Abstract
This study concerns the solution of a class of nonlinear second order partial differential equations on the Connection Machine CM-2 massively parallel computer. To solve the nonlinear problem, an “outer” successive approximation technique is first applied in order to iteratively linearize the problem. This results in a sequence of systems of linear equations to be solved for successive nonlinear iterates. A preconditioned conjugate gradient (CG) method is used to solve each “inner” linear system. Either Jacobi preconditioning or a fast direct solver is employed as preconditioner for the conjugate gradient method. The implementation of these methods on the Connection Machine is discussed, and the results of numerical experiments with nested iteration are presented.
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