A Domain Decomposition Algorithm With Finite Element-Boundary Element Coupling
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摘要: 提出了一种有限元-边界元耦合分域算法．该算法将所分析问题的区域分解成有限元和边界元子域，在满足两子域界面上位移和面力协调连续的条件下，通过迭代求解得到问题的解．在迭代求解过程中，引入动态松弛系数，使收敛得以加速．该方法在两子域界面上有限单元结点和边界单元结点的位置相互独立，无需协调一致，对诸如裂纹扩展过程的模拟具有独特的优势．用所提出的耦合算法分析算例，得到的结果与有限元法、边界元法和另一种耦合算法的数值计算结果一致，验证了这种算法的正确性和可行性．Abstract: A domain decomposition algorithm coupling the finite element and the boundary element is presented.It essentially involves subdivision of the analyzed domain into sub-regions being indepen dently modeled by the two methods,i.e.,the finite element method (FEM) and the boundary element method(BEM).The original problem was restored with continuity and equilibrium conditions being satisfied on the interface of the two sub-regions using an iterative algorithm.To speed up the conver gence rate of the iterative algorithm,a dynamically changing relaxation parameter during iteration was introduced.An advantage of the proposed algorithm is that the locations of the nodes on the interface of the two sub-domains can be inconsistent.The validity of the algorithm is demonstrated by the con sistence of the results of a numerical example obtained by the proposed method and those by the FEM,the BEM and a present finite element-boundary element (FE-BE) coupling method.
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