Multigrid-Augmented Deep Learning Preconditioners for the Helmholtz Equation
From MaRDI portal
Publication:6108146
DOI10.1137/21m1433514arXiv2203.11025OpenAlexW3208705508MaRDI QIDQ6108146
Publication date: 29 June 2023
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2203.11025
iterative methodsHelmholtz equationmultigridconvolutional neural networksdeep learningshifted Laplacian
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Artificial neural networks and deep learning (68T07) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)
Cites Work
- Unnamed Item
- Fast Huygens sweeping methods for Helmholtz equations in inhomogeneous media in the high frequency regime
- A perfectly matched layer for the Helmholtz equation in a semi-infinite strip
- Accelerating the shifted Laplace preconditioner for the Helmholtz equation by multilevel deflation
- Hidden physics models: machine learning of nonlinear partial differential equations
- The double absorbing boundary method for the Helmholtz equation
- Numerical solution of the parametric diffusion equation by deep neural networks
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- A Parallel Sweeping Preconditioner for Heterogeneous 3D Helmholtz Equations
- Flexible Variants of Block Restarted GMRES Methods with Application to Geophysics
- On the convergence of shifted Laplace preconditioner combined with multilevel deflation
- An improved two-grid preconditioner for the solution of three-dimensional Helmholtz problems in heterogeneous media
- Julia: A Fresh Approach to Numerical Computing
- Full Waveform Inversion and the Truncated Newton Method
- A multigrid-based shifted Laplacian preconditioner for a fourth-order Helmholtz discretization
- Smoothed aggregation for Helmholtz problems
- A multigrid solver to the Helmholtz equation with a point source based on travel time and amplitude
- Complex Additive Geometric Multilevel Solvers for Helmholtz Equations on Spacetrees
- Radiation boundary conditions for acoustic and elastic wave calculations
- A Class of Iterative Solvers for the Helmholtz Equation: Factorizations, Sweeping Preconditioners, Source Transfer, Single Layer Potentials, Polarized Traces, and Optimized Schwarz Methods
- Solving high-dimensional partial differential equations using deep learning
- Solving parametric PDE problems with artificial neural networks
- Scalable Convergence Using Two-Level Deflation Preconditioning for the Helmholtz Equation
- Domain Decomposition with Local Impedance Conditions for the Helmholtz Equation with Absorption
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- Learning data-driven discretizations for partial differential equations
- SwitchNet: A Neural Network Model for Forward and Inverse Scattering Problems
- Butterfly Factorization
- A Flexible Inner-Outer Preconditioned GMRES Algorithm
- A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems
- Strong Solutions for PDE-Based Tomography by Unsupervised Learning
