Two-level methods for the single layer potential in R3
Two-level methods for the single layer potential in R3
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DOI：
10.1007/bf02684335
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发表时间：
1998-01-01
期刊：
影响因子：
3.7
通讯作者：
Weisse, J
中科院分区：
文献类型：
--
作者：
Mund, P;Stephan, EP;Weisse, J
我们考虑R-3中开曲面片上的第一类弱奇异积分方程解。为了得到近似解，我们使用了h-型Galerkin边界元方法。此外，对于Gamma的非重叠区域分解，我们引入了两级加性Schwarz算子，并估计了这些算子关于网格大小的条件数。基于这些算子，我们得到了精确解与Galerkin解之差的后验误差估计。该估计还考虑了由Galerkin方程的近似解产生的误差。对于均匀网格，在饱和条件的假设下，我们证明了我们估计的可靠性和有效性。基于这一估计，我们引入了一种自适应多层算法，该算法具有易于计算的局部误差指标，允许对局部细化进行方向控制。用平面和曲面的数值算例说明了理论结果。
We consider weakly singular integral equations of the first kind on open surface pieces Gamma in R-3. To obtain approximate solutions we use the h-version Galerkin boundary element method. Furthermore we introduce two-level additive Schwarz operators for non-overlapping domain decompositions of Gamma and we estimate the conditions numbers of these operators with respect to the mesh size. Based on these operators we derive an a posteriori error estimate for the difference between the exact solution and the Galerkin solution. The estimate also involves the error which comes from an approximate solution of the Galerkin equations. For uniform meshes and under the assumption of a saturation condition we show reliability and efficiency of our estimate. Based on this estimate we introduce an adaptive multilevel algorithm with easily computable local error indicators which allows direction control of the local refinements. The theoretical results are illustrated by numerical examples for plane and curved surfaces.