Hybrid simulation of multidimensional p.d.e.'s via solution of many one dimensional problems I. Theoretical basis and hybrid implementation

A method for the hybrid simulation of multi-dimensional p.d.e.'s over rectangles using the Laplace-modified Galerkin scheme is described. By using an appropriate perturbation the system can be simulated via simulation of a collection of one-dimensional problems. Hybrid implementation of the method is described in detail. The implementation is modular in nature and an increase in the dimension of the problem simply increases the number of modules required for simulation.