Fictitious centre RBF method for high order BVPs in multiply connected domains

Andreas Karageorghis; Amir Noorizadegan; C. S. Chen

doi:10.1016/j.aml.2021.107711

Fictitious centre RBF method for high order BVPs in multiply connected domains

Andreas Karageorghis^*
, Amir Noorizadegan
, C. S. Chen

^*Corresponding author for this work

Department of Mathematics

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

11 Citations (Scopus)

Abstract

We propose a Kansa-radial basis function (RBF) collocation method for the solution of 2D and 3D high order (i.e. of order 2N where N∈N,N≥3) boundary value problems (BVPs) in multiply connected domains. These problems include N boundary conditions (BCs), and thus we need to select N distinct sets of boundary centres. One set is positioned on the physical boundary of the problem while the rest are placed outside the exterior boundary of the domain. The efficacy of the proposed approach is demonstrated by applying it to a 2D and a 3D high order BVP in multiply connected domains.

Original language	English
Article number	107711
Number of pages	6
Journal	Applied Mathematics Letters
Volume	125
Early online date	1 Oct 2021
DOIs	https://doi.org/10.1016/j.aml.2021.107711
Publication status	Published - Mar 2022

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SDG 9 Industry, Innovation, and Infrastructure

User-Defined Keywords

Fictitious point method
High order PDEs
Kansa method
Multiply connected domains
Multiquadrics
RBFs

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10.1016/j.aml.2021.107711

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title = "Fictitious centre RBF method for high order BVPs in multiply connected domains",

abstract = "We propose a Kansa-radial basis function (RBF) collocation method for the solution of 2D and 3D high order (i.e. of order 2N where N∈N,N≥3) boundary value problems (BVPs) in multiply connected domains. These problems include N boundary conditions (BCs), and thus we need to select N distinct sets of boundary centres. One set is positioned on the physical boundary of the problem while the rest are placed outside the exterior boundary of the domain. The efficacy of the proposed approach is demonstrated by applying it to a 2D and a 3D high order BVP in multiply connected domains.",

keywords = "Fictitious point method, High order PDEs, Kansa method, Multiply connected domains, Multiquadrics, RBFs",

author = "Andreas Karageorghis and Amir Noorizadegan and Chen, \{C. S.\}",

note = "The second author is supported by the Ministry of Science and Technology (MOST), Taiwan , under Grants 107-2221-E-002-023-MY2 and 108-2221-E-002-005-MY3. The third author gratefully acknowledges 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). Publisher Copyright: {\textcopyright} 2021 Elsevier Ltd",

year = "2022",

month = mar,

doi = "10.1016/j.aml.2021.107711",

language = "English",

volume = "125",

journal = "Applied Mathematics Letters",

issn = "0893-9659",

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TY - JOUR

T1 - Fictitious centre RBF method for high order BVPs in multiply connected domains

AU - Karageorghis, Andreas

AU - Noorizadegan, Amir

AU - Chen, C. S.

N1 - The second author is supported by the Ministry of Science and Technology (MOST), Taiwan , under Grants 107-2221-E-002-023-MY2 and 108-2221-E-002-005-MY3. The third author gratefully acknowledges 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). Publisher Copyright: © 2021 Elsevier Ltd

PY - 2022/3

Y1 - 2022/3

N2 - We propose a Kansa-radial basis function (RBF) collocation method for the solution of 2D and 3D high order (i.e. of order 2N where N∈N,N≥3) boundary value problems (BVPs) in multiply connected domains. These problems include N boundary conditions (BCs), and thus we need to select N distinct sets of boundary centres. One set is positioned on the physical boundary of the problem while the rest are placed outside the exterior boundary of the domain. The efficacy of the proposed approach is demonstrated by applying it to a 2D and a 3D high order BVP in multiply connected domains.

AB - We propose a Kansa-radial basis function (RBF) collocation method for the solution of 2D and 3D high order (i.e. of order 2N where N∈N,N≥3) boundary value problems (BVPs) in multiply connected domains. These problems include N boundary conditions (BCs), and thus we need to select N distinct sets of boundary centres. One set is positioned on the physical boundary of the problem while the rest are placed outside the exterior boundary of the domain. The efficacy of the proposed approach is demonstrated by applying it to a 2D and a 3D high order BVP in multiply connected domains.

KW - Fictitious point method

KW - High order PDEs

KW - Kansa method

KW - Multiply connected domains

KW - Multiquadrics

KW - RBFs

UR - https://www.scopus.com/pages/publications/85117122295

U2 - 10.1016/j.aml.2021.107711

DO - 10.1016/j.aml.2021.107711

M3 - Journal article

AN - SCOPUS:85117122295

SN - 0893-9659

VL - 125

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

M1 - 107711

ER -

Fictitious centre RBF method for high order BVPs in multiply connected domains

Abstract

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