A parallel least-squares spectral element solver for incompressible flow problems on unstructured grids

The parallelisation of the least-squares spectral element formulation of the Stokes problem is discussed for incompressible flow problems on unstructured grids. The method leads to a large symmetric positive definite algebraic system, that is solved iteratively by the conjugate gradient method. To improve the convergence rate, both Jacobi and Additive Schwarz preconditioners are applied. Numerical simulations have been performed to validate the scalability of the different parts of the proposed method. The experiments entailed simulating several large-scale incompressible flows on a Cray T3E and on an SGI Origin 3800.