MOLT based fast high-order three dimensional A-stable scheme for wave propagation

We present a fast (linear-time), high-order, multi-dimensional, A-stable implicit wave solver applicable for electromagnetic (EM) problems, specifically targeting plasma science. This approach uses a Method of Lines Transpose (MOLT) formulation combined with an Alternating Direction Implicit (ADI) scheme. In this scheme, a PDE is first discretized in time, and then the resulting boundary-value problems are solved using a Green's function method. In particular, inverse of the resulting modified Helmholtz operator is analytically constructed and evaluated efficiently using an O(N) recursive fast convolution algorithm. Extension to multi-dimensions is formed using an ADI scheme, and each line is solved independently. In this work, we propose a higher order 3D scheme which is able to deal with complicated geometries. The scheme is successfully evaluated using several 3D test problems.