Fast Numerical Techniques for Electromagnetic Problems in Frequency Domain

Nilsson, M. 2003. Fast Numerical Techniques for Electromagnetic Problems in Frequency Domain. Acta Universitatis Upsaliensis. Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 916. 38 pp. Uppsala. ISBN 91-554-5827-0 The Method of Moments is a numerical technique for solving electromagnetic problems with integral equations. The method discretizes a surface in three dimensions, which reduces the dimension of the problem with one. A drawback of the method is that it yields a dense system of linear equations. This effectively prohibits the solution of large scale problems. Papers I-III describes the Fast Multipole Method. It reduces the cost of computing a dense matrix vector multiplication. This implies that large scale problems can be solved on personal computers. In Paper I the error introduced by the Fast Multipole Method is analyzed. Paper II and Paper III describe the implementation of the Fast Multipole Method. The problem of computing the monostatic Radar Cross Section involves many right hand sides. Since the Fast Multipole Method computes a matrix times a vector, iterative techniques are used to solve the linear systems. It is important that the solution time for each system is as low as possible. Otherwise the total solution time becomes too large. Different techniques for reducing the work in the iterative solver are described in Paper IV-VI. Paper IV describes a block Quasi Minimal Residual method for several right hand sides and a Sparse Approximate Inverse preconditioner that reduce the number of iterations significantly. In Paper V and Paper VI a method based on linear algebra called the Minimal Residual Interpolation method is described. It reduces the work in an iterative solver by accurately computing an initial guess for the iterative method. In Paper VII a hybrid method between Physical Optics and the Fast Multipole Method is described. It can handle large problems that are out of reach for the Fast Multipole Method.