A Parallel Wavelet‐Based Algebraic Multigrid Black‐Box Solver and Preconditioner

Abstract

This work introduces a new parallel wavelet-based algorithm for algebraic multigrid method (PWAMG) using a variation of the standard parallel implementation of discrete wavelet transforms. This new approach eliminates the grid coarsening process in traditional algebraic multigrid setup phase simplifying its implementation on distributed memory machines. The PWAMG method is used as a parallel black-box solver and as a preconditioner in some linear equations systems resulting from circuit simulations and 3D finite elements electromagnetic problems. The numerical results evaluate the efficiency of the new approach as a standalone solver and as preconditioner for the biconjugate gradient stabilized iterative method.

A new multilevel smoothing method for wavelet-based algebraic multigrid poisson problem solver

“…Additionally, the multilevel approach has suitable characteristics for parallelization in distributed memory computers, since it can be applied independently in the rows and columns of the matrix exactly in the same way presented in [19] for the WAMG method. So, it can be a good alternative to inherently sequential approaches such as the smoothers based on incomplete LU decompositions, which are robust but has less parallelization potential [22].…”

“…More recently, other wavelet-based multigrid approaches have shown the efficiency and potentiality of this combination in different areas. Especially in problems related to the computation of electromagnetic fields, the combination of multigrid and wavelets has revealed to be very efficient and promising, presenting in many cases a better performance than some of the most advanced and current traditional multigrid algorithms [19].…”

Kinetic-Monte-Carlo-Based Parallel Evolution Simulation Algorithm of Dust Particles

“…In the current conditions, it is hard to simulate the KMC evolution of dust particles in a large-scale urban environment by one computer. Therefore, the parallel computing method can be used to shorten the simulation time [30][31][32][33].…”