Multithreaded Filtering Preconditioner for Diffusion Equation on Structured Grid

TL;DR

This paper introduces a parallel, nested frequency filtering preconditioner for diffusion equations on structured grids, demonstrating robustness, efficiency, and significant speedup over existing methods on large-scale problems.

Contribution

A novel parallel nested frequency filtering preconditioner that is robust, memory-efficient, and faster than algebraic multigrid methods for large diffusion problems.

Findings

Achieved a speedup of 3.3 times on a quad-core processor.

Successfully solved problems with over 42 million unknowns.

Preconditioner is robust to jumps in diffusion coefficients.

Abstract

A parallel and nested version of a frequency filtering preconditioner is proposed for linear systems corresponding to diffusion equation on a structured grid. The proposed preconditioner is found to be robust with respect to jumps in the diffusion coefficients. The storage requirement for the preconditioner is O(N),where N is number of rows of matrix, hence, a fairly large problem of size more than 42 million unknowns has been solved on a quad core machine with 64GB RAM. The parallelism is achieved using twisted factorization and SIMD operations. The preconditioner achieves a speedup of 3.3 times on a quad core processor clocked at 4.2 GHz, and compared to a well known algebraic multigrid method, it is significantly faster in both setup and solve times for diffusion equations with jumps.