Weak formulation of finite element method using wavelet basis functions

Siu Lau Ho; Shiyou Yang; H. C. Wong

doi:10.1109/20.952577

Weak formulation of finite element method using wavelet basis functions

Siu Lau Ho, Shiyou Yang, H. C. Wong

The Hong Kong Polytechnic University

Research output: Journal article publication › Conference article › Academic research › peer-review

11 Citations (Scopus)

Abstract

This paper details the development of the weak form formulations of finite element type methods using wavelets as basis functions. Such approaches are different from most wavelets based ones that are derived from the strong form. The advantages of the proposed formulation are that there is no need to enforce natural boundary conditions and that the lower order derivatives of the wavelet bases are involved in the connection coefficients. Various approaches to deal with essential boundary and interface conditions are investigated, and algorithms to compute the associated connection coefficients are derived. To validate the proposed method, two numerical examples are described.

Original language	English
Pages (from-to)	3203-3207
Number of pages	5
Journal	IEEE Transactions on Magnetics
Volume	37
Issue number	5 I
DOIs	https://doi.org/10.1109/20.952577
Publication status	Published - 1 Sept 2001
Event	Ninth Biennial Electromagnetic Field Computation (CEFC) - Milwaukee, WI, United States Duration: 4 Jun 2001 → 7 Jun 2001

Keywords

Connection coefficients
Galerkin approach
Wavelet bases
Wavelet-Galerkin method
Weak form

ASJC Scopus subject areas

Electrical and Electronic Engineering
Physics and Astronomy (miscellaneous)

More information

10.1109/20.952577

http://hdl.handle.net/10397/876

Cite this

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title = "Weak formulation of finite element method using wavelet basis functions",

abstract = "This paper details the development of the weak form formulations of finite element type methods using wavelets as basis functions. Such approaches are different from most wavelets based ones that are derived from the strong form. The advantages of the proposed formulation are that there is no need to enforce natural boundary conditions and that the lower order derivatives of the wavelet bases are involved in the connection coefficients. Various approaches to deal with essential boundary and interface conditions are investigated, and algorithms to compute the associated connection coefficients are derived. To validate the proposed method, two numerical examples are described.",

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AU - Wong, H. C.

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N2 - This paper details the development of the weak form formulations of finite element type methods using wavelets as basis functions. Such approaches are different from most wavelets based ones that are derived from the strong form. The advantages of the proposed formulation are that there is no need to enforce natural boundary conditions and that the lower order derivatives of the wavelet bases are involved in the connection coefficients. Various approaches to deal with essential boundary and interface conditions are investigated, and algorithms to compute the associated connection coefficients are derived. To validate the proposed method, two numerical examples are described.

AB - This paper details the development of the weak form formulations of finite element type methods using wavelets as basis functions. Such approaches are different from most wavelets based ones that are derived from the strong form. The advantages of the proposed formulation are that there is no need to enforce natural boundary conditions and that the lower order derivatives of the wavelet bases are involved in the connection coefficients. Various approaches to deal with essential boundary and interface conditions are investigated, and algorithms to compute the associated connection coefficients are derived. To validate the proposed method, two numerical examples are described.

KW - Connection coefficients

KW - Galerkin approach

KW - Wavelet bases

KW - Wavelet-Galerkin method

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EP - 3207

JO - IEEE Transactions on Magnetics

JF - IEEE Transactions on Magnetics

IS - 5 I

T2 - Ninth Biennial Electromagnetic Field Computation (CEFC)

Y2 - 4 June 2001 through 7 June 2001

ER -

Weak formulation of finite element method using wavelet basis functions

Abstract

Keywords

ASJC Scopus subject areas

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