear systems of equations that arise in many applications. Unlike geometric …
Multigrid-augmented deep learning preconditioners for the Helmholtz equation
Y Azulay, E Treister - SIAM Journal on Scientific Computing, 2022 - SIAM
In this paper, we present a data-driven approach to iteratively solve the discrete
heterogeneous Helmholtz equation at high wavenumbers. In our approach, we combine …
heterogeneous Helmholtz equation at high wavenumbers. In our approach, we combine …
Blending neural operators and relaxation methods in PDE numerical solvers
Neural networks suffer from spectral bias and have difficulty representing the high-frequency
components of a function, whereas relaxation methods can resolve high frequencies …
components of a function, whereas relaxation methods can resolve high frequencies …
Accelerating the shifted Laplace preconditioner for the Helmholtz equation by multilevel deflation
Many important physical phenomena can be described by the Helmholtz equation. We
investigate to what extent the convergence of the shifted Laplacian preconditioner for the …
investigate to what extent the convergence of the shifted Laplacian preconditioner for the …
A general interpolation strategy for algebraic multigrid using energy minimization
Algebraic multigrid methods solve sparse linear systems Ax=b by automatic construction of a
multilevel hierarchy. This hierarchy is defined by grid transfer operators that must accurately …
multilevel hierarchy. This hierarchy is defined by grid transfer operators that must accurately …
A fast solver for the Helmholtz equation based on the generalized multiscale finite-element method
Conventional finite-element methods for solving the acoustic-wave Helmholtz equation in
highly heterogeneous media usually require finely discretized mesh to represent the …
highly heterogeneous media usually require finely discretized mesh to represent the …
Multigrid-augmented deep learning for the helmholtz equation: Better scalability with compact implicit layers
B Lerer, I Ben-Yair, E Treister - arXiv preprint arXiv:2306.17486, 2023 - arxiv.org
We present a deep learning-based iterative approach to solve the discrete heterogeneous
Helmholtz equation for high wavenumbers. Combining classical iterative multigrid solvers …
Helmholtz equation for high wavenumbers. Combining classical iterative multigrid solvers …
Smoothed aggregation solvers for anisotropic diffusion
JB Schroder - Numerical Linear Algebra with Applications, 2012 - Wiley Online Library
SUMMARY A smoothed aggregation‐based algebraic multigrid solver for anisotropic
diffusion problems is presented. Algebraic multigrid is a popular and effective method for …
diffusion problems is presented. Algebraic multigrid is a popular and effective method for …
Multigrid-Augmented Deep Learning Preconditioners for the Helmholtz Equation Using Compact Implicit Layers
B Lerer, I Ben-Yair, E Treister - SIAM Journal on Scientific Computing, 2024 - SIAM
We present a deep learning–based iterative approach to solve the discrete heterogeneous
Helmholtz equation for high wavenumbers. Combining classical iterative multigrid solvers …
Helmholtz equation for high wavenumbers. Combining classical iterative multigrid solvers …