Gauss-Jacobi quadratures for hypersingular integrals
This paper introduces the use of finite part integration for hypersingular boundary integrals, with particular emphasis being placed on demonstrating the consistency between the underlying physical concept and the mathematical definition. Gaussian interpolative quadratures are then derived for the r...
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| Format: | Journal article |
| Language: | English |
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2014
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| _version_ | 1826259372256264192 |
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| author | Korsunsky, A |
| author2 | Elliott, L |
| author_facet | Elliott, L Korsunsky, A |
| author_sort | Korsunsky, A |
| collection | OXFORD |
| description | This paper introduces the use of finite part integration for hypersingular boundary integrals, with particular emphasis being placed on demonstrating the consistency between the underlying physical concept and the mathematical definition. Gaussian interpolative quadratures are then derived for the regular, Cauchy-singular, and hypersingular integrals. The resulting formulae depend on the Jacobi polynomials <em>p<sub>n</sub></em><sup>(α,β)</sup> and the associated functions <em>q<sub>n</sub><sup>(α,β)</sup></em>, and the properties and numerical evaluation of these functions are discussed in the following section. The use of the hypersingular Gaussian quadrature technique is then demonstrated in application to the solution of boundary integral equations in fracture mechanics. |
| first_indexed | 2024-03-06T18:48:49Z |
| format | Journal article |
| id | oxford-uuid:0f788d14-50a5-43c0-b47e-7245a143713a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:48:49Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | oxford-uuid:0f788d14-50a5-43c0-b47e-7245a143713a2022-03-26T09:51:22ZGauss-Jacobi quadratures for hypersingular integralsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:0f788d14-50a5-43c0-b47e-7245a143713aEngineering & allied sciencesEnglishOxford University Research Archive - Valet2014Korsunsky, AElliott, LIngham, DLesnic, DThis paper introduces the use of finite part integration for hypersingular boundary integrals, with particular emphasis being placed on demonstrating the consistency between the underlying physical concept and the mathematical definition. Gaussian interpolative quadratures are then derived for the regular, Cauchy-singular, and hypersingular integrals. The resulting formulae depend on the Jacobi polynomials <em>p<sub>n</sub></em><sup>(α,β)</sup> and the associated functions <em>q<sub>n</sub><sup>(α,β)</sup></em>, and the properties and numerical evaluation of these functions are discussed in the following section. The use of the hypersingular Gaussian quadrature technique is then demonstrated in application to the solution of boundary integral equations in fracture mechanics. |
| spellingShingle | Engineering & allied sciences Korsunsky, A Gauss-Jacobi quadratures for hypersingular integrals |
| title | Gauss-Jacobi quadratures for hypersingular integrals |
| title_full | Gauss-Jacobi quadratures for hypersingular integrals |
| title_fullStr | Gauss-Jacobi quadratures for hypersingular integrals |
| title_full_unstemmed | Gauss-Jacobi quadratures for hypersingular integrals |
| title_short | Gauss-Jacobi quadratures for hypersingular integrals |
| title_sort | gauss jacobi quadratures for hypersingular integrals |
| topic | Engineering & allied sciences |
| work_keys_str_mv | AT korsunskya gaussjacobiquadraturesforhypersingularintegrals |