CSYM - an iterative solution method for systems of linear equations with complex symmetric coefficient matrix

We give a short overview over existing iterative algorithms for solving complex symmetric systems of linear equations, which can take advantage of this special structure. This type of system occurs when the method of moments is used to solve the electric field integral equation (EFIE). The relatively new method, CSYM, is described and the differences and advantages over existing methods are pointed out, namely the minimal residual property, short term recurrence relations and no potentially serious breakdowns. We tested CSYM on matrices resulting from a discretisation of the EFIE to solve a scattering problem. The method of moments is applied in combination with a multilevel fast multipole method. When applied to systems having more than 100 000 unknowns, CSYM rapidly reduces the residual during the first iterations while solvers which do not minimize the residual in any sense are less efficient in this stage.