Multigrid elliptic equation solver with adaptive mesh refinement

TL;DR

This paper details a parallel multigrid elliptic equation solver that employs adaptive mesh refinement based on truncation error estimates, achieving second order accuracy and computational efficiency.

Contribution

It introduces a novel adaptive mesh refinement technique integrated with multigrid methods, optimizing accuracy and computational savings.

Findings

Confirmed second order accuracy through code tests

Demonstrated computational savings with adaptive refinement

Validated effectiveness of truncation error estimates

Abstract

In this paper we describe in detail the computational algorithm used by our parallel multigrid elliptic equation solver with adaptive mesh refinement. Our code uses truncation error estimates to adaptively refine the grid as part of the solution process. The presentation includes a discussion of the orders of accuracy that we use for prolongation and restriction operators to ensure second order accurate results and to minimize computational work. Code tests are presented that confirm the overall second order accuracy and demonstrate the savings in computational resources provided by adaptive mesh refinement.