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 …

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 …

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 …

Neural networks suffer from spectral bias and have difficulty representing the high-frequency
components of a function, whereas relaxation methods can resolve high frequencies …

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 …

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 …

Conventional finite-element methods for solving the acoustic-wave Helmholtz equation in
highly heterogeneous media usually require finely discretized mesh to represent the …

We present a deep learning-based iterative approach to solve the discrete heterogeneous
Helmholtz equation for high wavenumbers. Combining classical iterative multigrid solvers …

SUMMARY A smoothed aggregation‐based algebraic multigrid solver for anisotropic
diffusion problems is presented. Algebraic multigrid is a popular and effective method for …

We present a deep learning–based iterative approach to solve the discrete heterogeneous
Helmholtz equation for high wavenumbers. Combining classical iterative multigrid solvers …