NEWTON-KRYLOV-SCHWARZ METHODS - INTERFACING SPARSE LINEAR SOLVERS WITH NONLINEAR APPLICATIONS

Parallel implicit solution methods are increasingly important in large -scale applications, since reliable lour-residual solutions to individ ual steady-state analyses are often needed repeatedly in multidiscipli nary analysis and optimization. We review a class of linear implicit m ethods called Krylov-Schwarz and a class of nonlinear implicit methods called Newton-Krylov. Newton-Krylov methods are suited for problems i n which it is unreasonable to compute or store a true Jacobian, given a strong enough preconditioner for the inner linear system that needs to be solved for each Newton correction. Schwarz-type domain decomposi tion preconditioning provides good data locality for parallel implemen tations over a range of granularities. Their composition forms a class of methods called Newton-Krylov-Schwarz with strong potential for par allel implicit solution, as illustrated on an aerodynamics application .