Application of Multipole Expansions To Boundary Element Method

The Boundary Element Method (BEM) has long been considered to be a viable alternative to the Finite Element Method (FEM) for doing engineering analysis. The BEM reduces the dimensions of the problem by one and leads to smaller system of equations. One of the inherent limitations of the BEM has been the long time required for the solution of large problems. This makes the BEM prohibitively expensive to use while solving large problems involving crack propagation, elastodynamics, etc. This thesis is a successful attempt at reducing the solution time for the BEM. An iterative solver has been developed and the advantages it offers over the direct solver have been presented. The fast multipole method is a method used to reduce the number of computations while solving N body problems in astrophysics and molecular dynamics. A numerical formulation for accelerating the computation of boundary integrals based on the fast multipole method has been presented. An algorithm has been developed and it has been applied to the BEM for two-dimensional potential problems. It has been found that the use of this algorithm leads to savings in CPU time for large number of nodes. This method is very promising and future research can concentrate on improving the code so that more significant savings in time can be obtained.