On the Shape-Dependent Problem of Singularity Cancellation Transformations for Weakly Near-Singular Integrals

Autor:	Tapan K. Sarkar, Yu Zhang, Ming-Da Zhu
Rok vydání:	2021
Předmět:	Singularity Relation (database) ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Convergence (routing) MathematicsofComputing_NUMERICALANALYSIS Applied mathematics Numerical verification Electrical and Electronic Engineering Singular integral Integral equation Mathematics
Zdroj:	IEEE Transactions on Antennas and Propagation. 69:5837-5850
ISSN:	1558-2221 0018-926X
DOI:	10.1109/tap.2021.3069483
Popis:	The singularity cancellation transformations are well-known for calculating weakly singular and near-singular integrals in integral equation solutions. However, some singularity cancellation methods suffer from the shape-dependent problem of inaccuracy and inefficiency for deformed triangles. By the theoretical analysis and numerical verification in this article, the relation between the near-singularity and shape-dependence of the singularity cancellation schemes is discussed. Moreover, a novel framework for devising cancellation transformations of weakly near-singular integrals is presented, which results in fast convergence for both regular and irregular triangular domains. Some numerical results are given to illustrate the validity of the theoretical framework and the efficiency of the proposed transformations.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::b198f0c4e88b57b9146fe09d226c837d https://doi.org/10.1109/tap.2021.3069483 Zobrazit plný text záznamu