张量分析在多极边界元法中的应用

Application of Tensor Analysis to the Fast Multipole BEM

目的多极边界元法是一种新型的边界元数值算法,在此基础上建立科学的数学理论.方法张量分析法,多极展开法,三维位势问题多极边界元法.结果得到且证明了三维位势问题多极边界元法核函数分解定理,完善了三维位势问题多极边界元法的数学理论.结论建立了三维位势问题多极边界元法的一般理论,完善了三维位势问题多极边界元法的数学方法.

Objective The Fast Multipole-Boundary Element Method （FM-BEM） is the new algorithm of the Boundary Element Method （BEM）. On this basis, the scientific mathematical theory will be established. Methods Tensor analysis, the Fast Multipole Method （FMM）, the Three-Dimensional for Potential Problems Based on Fast Multipole-BEM. Results The theorem of the Fast Multipole Method （FMM） expansions of the kernels for FM-BEM based on 3D Elastic Problems is obtained and proved; the mathematical theory of the FM-BEM for 3D potential problems is perfected. Conclusion The three-dimensional Fast Multipole BEM for potential problems is established primarily; the mathematical method of the three-dimensional FM-BEM is perfected.