ISOTROPIC FINITE DIFFERENCE DISCRETIZATION OF LAPLACIAN OPERATOR

Hyun Geun Lee; Seokjun Ham; Junseok Kim

doi:10.30546/1683-6154.22.2.2023.259

ISOTROPIC FINITE DIFFERENCE DISCRETIZATION OF LAPLACIAN OPERATOR

Hyun Geun Lee, Seokjun Ham, Junseok Kim

Department of Mathematics

Korea University

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this paper, we review and investigate isotropic finite difference discretizations of the two-dimensional (2D) and three-dimensional (3D) Laplacian operators. In particular, we propose benchmark functions to quantitatively evaluate the isotropy of the discrete Laplacian operators in 2D and 3D spaces. The benchmark functions have analytic 2D and 3D Laplacian solutions so that we can exactly compute the errors between the numerical and analytic solutions.

Original language	English
Pages (from-to)	259-274
Number of pages	16
Journal	Applied and Computational Mathematics
Volume	22
Issue number	2
DOIs	https://doi.org/10.30546/1683-6154.22.2.2023.259
State	Published - 2023

Keywords

Discrete Laplacian Operator
Finite Difference Method
Isotropic Discretization
Isotropic Stencil

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abstract = "In this paper, we review and investigate isotropic finite difference discretizations of the two-dimensional (2D) and three-dimensional (3D) Laplacian operators. In particular, we propose benchmark functions to quantitatively evaluate the isotropy of the discrete Laplacian operators in 2D and 3D spaces. The benchmark functions have analytic 2D and 3D Laplacian solutions so that we can exactly compute the errors between the numerical and analytic solutions.",

keywords = "Discrete Laplacian Operator, Finite Difference Method, Isotropic Discretization, Isotropic Stencil",

author = "Lee, {Hyun Geun} and Seokjun Ham and Junseok Kim",

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AU - Kim, Junseok

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AB - In this paper, we review and investigate isotropic finite difference discretizations of the two-dimensional (2D) and three-dimensional (3D) Laplacian operators. In particular, we propose benchmark functions to quantitatively evaluate the isotropy of the discrete Laplacian operators in 2D and 3D spaces. The benchmark functions have analytic 2D and 3D Laplacian solutions so that we can exactly compute the errors between the numerical and analytic solutions.

KW - Discrete Laplacian Operator

KW - Finite Difference Method

KW - Isotropic Discretization

KW - Isotropic Stencil

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EP - 274

JO - Applied and Computational Mathematics

JF - Applied and Computational Mathematics

IS - 2

ER -

ISOTROPIC FINITE DIFFERENCE DISCRETIZATION OF LAPLACIAN OPERATOR

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