On the stability and efficiency of high-order parallel algorithms for 3D wave problems

In this work, we investigate the stability conditions for four new high-order ADI type schemes proposed to solve 3D wave equations with a non-constant sound speed coefficient. This analysis is mainly based on the spectral method, therefore a basic benchmark problem is formulated with a constant sound speed coefficient. For a case of general non-constant coefficient the stability analysis is done by using the energy method. Our main conclusion states that the selected ADI type schemes use different factorization operators (mainly due to the need to approximate the artificial boundary conditions on the split time levels), but the general structure of the stability factors are similar for all schemes and thus the obtained CFL conditions are also very similar. The second goal is to compare the accuracy and efficiency of the selected ADI solvers. This analysis also includes parallel versions of these schemes. Two schemes are selected as the most effective and accurate.