On the determination of locating the source points of the MFS using effective condition number

C. S. Chen; Amir Noorizadegan; D. L. Young; Chuin Shan Chen

doi:10.1016/j.cam.2022.114955

On the determination of locating the source points of the MFS using effective condition number

C. S. Chen
, Amir Noorizadegan
, D. L. Young^*
, Chuin Shan Chen^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

34 Citations (Scopus)

Abstract

The method of fundamental solutions (MFS) is a highly accurate numerical method for solving homogeneous solutions subject to a properly selection of the sources location. In this work, we choose the effective condition number as a tool for the determination of a good source location of the MFS that leads to highly accurate results with low computational cost. Three approaches for the location of the fictitious source points are considered. An efficient algorithm for the evaluation of the effective condition number is proposed. We also compare the proposed method with the well-known LOOCV (leave-one-out cross validation) and show the advantages and shortcomings of each approach. Five numerical examples with different geometric shapes of the domain for both harmonic and non-harmonic boundary conditions in 2D and 3D are presented.

Original language	English
Article number	114955
Journal	Journal of Computational and Applied Mathematics
Volume	423
Early online date	24 Nov 2022
DOIs	https://doi.org/10.1016/j.cam.2022.114955
Publication status	Published - 15 May 2023

User-Defined Keywords

Effective condition number
Leave-one-out cross validation
Method of fundamental solutions
Uncertainty principle

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1016/j.cam.2022.114955

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title = "On the determination of locating the source points of the MFS using effective condition number",

abstract = "The method of fundamental solutions (MFS) is a highly accurate numerical method for solving homogeneous solutions subject to a properly selection of the sources location. In this work, we choose the effective condition number as a tool for the determination of a good source location of the MFS that leads to highly accurate results with low computational cost. Three approaches for the location of the fictitious source points are considered. An efficient algorithm for the evaluation of the effective condition number is proposed. We also compare the proposed method with the well-known LOOCV (leave-one-out cross validation) and show the advantages and shortcomings of each approach. Five numerical examples with different geometric shapes of the domain for both harmonic and non-harmonic boundary conditions in 2D and 3D are presented.",

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author = "Chen, \{C. S.\} and Amir Noorizadegan and Young, \{D. L.\} and Chen, \{Chuin Shan\}",

note = "The first author thanks the financial support of the Ministry of Science and Technology (MOST), Taiwan, under the recruitment of visiting science and technology personnel with subsidies (109-2811-E-002-516 and 110-2811-E-002-518). The second, third, and fourth authors gratefully acknowledge the financial support of the Ministry of Science and Technology (MOST) of Taiwan under grant numbers MOST 107-2221-E-002-023-MY2, 108-2221-E-002-005-MY3, and 109-2221-E002-006-MY3. Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.",

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AU - Chen, C. S.

AU - Noorizadegan, Amir

AU - Young, D. L.

AU - Chen, Chuin Shan

N1 - The first author thanks the financial support of the Ministry of Science and Technology (MOST), Taiwan, under the recruitment of visiting science and technology personnel with subsidies (109-2811-E-002-516 and 110-2811-E-002-518). The second, third, and fourth authors gratefully acknowledge the financial support of the Ministry of Science and Technology (MOST) of Taiwan under grant numbers MOST 107-2221-E-002-023-MY2, 108-2221-E-002-005-MY3, and 109-2221-E002-006-MY3. Publisher Copyright: © 2022 Elsevier B.V.

PY - 2023/5/15

Y1 - 2023/5/15

N2 - The method of fundamental solutions (MFS) is a highly accurate numerical method for solving homogeneous solutions subject to a properly selection of the sources location. In this work, we choose the effective condition number as a tool for the determination of a good source location of the MFS that leads to highly accurate results with low computational cost. Three approaches for the location of the fictitious source points are considered. An efficient algorithm for the evaluation of the effective condition number is proposed. We also compare the proposed method with the well-known LOOCV (leave-one-out cross validation) and show the advantages and shortcomings of each approach. Five numerical examples with different geometric shapes of the domain for both harmonic and non-harmonic boundary conditions in 2D and 3D are presented.

AB - The method of fundamental solutions (MFS) is a highly accurate numerical method for solving homogeneous solutions subject to a properly selection of the sources location. In this work, we choose the effective condition number as a tool for the determination of a good source location of the MFS that leads to highly accurate results with low computational cost. Three approaches for the location of the fictitious source points are considered. An efficient algorithm for the evaluation of the effective condition number is proposed. We also compare the proposed method with the well-known LOOCV (leave-one-out cross validation) and show the advantages and shortcomings of each approach. Five numerical examples with different geometric shapes of the domain for both harmonic and non-harmonic boundary conditions in 2D and 3D are presented.

KW - Effective condition number

KW - Leave-one-out cross validation

KW - Method of fundamental solutions

KW - Uncertainty principle

UR - https://www.scopus.com/pages/publications/85143522510

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DO - 10.1016/j.cam.2022.114955

M3 - Journal article

AN - SCOPUS:85143522510

SN - 0377-0427

VL - 423

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

M1 - 114955

ER -

On the determination of locating the source points of the MFS using effective condition number

Abstract

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UN SDGs

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