Iterative numerical methods for linear systems, Multigrid methods; domain decomposition for boundary value problems involving PDEs, drift-diffusion equations, semiconductor device, preconditioned conjugate gradient methods, Numerical computation of matrix norms, conditioning, scaling, Numerical computation of solutions to systems of equations, Parallel numerical computation, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Technical applications of optics and electromagnetic theory, domain decomposition, Applications to the sciences, massively parallel computation, finite element methods, Schur complement, Gummel's method, PDEs in connection with optics and electromagnetic theory