A Neural Multigrid Solver for Helmholtz Equations with High Wavenumber and Heterogeneous Media
Fuente:
arXiv
Saved in:
| Main Authors: | Cui, Chen, Jiang, Kai, Shu, Shi |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Similar Items
A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations
by: Yuan, Long, et al.
Published: (2025)
by: Yuan, Long, et al.
Published: (2025)
Scalable Multigrid Solver for the Helmholtz Equation: Real-Shifted Coarse Grid Correction
by: Yovel, Rachel, et al.
Published: (2026)
by: Yovel, Rachel, et al.
Published: (2026)
Deep Learning Accelerated Algebraic Multigrid Methods for Polytopal Discretizations of Second-Order Differential Problems
by: Antonietti, Paola F., et al.
Published: (2025)
by: Antonietti, Paola F., et al.
Published: (2025)
A neuron-wise subspace correction method for the finite neuron method
by: Park, Jongho, et al.
Published: (2022)
by: Park, Jongho, et al.
Published: (2022)
Multiscale Neural Networks for Approximating Green's Functions
by: Hao, Wenrui, et al.
Published: (2024)
by: Hao, Wenrui, et al.
Published: (2024)
A Hybrid Iterative Neural Solver Based on Spectral Analysis for Parametric PDEs
by: Cui, Chen, et al.
Published: (2024)
by: Cui, Chen, et al.
Published: (2024)
Multigrid-Augmented Deep Learning Preconditioners for the Helmholtz Equation using Compact Implicit Layers
by: Lerer, Bar, et al.
Published: (2023)
by: Lerer, Bar, et al.
Published: (2023)
Towards a Multigrid Preconditioner Interpretation of Hierarchical Poincaré-Steklov Solvers
by: Lorca, J. P. Lucero
Published: (2025)
by: Lorca, J. P. Lucero
Published: (2025)
A framework of discontinuous Galerkin neural networks for iteratively approximating residuals
by: Yuan, Long, et al.
Published: (2025)
by: Yuan, Long, et al.
Published: (2025)
A Deep Learning algorithm to accelerate Algebraic Multigrid methods in Finite Element solvers of 3D elliptic PDEs
by: Caldana, Matteo, et al.
Published: (2023)
by: Caldana, Matteo, et al.
Published: (2023)
The Neural Approximated Virtual Element Method for Elasticity Problems
by: Berrone, Stefano, et al.
Published: (2025)
by: Berrone, Stefano, et al.
Published: (2025)
Discontinuous hybrid neural networks for the one-dimensional partial differential equations
by: Wang, Xiaoyu, et al.
Published: (2025)
by: Wang, Xiaoyu, et al.
Published: (2025)
A Theory of Relaxation-Based Algebraic Multigrid
by: Moussa, Rayan, et al.
Published: (2026)
by: Moussa, Rayan, et al.
Published: (2026)
Neural Network Dual Norms for Minimal Residual Finite Element Methods
by: Alsobhi, Hamd, et al.
Published: (2025)
by: Alsobhi, Hamd, et al.
Published: (2025)
MAGNET: an open-source library for mesh agglomeration by Graph Neural Networks
by: Antonietti, Paola F., et al.
Published: (2025)
by: Antonietti, Paola F., et al.
Published: (2025)
Neural Approximate Inverse Preconditioners
by: Xu, Tianshi, et al.
Published: (2025)
by: Xu, Tianshi, et al.
Published: (2025)
On Optimal Algebraic Multigrid Methods
by: Ramos, Luis García, et al.
Published: (2019)
by: Ramos, Luis García, et al.
Published: (2019)
Construction of local reduced spaces for Friedrichs' systems via randomized training
by: Engwer, Christian, et al.
Published: (2024)
by: Engwer, Christian, et al.
Published: (2024)
Deep collocation method: A framework for solving PDEs using neural networks with error control
by: Weng, Mingxing, et al.
Published: (2025)
by: Weng, Mingxing, et al.
Published: (2025)
Learning a generalized multiscale prolongation operator
by: Liu, Yucheng, et al.
Published: (2024)
by: Liu, Yucheng, et al.
Published: (2024)
Schwarz preconditioner with $H_k$-GenEO coarse space for the indefinite Helmholtz problem
by: Dolean, Victorita, et al.
Published: (2024)
by: Dolean, Victorita, et al.
Published: (2024)
Can Symmetric Positive Definite (SPD) coarse spaces perform well for indefinite Helmholtz problems?
by: Dolean, Victorita, et al.
