Unconditionally stable high-order picard iteration algorithm for computational electromagnetics

An iterative numerical time marching algorithm which is applicable for solving time dependent anisotropic nonlinear Maxwell equations is presented. The method is based on high-order discretization of classical Picard iteration. Using linearization in the iteration space, a highly convergent implicit formulation is derived. The dissipation error is completely eliminated when Picard iteration converges since no linearization is done in time. In addition, the order of accuracy in space and time can be increased arbitrarily without violating unconditional stability of the scheme. Numerical test cases are performed to validate the convergence and accuracy of the proposed method.