Fast Methods for Boundary Integral Equations

Solving integral equations on surfaces with complicated geometry is important for many applications in electromagnetics, fluids and computer graphics. These problems lead to large linear systems with fully populated matrices. With fast methods, such as the Fast Multipole Method (FMM) or wavelets, the complexity of the matrix vector multiplication can be reduced from quadratic to linear or almost linear complexity. The figure shows the equilibrium charge distribution for the Stanford Bunny, a commonly used test model. This example leads to a dense linear system with 69451 unknowns. Using the FMM, the solution time of this example is approximately 10 minutes on a DEC alfa workstation. Professor Tausch is working on fast methods which have applications in electromagnetics, fluid flow, and computer graphics.