Published: (2024)
by: Dolean, Victorita, et al.
Published: (2024)
Multigrid Primer: Basic Principles
by: McCormick, Stephen F., et al.
Published: (2026)
by: McCormick, Stephen F., et al.
Published: (2026)
Multigrid solvers for multipoint flux approximations of the Darcy problem on rough quadrilateral grids
by: Arrarás, Andrés, et al.
Published: (2024)
by: Arrarás, Andrés, et al.
Published: (2024)
Multigrid with Linear Storage Complexity
by: Bauer, Daniel, et al.
Published: (2025)
by: Bauer, Daniel, et al.
Published: (2025)
Local Solvers for High-Order Patch Smoothers via p-Multigrid
by: Wichrowski, Michał
Published: (2025)
by: Wichrowski, Michał
Published: (2025)
The Reduced Basis Multigrid scheme for the Virtual Element Method
by: Antonietti, Paola F., et al.
Published: (2025)
by: Antonietti, Paola F., et al.
Published: (2025)
Efficient multigrid solvers for mixed-degree local discontinuous Galerkin multiphase Stokes problems
by: Saye, Robert I.
Published: (2025)
by: Saye, Robert I.
Published: (2025)
A comparative study of efficient multigrid solvers for high-order local discontinuous Galerkin methods: Poisson, elliptic interface, and multiphase Stokes problems
by: Saye, Robert I.
Published: (2024)
by: Saye, Robert I.
Published: (2024)
Geometric Generalization of Neural Operators from Kernel Integral Perspective
by: Han, Mingyu, et al.
Published: (2026)
by: Han, Mingyu, et al.
Published: (2026)
Fourier Beyond Dispersion: Wavenumber Explicit and Precise Accuracy of FDMs for the Helmholtz Equation
by: Zhang, Hui
Published: (2024)
by: Zhang, Hui
Published: (2024)
Parallel Energy-Minimization Prolongation for Algebraic Multigrid
by: Janna, Carlo, et al.
Published: (2022)
by: Janna, Carlo, et al.
Published: (2022)
On Edge Multiscale Space based Hybrid Schwarz Preconditioner for Helmholtz Problems with Large Wavenumbers
by: Fu, Shubin, et al.
Published: (2024)
by: Fu, Shubin, et al.
Published: (2024)
A two-grid method with dispersion matching for finite-element Helmholtz problems
by: Stolk, Christiaan C.
Published: (2025)
by: Stolk, Christiaan C.
Published: (2025)
Meshless Shape Optimization using Neural Networks and Partial Differential Equations on Graphs
by: Martinet, Eloi, et al.
Published: (2025)
by: Martinet, Eloi, et al.
Published: (2025)
Towards Matrix-Free Patch Smoothers for the Stokes Problem: Evaluating Local p-Multigrid Solvers
by: Wichrowski, Michał
Published: (2026)
by: Wichrowski, Michał
Published: (2026)
Least Squares with Equality constraints Extreme Learning Machines for the resolution of PDEs
by: De Falco, Davide Elia, et al.
Published: (2025)
by: De Falco, Davide Elia, et al.
Published: (2025)
The lowest-order Neural Approximated Virtual Element Method on polygonal elements
by: Berrone, Stefano, et al.
Published: (2024)
by: Berrone, Stefano, et al.
Published: (2024)
Accelerating non-local exchange in generalized optimized Schwarz methods
by: Atchekzai, Roxane, et al.
Published: (2024)
by: Atchekzai, Roxane, et al.
Published: (2024)
MGCNN: a learnable multigrid solver for sparse linear systems from PDEs on structured grids
by: Xie, Yan, et al.
Published: (2023)
by: Xie, Yan, et al.
Published: (2023)
Similar Items
-
A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations
by: Yuan, Long, et al.
Published: (2025) -
Scalable Multigrid Solver for the Helmholtz Equation: Real-Shifted Coarse Grid Correction
by: Yovel, Rachel, et al.
Published: (2026) -
Deep Learning Accelerated Algebraic Multigrid Methods for Polytopal Discretizations of Second-Order Differential Problems
by: Antonietti, Paola F., et al.
Published: (2025) -
A neuron-wise subspace correction method for the finite neuron method
by: Park, Jongho, et al.
Published: (2022) -
Multiscale Neural Networks for Approximating Green's Functions
by: Hao, Wenrui, et al.
Published: (2024)