Fictitious finite integration method for solving high order partial differential equations

M. Lei; P. Y. Liu; Y.C. Hon

doi:10.1016/j.enganabound.2023.04.012

Fictitious finite integration method for solving high order partial differential equations

M. Lei
, P. Y. Liu
, Y.C. Hon^*

^*Corresponding author for this work

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

6 Citations (Scopus)

Abstract

In this paper, we combine the finite integration method (FIM) with the technique of fictitious points to solve high order partial differential equations (HOPDEs). Two type of fictitious finite integration method (FFIM) are proposed and analyzed. The first type FFIM (FFIM-I) constructs the first order integration matrices by shifted Chebyshev polynomials so that the analytical high order integration matrices can be recursively obtained. Compared with the classical FIM, whose high order integration matrices are approximated directly through low order integration matrices, this FFIM-I leads to higher accuracy. Based on FFIM-I, the second type FFIM (FFIM-II) is proposed in which the fictitious points are located freely either inside or outside the problem domain. The FFIM-II can further improve the performance of FFIM-I in solving HOPDEs. The advantage of this fictitious finite integration method will be demonstrated by making comparisons among FIM, FFIM-I and FFIM-II through several 2D and 3D numerical experiments.

© 2023 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	235-242
Journal	Engineering Analysis with Boundary Elements
Volume	152
Online published	16 Apr 2023
DOIs	https://doi.org/10.1016/j.enganabound.2023.04.012
Publication status	Published - Jul 2023

Funding

The research was supported by grants from Youth Science and Technology Research Foundation of Shanxi Province (No. 202103021223059), the School Foundation of Taiyuan University of Technology (No. 2022QN099), the Guangzhou Basic and Applied Basic Research (No. 202102020340), Guangdong Basic and Applied Basic Research Foundation (No. 2021A1515110680) and Research Grant Council of the Hong Kong Special Administrative Region (No. CityU 11316822).

Research Keywords

High order PDEs
Finite integration method
Shifted Chebyshev polynomials
Fictitious point technique

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RGC-funded

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10.1016/j.enganabound.2023.04.012

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@article{b6f5d3f4efe34a8b92ede1bcfc8d7f84,

title = "Fictitious finite integration method for solving high order partial differential equations",

abstract = "In this paper, we combine the finite integration method (FIM) with the technique of fictitious points to solve high order partial differential equations (HOPDEs). Two type of fictitious finite integration method (FFIM) are proposed and analyzed. The first type FFIM (FFIM-I) constructs the first order integration matrices by shifted Chebyshev polynomials so that the analytical high order integration matrices can be recursively obtained. Compared with the classical FIM, whose high order integration matrices are approximated directly through low order integration matrices, this FFIM-I leads to higher accuracy. Based on FFIM-I, the second type FFIM (FFIM-II) is proposed in which the fictitious points are located freely either inside or outside the problem domain. The FFIM-II can further improve the performance of FFIM-I in solving HOPDEs. The advantage of this fictitious finite integration method will be demonstrated by making comparisons among FIM, FFIM-I and FFIM-II through several 2D and 3D numerical experiments. {\textcopyright} 2023 Elsevier Ltd. All rights reserved.",

keywords = "High order PDEs, Finite integration method, Shifted Chebyshev polynomials, Fictitious point technique",

author = "M. Lei and Liu, \{P. Y.\} and Y.C. Hon",

year = "2023",

month = jul,

doi = "10.1016/j.enganabound.2023.04.012",

language = "English",

volume = "152",

pages = "235--242",

journal = "Engineering Analysis with Boundary Elements",

issn = "0955-7997",

publisher = "Elsevier Ltd.",

}

TY - JOUR

T1 - Fictitious finite integration method for solving high order partial differential equations

AU - Lei, M.

AU - Liu, P. Y.

AU - Hon, Y.C.

PY - 2023/7

Y1 - 2023/7

N2 - In this paper, we combine the finite integration method (FIM) with the technique of fictitious points to solve high order partial differential equations (HOPDEs). Two type of fictitious finite integration method (FFIM) are proposed and analyzed. The first type FFIM (FFIM-I) constructs the first order integration matrices by shifted Chebyshev polynomials so that the analytical high order integration matrices can be recursively obtained. Compared with the classical FIM, whose high order integration matrices are approximated directly through low order integration matrices, this FFIM-I leads to higher accuracy. Based on FFIM-I, the second type FFIM (FFIM-II) is proposed in which the fictitious points are located freely either inside or outside the problem domain. The FFIM-II can further improve the performance of FFIM-I in solving HOPDEs. The advantage of this fictitious finite integration method will be demonstrated by making comparisons among FIM, FFIM-I and FFIM-II through several 2D and 3D numerical experiments. © 2023 Elsevier Ltd. All rights reserved.

AB - In this paper, we combine the finite integration method (FIM) with the technique of fictitious points to solve high order partial differential equations (HOPDEs). Two type of fictitious finite integration method (FFIM) are proposed and analyzed. The first type FFIM (FFIM-I) constructs the first order integration matrices by shifted Chebyshev polynomials so that the analytical high order integration matrices can be recursively obtained. Compared with the classical FIM, whose high order integration matrices are approximated directly through low order integration matrices, this FFIM-I leads to higher accuracy. Based on FFIM-I, the second type FFIM (FFIM-II) is proposed in which the fictitious points are located freely either inside or outside the problem domain. The FFIM-II can further improve the performance of FFIM-I in solving HOPDEs. The advantage of this fictitious finite integration method will be demonstrated by making comparisons among FIM, FFIM-I and FFIM-II through several 2D and 3D numerical experiments. © 2023 Elsevier Ltd. All rights reserved.

KW - High order PDEs

KW - Finite integration method

KW - Shifted Chebyshev polynomials

KW - Fictitious point technique

UR - https://www.scopus.com/pages/publications/85152363396

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85152363396&origin=recordpage

U2 - 10.1016/j.enganabound.2023.04.012

DO - 10.1016/j.enganabound.2023.04.012

M3 - RGC 21 - Publication in refereed journal

SN - 0955-7997

VL - 152

SP - 235

EP - 242

JO - Engineering Analysis with Boundary Elements

JF - Engineering Analysis with Boundary Elements

ER -

Fictitious finite integration method for solving high order partial differential equations

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GRF: Generalized Finite Integration Method for Nonlinear Peridynamic Model

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Fictitious finite integration method for solving high order partial differential equations

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GRF: Generalized Finite Integration Method for Nonlinear Peridynamic Model

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