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Numerical experiments of the dual null field method for Dirichlet problems of Laplace’s equation in elliptic domains with elliptic holes

Авторы: Li Zi.C., Huang H.Ts., Zhang Li.P., Lempert A., Lee M.G.

Журнал: The Bulletin of Irkutsk State University. Series: Mathematics

Том: 39

Номер:

Год: 2022

Отчётный год: 2022

Издательство:

Местоположение издательства:

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DOI: 10.26516/1997-7670.2022.39.80

Аннотация: Dual techniques have been used in many engineering papers to deal with singularity and ill-conditioning of the boundary element method (BEM). In the first part of the two-part article, our efforts were focused on studying the theoretical aspects of this problem, including the analysis of errors and the study of stability. We provided the theoretical analysis for Laplace equation in elliptic domains with elliptic holes. To bypass the degenerate scales of Dirichlet problems, the second and the first kinds of the field methods (NFM) are used for the exterior and the interior boundaries, simultaneously. This approach is called the dual field method (DNFM).This paper is the second part of the study. Numerical results for degenerate models of an elliptic domain with one elliptic hole at + = 2 are carried out to verify the theoretical analysis obtained. The collocation Trefftz method (CTM) is also designed for comparisons. Both the DNFM and the CTM can provide excellent numerical performances. The convergence rates are the same but the stability of CTM is excellent and can achieve the constant condition numbers, Cond = (1).

Индексируется WOS: Q5

Индексируется Scopus: Нет

Индексируется УБС: Нет

Индексируется РИНЦ: Да

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Индексируется CORE: Нет

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