This project has three research topics from the field of iterative solution methods for nonsymmetric linear systems of equations arising in the discretization of second-order PDEs. Of these, two focus on time-harmonic wave propagation and one on convection-diffusion problems. The first topic consists in extending algorithms for the solution of time-harmonic scattering problems for the Helmholtz equation, from 2D to 3D. Based on a discretization which uses an exact radiation condition - and hence permits small computational domains relative to the scatterer - these algorithms use an imbedding technique combined with a fast Helmhotz solver, resulting in fast and well-parallelizable algorithms for an application which is becoming increasingly important. The second topic is an investigation of recent algebraic multilevel techniques applied to exterior Helmholtz problems. These techniques could lead to an algorithm of optimal complexity for solving this type of problem. Finally, the third topic involves investigating effects of stabilization techniques for discretization of convection-diffusion problems on iterative solution of discrete problems.
