A naturally parallelizable computational method for inhomogeneous parabolic problems

A parallel numerical algorithm is introduced and analyzed for solving inhomogeneous initial boundary value parabolic problems. The scheme is based on the method recently introduced in Sheen, Sloan, and Thomee (2000) for homogeneous problems. We give a method based on a suitable choice of multiple parameters. Our scheme allows one to compute solutions in a wide range of time. Instead of using a standard time-marching method, which is not easily parallelizable, we take the Laplace transform in time of the parabolic problems. The resulting elliptic problems can be solved in parallel. Solutions are then computed by a discrete inverse Laplace transformation. The parallelization of the algorithm is natural in the sense that it requires no data communication among processors while solving the time-independent elliptic problems. Numerical results are also presented.