We describe an implementation of the Boundary Element Method for the 2-D Laplace's problem where the domains under study present some geometrical symmetry. The boundary conditions do not share the symmetry so that intuitive reasoning cannot be used to take part of symmetry. So, we use the Group Representation Theory that presents a rationale in this context. It consists in reducing the original problem to a family of smaller ones, the global solution is obtained from superposition of the partial solutions. It leads to a substantial gain in memory volume and achieves large computational cost savings. We consider the non-abelian symmetry groups that represent the most general case. We present the case of the dihedral group D/sub 3/ as an example.
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机译:我们描述了二维拉普拉斯问题的边界元方法的实现,其中所研究的区域呈现出一些几何对称性。边界条件不共享对称性,因此不能使用直观推理来参与对称性。因此,我们使用群体表示理论在这种情况下提出了基本原理。它包括将原始问题简化为一系列较小的问题,全局解决方案是通过部分解决方案的叠加获得的。它大大增加了存储容量,并节省了大量计算成本。我们考虑代表最一般情况的非阿贝尔对称群。我们以二面体组D / sub 3 /为例。
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