Postdoctoral Research Associateship in Computer Science: Parallel Conjugate Gradient and Multilevel Algorithms for PDEs

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A new symmetrization method for the numerical solution of partial differential equations on emerging parallel computers will be studied. The algorithmic development of the method in the context of massive parallelization will be emphasized. The method of symmetrization is attractive for an elliptic partial differential operator, A=S+BT in that it transforms the problem in A to one in an operator that is self-adjoint and that closely resembles S, the self-adjoint part. Thus, by invoking symmetry even for nonself-adjoint problems, it allows the use of efficient and robust versions of multilevel and conjugate gradient algorithms for the solution of the arising linear systems of equations. The use of multilevel and conjugate gradient algorithms in the implementation of the method on a parallel computer will provide the opportunity to study parallelization in a context where a multilevel algorithm itself is used as in inner solver for an algorithm composed of inner and outer iterations. The algorithms will be tested in a massively parallel environment offered by the Connection Machine.