Abstract
Numerical methods for Finite Element Method (FEM) analysis of the exterior Helmholtz problem with local and Dirichlet-to-Neumann (DtN) boundary conditions are reviewed. Efficient preconditionings of Conjugate Orthogonal Conjugate Gradient (COCG) method for the resulting complex-symmetric (non-Hermitian) matrix systems are discussed including Incomplete Cholesky (IC) and Complex Shifted IC factorization with dropping tolerance. We evaluate the convergence of preconditioned COCG methods under varying wave numbers of Helmholtz equation and consider also on effectiveness of these preconditionings through eigenvalue analysis.
