A Vanka-type multigrid solver for complex-shifted Laplacian systems from diagonalization-based parallel-in-time algorithms

TL;DR

This paper introduces a Vanka-type multigrid solver tailored for complex-shifted Laplacian systems, demonstrating its effectiveness through local Fourier analysis and numerical validation within parallel-in-time algorithms for evolution equations.

Contribution

It presents a novel Vanka-type multigrid method specifically designed for complex-shifted Laplacian systems in parallel-in-time algorithms, with proven uniform smoothing properties.

Findings

The Vanka-type smoother achieves a uniform smoothing factor.

Numerical examples verify the theoretical analysis.

The method improves efficiency for complex-shifted Laplacian systems.

Abstract

We propose and analyze a Vanka-type multigrid solver for solving a sequence of complex-shifted Laplacian systems arising in diagonalization-based parallel-in-time algorithms for evolutionary equations. Under suitable assumption, local Fourier analysis shows the proposed Vanka-type smoother achieves a uniform smoothing factor, which is verified by several numerical examples.