【摘 要】
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A novel version of the Method of Fundamental Solutions is presented.The approach is based on some external boundaries rather than external sources.Instead o
【机 构】
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SzéchenyiIstvánUniversity,H-9026Gy(o)r,Hungary
【出 处】
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第7届Trefftz工程计算方法(ICTM2015)暨第3届基本解工程应用方法(MFS)
论文部分内容阅读
A novel version of the Method of Fundamental Solutions is presented.The approach is based on some external boundaries rather than external sources.Instead of the original problem,another problem is to be solved which is defined in an extended domain.If the distance of the original and the external boundary is not too large(more precisely,the distance is in the same order of magnitude than the characteristic distance of the boundary collocation points),this is a well-conditioned problem: the condition number is much less than that of the system produced by the traditional Method of Fundamental Solutions.While the original boundary is fixed,the external boundary can be defined in a flexible way.To solve the extended problem,simple finite volume schemes and quadtree/octtree-based multi-level methods are used.The resulting method can be considered a meshless technique.The external boundary conditions can be determined and updated at each level by simple Richardson-type iterations.There is no need to know and use the fundamental solution of the partial differential equation to be solved,thus,the approach can be extended to more general partial differential equations in a natural way.The multi-level technique significantly reduces the necessary number of arithmetic operations,i.e.the approach is efficient from a computational point of view.In addition to this,the problem of large,dense and ill-conditioned systems is completely avoided.
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