Successive underrelaxation (SUR) and generalised conjugate gradient (GCG) methods for hyperbolic difference equations on a parallel computer

When we consider the numerical solution of the 2-dimensional linear hyperbolic problem by implicit difference equations we need to solve a set of linear systems Ax = b with many rightband sides b, where A is large, sparse and nonsymmetric. The SUR (Successive Underrelaxation) and GCG (Generalised Conjugate Gradient) methods are used for solving the linear systems. We compare the two methods on sequential and parallel computations. Numerical results indicate that the SUR method is nearly twice as fast as the GCG method and the SUR method has an almost linear speedup.