PYTHIA: An Expert System to Support the Numerical Simulation of PDE Based Applications on Parallel Machines

It is clear that accuracy and execution time are often the main performance objectives of a user of numerical simulation models based on partial differential equations (PDEs). In a PDE computation, accuracy is controlled through the refinement of the grid and the discretization scheme used, while execution time depends on the speed of the targeted machiae and the efficiency of the PDE solver. For s given machiae, the computation of s solution within a certain accuracy ("epsilon") and time frame ("W") requires the selection of appropriate grid, discretization and solution scheme (method) plus an appropriate machine. If the machine parallel, then the selection of its configuration (number of processors) and the partitioning of the computation into load balanced, optimally parallel subtasks is also required. Unfortunately, the above parameters that affect the performance of a computation depend on various mathematical properties and characteristics of the specified PDE model and its unknown solution. Hence, the acquisition of knowledge about the mathematical behavior of the given PDE model and the appropriate selection of these parameters to achieve the computational objectives of the user constitute a "hard" problem. We believe that future numerical simulation systems should be capable of making these decisions for the average user while allowing knowledgeable users to be involved with the decision process.