Preconditioning for Large-Scale Boundary Integral Equations in Electromagnetics [Open Problems in CEM]

The boundary-element method is a popular approach for solving electromagnetic applications. It can reduce a three-dimensional problem to solving a two-dimensional surface problem, simplifying considerably the mesh generation, and limiting grid-dispersion errors. The Method of Moments discretization of boundary integral equations leads to a very large and dense linear systems. It is mandatory to use iterative methods and robust preconditioning for the solution. Identifying the best class of method with respect to numerical stability, inherent parallelism, and good scalability with respect to the frequency of the problem is still an open research issue.