Thursday, December 1, 9:30 am in room MTH 3206, University of Maryland, College Park

Joint Numerical Analysis, Computational Science, Engineering Seminar

The Computation of Integrals in Potential Theory with Application to Magnetics and Electrodeposition

Dr. Anita Mayo

IBM Research Center, Yorktown Heights, N.Y.

(If you want to speak to Dr. Mayo while she is here please contact Dr. Jane Cullum, cullumj@cs.umd.edu)

We present a high order accurate method for rapidly evaluating certain integrals in potential theory on general two and three dimensional regions. The kernels of the integrals are a fundamental solution, or a linear combination of the derivatives of a fundamental solution of some second order linear elliptic differential equation. What is different and important about these methods is that they avoid the the use of any standard quadrature formula, the exact evaluation of any integral, and even any evaluation of the kernel. Instead, they rely on rapid methods for solving the differential equation which the kernel satisfies. In fact, the number of operations needed to evaluate the volume integral is essentially equal to the number of operations needed to solve the differential equation on a regular rectangular grid. The ability to evaluate these integrals rapidly is important when integral equation methods are used for solving inhomogeneous differential equations, and can allow one to efficiently solve equations which are not normally solved using integral equation methods. These integrals are also needed when using the Biot Savart law to evaluate the magnetic field induced by conducting wires.