New efficient implicit time integration method for DGTD applied to sequential multidomain and multiscale problems

The discontinuous Galerkin’s (DG) method is an efficient technique for packaging problems. It divides an original computational region into several subdomains, i.e., splits a large linear system into several smaller and balanced matrices. Once the spatial discretization is solved, an optimal time integration method is necessary. For explicit time stepping schemes, the smallest edge length in the entire discretized domain determines the maximal time step interval allowed by the stability criterion, thus they require a large number of time steps for packaging problems. Implicit time stepping schemes are unconditionally stable, thus domains with small structures can use a large time step interval. However, this approach requires inversion of matrices which are generally not positive definite as in explicit shemes for the first-order Maxwell’s equations and thus becomes costly to solve for large problems. This work presents an algorithm that exploits the sequential way in which the subdomains are usually placed for layered structures in packaging problems. Specifically, a reordering of interface and volume unknowns combined with a block LDU (Lower-Diagonal-Upper) decomposition allows improvements in terms of memory cost and time of execution, with respect to previous DGTD implementations.