Adaptive Solution of Partial Differential Equations on Parallel Computers Using an Equational Language

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This project will develop software tools for the automatic adaptive solution of systems of partial differential equations on parallel and vector computers. The adaptive techniques will be capable of solving a wide variety of partial differential systems using finite element methods that contain combinations of mesh moving, local refinement, and error estimation procedures. The adaptive software will be developed using the equational language system MODEL. This sophisticated system contains facilities for the convenient description of complex mathematical systems and for the automatic detection of parallelism and the scheduling of parallel processors. The research will necessitate (i) improving the mesh moving, local refinement, and error estimation techniques; (ii) dynamic scheduling algorithms for assigning processors as computational cells are added to or deleted from a mesh; (iii) balancing the computational load on the processors of the parallel system, and (iv) developing a multigrid solution strategy for solving linear algebraic systems. The resulting software will enable scientists and engineers to solve a wide variety of complex problems on several computing environments.