Licentiate thesis 2002-004

Iterative Solution of Maxwell's Equations in Frequency Domain

Martin Nilsson

June 2002


We have developed an iterative solver for the Moment Method. It computes a matrix vector product with the multilevel Fast Multipole Method, which makes the method scale with the number of unknowns. The iterative solver is of Block Quasi-Minimum Residual type and can handle several right hand sides at once. The linear system is preconditioned with a Sparse Approximate Inverse, which is modified to handle dense matrices. The solver is parallelized on shared memory machines using OpenMP.

To verify the method some tests are conducted on varying geometries. We use simple geometries to show that the method works. We show that the method scales on several processors of a shared memory machine. To prove that the method works for real life problems, we do some tests on large scale aircrafts. The largest test is a one million unknown simulation on a full scale model of a fighter aircraft.

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