Enriched Meshfree Method for an Accurate Numerical Solution of the Motz Problem
We present an enriched meshfree solution of the Motz problem. The Motz problem has been known as a benchmark problem to verify the efficiency of numerical methods in the presence of a jump boundary data singularity at a point, where an abrupt change occurs for the boundary condition. We propose a si...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/6324754 |
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| author | Won-Tak Hong |
| author_facet | Won-Tak Hong |
| author_sort | Won-Tak Hong |
| collection | DOAJ |
| description | We present an enriched meshfree solution of the Motz problem. The Motz problem has been known as a benchmark problem to verify the efficiency of numerical methods in the presence of a jump boundary data singularity at a point, where an abrupt change occurs for the boundary condition. We propose a singular basis function enrichment technique in the context of partition of unity based meshfree method. We take the leading terms of the local series expansion at the point singularity and use them as enrichment functions for the local approximation space. As a result, we obtain highly accurate leading coefficients of the Motz problem that are comparable to the most accurate numerical solution. The proposed singular enrichment technique is highly effective in the case of the local series expansion of the solution being known. The enrichment technique that is used in this study can be applied to monotone singularities (of type rα with α<1) as well as oscillating singularities (of type rαsin(ϵlogr)). It is the first attempt to apply singular meshfree enrichment technique to the Motz problem. |
| format | Article |
| id | doaj-art-fc75db95910148ba83a9ada2add7aaf9 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-fc75db95910148ba83a9ada2add7aaf92025-02-03T01:04:26ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/63247546324754Enriched Meshfree Method for an Accurate Numerical Solution of the Motz ProblemWon-Tak Hong0Department of Mathematics & Finance, Gachon University, 1342 Seongnamdaero, Sujeong-gu, Seongnam-si, Gyeonggi-do 13120, Republic of KoreaWe present an enriched meshfree solution of the Motz problem. The Motz problem has been known as a benchmark problem to verify the efficiency of numerical methods in the presence of a jump boundary data singularity at a point, where an abrupt change occurs for the boundary condition. We propose a singular basis function enrichment technique in the context of partition of unity based meshfree method. We take the leading terms of the local series expansion at the point singularity and use them as enrichment functions for the local approximation space. As a result, we obtain highly accurate leading coefficients of the Motz problem that are comparable to the most accurate numerical solution. The proposed singular enrichment technique is highly effective in the case of the local series expansion of the solution being known. The enrichment technique that is used in this study can be applied to monotone singularities (of type rα with α<1) as well as oscillating singularities (of type rαsin(ϵlogr)). It is the first attempt to apply singular meshfree enrichment technique to the Motz problem.http://dx.doi.org/10.1155/2016/6324754 |
| spellingShingle | Won-Tak Hong Enriched Meshfree Method for an Accurate Numerical Solution of the Motz Problem Advances in Mathematical Physics |
| title | Enriched Meshfree Method for an Accurate Numerical Solution of the Motz Problem |
| title_full | Enriched Meshfree Method for an Accurate Numerical Solution of the Motz Problem |
| title_fullStr | Enriched Meshfree Method for an Accurate Numerical Solution of the Motz Problem |
| title_full_unstemmed | Enriched Meshfree Method for an Accurate Numerical Solution of the Motz Problem |
| title_short | Enriched Meshfree Method for an Accurate Numerical Solution of the Motz Problem |
| title_sort | enriched meshfree method for an accurate numerical solution of the motz problem |
| url | http://dx.doi.org/10.1155/2016/6324754 |
| work_keys_str_mv | AT wontakhong enrichedmeshfreemethodforanaccuratenumericalsolutionofthemotzproblem |