Parallel computations for the simulation of seismic waves on the basis of the additive Schwartz method

The Laguerre time transform for the elastic wave equations leads to a definite spatial operator independent of a separation parameter. This allows one to perform parallel computations on the basis of Schwartz alternations using a domain decomposition with overlapping. On each alternation step, the resulting system of linear algebraic equations in each subdomain is solved independently, so one can use a direct solver on the basis of the LU-decomposition. Since the spatial operator is independent of separation parameters, this decomposition can be performed only once and be saved in RAM for each elementary subdomain to use for all right-hand sides. This approach is implemented and the corresponding software for high performance computers with hybrid parallel architecture is developed. A number of numerical results illustrating the analysis of scalability are discussed.