Parallel auxiliary space AMG for H (curl) problems

TV Kolev, PS Vassilevski - Journal of Computational Mathematics, 2009 - JSTOR
In this paper we review a number of auxiliary space based preconditioners for the second
order definite and semi-definite Maxwell problems discretized with the lowest order Nedelec …

Accelerating algebraic multigrid methods via artificial neural networks

PF Antonietti, M Caldana, L Dede' - Vietnam Journal of Mathematics, 2023 - Springer
We present a novel deep learning-based algorithm to accelerate—through the use of
Artificial Neural Networks (ANNs)—the convergence of Algebraic Multigrid (AMG) methods …

An algebraic multigrid approach based on a compatible gauge reformulation of Maxwell's equations

PB Bochev, JJ Hu, CM Siefert, RS Tuminaro - SIAM Journal on Scientific …, 2008 - SIAM
With the rise in popularity of compatible finite element, finite difference, and finite volume
discretizations for the time domain eddy current equations, there has been a corresponding …

Accelerating algebraic multigrid methods via artificial neural networks

PF Antonietti, M Caldana, L Dede - arXiv preprint arXiv:2111.01629, 2021 - arxiv.org
We present a novel deep learning-based algorithm to accelerate-through the use of Artificial
Neural Networks (ANNs)-the convergence of Algebraic Multigrid (AMG) methods for the …

Auxiliary space preconditioning for edge elements

R Hiptmair, J Xu - IEEE Transactions on Magnetics, 2008 - ieeexplore.ieee.org
We present a general approach to preconditioning large sparse linear systems of equations
arising from conforming finite-element discretizations of-elliptic variational problems. Like …

Parallel numerical solution of the time‐harmonic Maxwell equations in mixed form

D Li, C Greif, D Schötzau - Numerical Linear Algebra with …, 2012 - Wiley Online Library
We develop a fully scalable parallel implementation of an iterative solver for the time-
harmonic Maxwell equations with vanishing wave numbers. We use a mixed finite element …

大地电磁法正演中多重网格法求解的广义傅里叶谱分析

柳建新, 郭荣文, 童孝忠, 刘颖… - 吉林大学学报(地球科学版), 2011 - xuebao.jlu.edu.cn
为了准确预测和分析多重网格法用于大地电磁法正演计算的收敛效果, 对多重网格法的收敛性
进行了广义傅里叶谱分析. 通常情况下, 系数矩阵的傅里叶谱是复数, 为了直观地判断 …

[图书][B] Auxiliary space AMG for H (curl) problems

TV Kolev, PS Vassilevski - 2008 - Springer
The search for efficient preconditioners for H (curl) problems on unstructured meshes has
intensified in the last few years. The attempts to directly construct AMG (algebraic multigrid) …

Parallel Element-Based Algebraic Multigrid for (curl) and (div) Problems Using the ParELAG Library

DZ Kalchev, PS Vassilevski, U Villa - SIAM Journal on Scientific Computing, 2023 - SIAM
This paper presents the use of element-based algebraic multigrid (AMGe) hierarchies,
implemented in the Parallel Element Agglomeration Algebraic Multigrid Upscaling and …

Preconditioning for time-harmonic Maxwell's equations using the Laguerre transform

AV Terekhov - arXiv preprint arXiv:2309.11023, 2023 - arxiv.org
A method of numerically solving the Maxwell equations is considered for modeling harmonic
electromagnetic fields. The vector finite element method makes it possible to obtain a …