各向异性外问题的非均匀网格的自然边界元法及其耦合法

Natural BEM with Non-uniform Grids and its Coupling Method for Exterior Anisotropic Problems

本文对于无界区域上各向异性外问题提出了在椭圆边界非均匀网格上的自然边界元法及其与有限元法的耦合法,证明相应的收敛定理和误差估计式,并且在这两种方法中引入基于等分布原理的移动网格技巧.最后,通过数值结果表明了误差收敛理论的正确性以及所提方法和技巧的有效性.

For the anisotropic problems in 2-D unbounded domains, this paper proposes a nat-ural BEM with non-uniform grids on the elliptic boundary and a coupling of NBEM and FEM with non-uniform grids on the elliptic artificial boundary. Then, the convergence theorems of the NBEM and the coupling method are proved. In addition, the moving mesh method based on equidistribution principle is introduced into the NBEM and the coupling method, respec-tively. Numerical examples verify the convergence theorems and demonstrate the advantage in accuracy and e？ciency of the proposed methods.