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| Improved average source boundary node method for plane potential problems |
| Received:January 28, 2019 Revised:April 20, 2019 |
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| DOI：10.7511/jslx20190128001 |
| KeyWord:plane potential problem Average Source Boundary Node Method(ASBNM) average source technology meshless/meshfree method |
| Author | Institution |
| 逄泽慧 |
山东理工大学 数学与统计学院, 淄博 |
| 张耀明 |
山东理工大学 数学与统计学院, 淄博 |
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| Abstract: |
| Average Source Boundary Node Method (ASBNM) is a recently proposed boundary-type meshless method.This method only uses the boundary nodes in the implementation and does not involve any element and integration notion,which is efficient,accurate,easy to implement and truly meshless.It is worth noting that for boundary-type meshless methods depending on boundary integral equations,regardless of their forms,a crucial but difficult issue is to estimate the diagonal elements of influence matrices accurately and efficiently.In this study,based on,a new scheme for directly calculating the diagonal elements of the influence matrices is proposed by the average source technique,which is an important improvement of the existing ASBNM.The new scheme transforms the calculation of diagonal elements into a purely geometric problem with respect to the boundary of solution domain.Therefore,it can be extended to any two-dimensional boundary value problems,such as elasticity problems,Stokes problems,etc.The numerical examples show the accuracy,convergence and computational efficiency of the proposed method. |
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