An Efficient High-order Numerical Solver for Diffusion Equations with Strong Anisotropy

TL;DR

This paper introduces a high-order discontinuous Galerkin finite element method with an efficient preconditioner for solving strongly anisotropic diffusion equations, demonstrating high accuracy and robustness in plasma physics applications.

Contribution

The paper develops a novel high-order interior penalty discontinuous Galerkin scheme with a robust preconditioning technique for anisotropic diffusion problems.

Findings

High-order scheme achieves accurate solutions

Preconditioning improves solver efficiency

Method is robust to mesh size and anisotropy

Abstract

In this paper, we present an interior penalty discontinuous Galerkin finite element scheme for solving diffusion problems with strong anisotropy arising in magnetized plasmas for fusion applications. We demonstrate the accuracy produced by the high-order scheme and develop an efficient preconditioning technique to solve the corresponding linear system, which is robust to the mesh size and anisotropy of the problem. Several numerical tests are provided to validate the accuracy and efficiency of the proposed algorithm.