Project Title: Parameter Estimation Technique for Dense Matrix Methods

Summary:

In computational electromagnetics one can observe a growing interest in Finite Difference Time Domain (FDTD) algorithms. FDTD is an implicit sparse matrix method and works with one iteration per time step which makes the method numerically efficient. The Method of Moments (MoM) and other dense matrix methods like 3D MMP require much more iterations when an iterative matrix solver, e.g. the method of Conjugate Gradients (CG) is applied. Since iterative matrix solvers are the key to efficient solutions of large problems, it is extremely important for dense matrix methods to find a technique that allows to drastically reduce the number of CG iterations. Dense matrix methods typically work in the frequency domain. Although the solution of a previous time step is a good estimate for the solution of the actual time step, this knowledge usually is wasted when dense matrix methods are applied. The Parameter Estimation Technique (PET) uses the information obtained in one or several previous time steps for obtaining an excellent initial guess for the parameters to be computed with CG algorithms. The rectangular MMP matrices often have a large condition number. This provides hard problems for CG. It has been found that higher order PET with power series extrapolation does not allow to reduce the number of CG iterations. Although a linear PET is helpful, one can generalize the PET by using arbitrary basis functions. When the PET basis is optimized with a genetic algorithm, one can obtain a drastic reduction of the CG iterations (factor>50).

Contacts: Ch.Hafner, IFH, ETZG95, ETH Zentrum, CH-8092 Zurich

Electronic Contacts: hafner@ifh.ee.ethz.ch

Index Terms: Computational Electromagnetics, Matrix Methods, Optimization

Supported by: SNF