Mathematical Sciences: Boundary Element Methods for IntegralEquations of the First Kind Governing 3-D Problems

这项研究计划将涉及一些有关三维椭圆问题的边界元方法的理论和实践课题。这些主题包括：1.伽辽金和配置法。2.网格细化和奇异单元。3.共轭梯度法。4.多重网格法。5.域子结构。6.向量处理。高效的数值方法和更强大的计算机将使我们能够解决科学和工程中更复杂和更现实的技术问题。本研究的结果将为一大类实际问题提供更好的算法。

This research program will be concerned with a number of theoretical and practical topics concerning boundary element methods for the solution of 3 dimensional elliptic problems. These topics include: 1. Galerkin and collocation methods. 2. Mesh refinement and singular elements. 3. Conjugate gradient methods. 4. Multigrid methods. 5. Domain substructuring. 6. Vector processing. Efficient numerical methods along with more powerful computers will enable us to solve more complex and realistic technical problems in science and engineering. The results from the present research will give better algorithms for a large class of practical problems.