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Application of conformal mappings and the numerical analysis of conditioning of the matrices in Trefftz method for some boundary value problems

机译:Trefftz方法中保形映射的应用和矩阵条件的数值分析在某些边值问题上

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摘要

Provided that the boundary value problem can be equivalently solved in conformally transformed domain, one can consider its mapping into unit disk domain. The problem can be solved for the new geometry and the solution can be retransformed back to the original problem domain. The paper presents this approach in order to validate whether it can be applied for improving ill-conditioning of the matrices and solutions obtained in indirect Trefftz methods.
机译:假设可以在保角变换域中等效解决边界值问题,则可以考虑将其映射到单位磁盘域中。可以为新的几何图形解决问题,并且可以将解决方案重新转换回原始问题域。本文提出了这种方法,以验证是否可以将其用于改善矩阵的不适状态以及间接Trefftz方法中获得的解决方案。

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