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

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

1 Citation (Scopus)

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
Publication status	Published - 2023

Bibliographical note

Funding Information:
H.G. Lee was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022R1A2C1011708). The corresponding author (J.S. Kim) was supported by the National Research Foundation (NRF), Korea, under project BK21 FOUR. The authors are grateful to the reviewers whose valuable suggestions and comments significantly improved the quality of this paper.

Publisher Copyright:
© 2023, Institute of Applied Mathematics of Baku State University. All rights reserved.

Keywords

Discrete Laplacian Operator
Finite Difference Method
Isotropic Discretization
Isotropic Stencil

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.30546/1683-6154.22.2.2023.259

Cite this

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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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doi = "10.30546/1683-6154.22.2.2023.259",

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N2 - 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.

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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DO - 10.30546/1683-6154.22.2.2023.259

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ISOTROPIC FINITE DIFFERENCE DISCRETIZATION OF LAPLACIAN OPERATOR

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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