A Direct Multigrid Poisson Solver for Oct-Tree Adaptive Meshes

TL;DR

This paper introduces a direct multigrid Poisson solver tailored for oct-tree adaptive meshes, enhancing efficiency and accuracy in parallel computing environments for finite-volume problems.

Contribution

It presents a novel direct multigrid method compatible with oct-tree adaptive meshes, improving upon previous finite-difference approaches by enabling shared boundaries and parallel implementation.

Findings

Demonstrates high accuracy in test cases

Efficient parallel performance within FLASH framework

Improved handling of adaptive mesh boundaries

Abstract

We describe a finite-volume method for solving the Poisson equation on oct-tree adaptive meshes using direct solvers for individual mesh blocks. The method is a modified version of the method presented by Huang and Greengard (2000), which works with finite-difference meshes and does not allow for shared boundaries between refined patches. Our algorithm is implemented within the FLASH code framework and makes use of the PARAMESH library, permitting efficient use of parallel computers. We describe the algorithm and present test results that demonstrate its accuracy.