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

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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.