An efficient high-order numerical solver for diffusion equations with strong anisotropy

David Green; Xiaozhe Hu; Jeremy Lore; Lin Mu; Mark L. Stowell

doi:10.1016/j.cpc.2022.108333

An efficient high-order numerical solver for diffusion equations with strong anisotropy

David Green, Xiaozhe Hu, Jeremy Lore, Lin Mu, Mark L. Stowell

Power Exhaust and Particle Control

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7 Scopus citations

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.

Original language	English
Article number	108333
Journal	Computer Physics Communications
Volume	276
DOIs	https://doi.org/10.1016/j.cpc.2022.108333
State	Published - Jul 2022

Funding

The first and third authors are supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725 . The fourth author is partially supported by the Ralph E. Powe Junior Faculty Enhancement Awards .

Funders	Funder number
U.S. Department of Energy	DE-AC05-00OR22725
Office of Science

Keywords

Anisotropic diffusion equation
High-order method
Interior penalty discontinuous Galerkin
Iterative methods
Subspace correction methods

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10.1016/j.cpc.2022.108333

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title = "An efficient high-order numerical solver for diffusion equations with strong 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.",

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AU - Hu, Xiaozhe

AU - Lore, Jeremy

AU - Mu, Lin

AU - Stowell, Mark L.

PY - 2022/7

Y1 - 2022/7

N2 - 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.

AB - 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.

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KW - High-order method

KW - Interior penalty discontinuous Galerkin

KW - Iterative methods

KW - Subspace correction methods

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An efficient high-order numerical solver for diffusion equations with strong anisotropy

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Keywords

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