Parallel Methods for Solving Time-Dependent Problems Using the Fourier-Laplace Transformation

In this paper we summarize recent progresses on the parallel method for solving time-dependent problems using the Fourier-Laplace transformation. Instead of solving the time-dependent prob-lems in the space-time domain, we solve them as follows. First take the Fourier-Laplace transfor-mation of given problems originally set in the space-time domain, and consider the corresponding problems in the space-frequency domain which form a set of indefinite, complex-valued elliptic problems. Such problems are solved in a natural parallel manner since each problem is inde-pendent of others. The Fourier-Laplace inversion formula will then recover the solution in the space-time domain