Numerical weather prediction using the Canadian GEM model involves the solution of separable elliptic boundary value (EBV) problems in spherical geometry. This type of equation arises either as Helmholtz or as horizontal diffusion problems.

The direct solution of the EBV problem involves a transform, in the variable-mesh case a full-matrix multiplication, where the cost per grid point rises linearly with the number of grid points along the transform direction. In order to improve the performance of the EBV problem, the matrix product in the direct solution is accelerated by using either the Strassen method or by exploiting the symmetry of the mesh. An iterative solution of the EBV has also been implemented and compared to the direct solution.

The purpose of this presentation is to report on the details of these implementations and to show the improved performance of the EBV problem solution either by accelerating the full-matrix in the direct solver or by using a preconditioned Conjugate Gradient iterative solver. The direct and iterative solvers have been tested on the NEC SX-4 and SX-5.