Fast Newton-Krylov method for unstructured grids

Three algorithms are presented and compared for the solution of the steady Euler equations on unstructured triangular grids. All are variations on Newton's method-one quasi- and two full-Newton schemes-and employ the BILU (n)-preconditioned generalized minimum residual method (GMRES) algorithm to solve the Jacobian matrix problem that arises at each iteration. The quasi-Newton scheme uses a first-order approximation to the Jacobian matrix with the standard GMRES implementation, in which matrix-vector products are formed in the usual explicit manner. The full-Newton schemes are distinguished by the implementation of GMRES: One employs the standard GMRES algorithm, and the other is matrix free using Frechet derivatives. The matrix-free, full-Newton algorithm is shown to be the fastest of the three algorithms. Optimal preconditioning, reordering, and storage strategies for the matrix-free, full-Newton algorithm are presented. Register and cache performance issues are briefly discussed

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