Accelerated stationary iterative methods for the numerical solution of electromagnetic wave scattering problems

摘要

The main focus of this work is to contribute to the development of iterativeudsolvers applied to the method of moments solution of electromagnetic waveudscattering problems.udIn recent years there has been much focus on current marching iterativeudmethods, such as Gauss-Seidel and others. These methods attempt to marchuda solution for the unknown basis function amplitudes in a manner that mimicsudthe physical processes which create the current. In particular the forwardudbackward method has been shown to produce solutions that, for some twodimensionaludscattering problems, converge more rapidly than non-current marchingudKrylov methods. The buffered block forward backward method extendsudthese techniques in order to solve three-dimensional scattering problems. Theudconvergence properties of the forward backward and buffered block forwardudbackward methods are analysed extensively in this thesis. In conjunction, severaludmeans of accelerating these current marching methods are investigatedudand implemented.udThe main contributions of this thesis can be summarised as follows:ud² An explicit convergence criterion for the buffered block forward backwardudmethod is specified. A rigorous numerical comparison of the convergenceudrate of the buffered block forward backward method, againstudthat of a range of Krylov solvers, is performed for a range of scatteringudproblems.ud² The acceleration of the buffered block forward backward method is investigatedudusing relaxation.ud² The efficient application of the buffered block forward backward methodudto problems involving multiple source locations is examined.ud² An optimally sized correction step is introduced designed to accelerateudthe convergence of current marching methods. This step is applied to theudforward backward and buffered block forward backward methods, andudapplied to two and three-dimensional problems respectively. Numericaludresults demonstrate the significantly improved convergence of the forwardudbackward and buffered block forward backward methods usingudthis step.