SIAM journal on scientific and statistical computing vol:13 issue:6 pages:1330-1346
The numerical solution of a parabolic partial differential equation is usually calculated by a timestepping method. This precludes the efficient use of vectorization and parallelism if the problem to be solved on each time level is not very large. In this paper an algorithm that overcomes the limitations of the standard marching schemes by solving the problem at all the time levels simultaneously is discussed. The method is applicable to linear and nonlinear problems on arbitrary domains. It can be used to solve initial-boundary value problems as well as time-periodic equations. We have implemented the method on an Intel iPSC/2-VX hypercube. The numerical properties of the method are illustrated by two numerical examples and its performance is compared to that of the best standard solvers.