Hybrid Newton - Krylov / Domain Decomposition

Newton-krylov Domain Decomposition Solvers for Adaptive Hp Approximations of the Steady Incompressible Navier-stokes Equations with Discontinuous Pressure Fields

Newton-krylov-schwarz: an Implicit Solver for Cfd

Newton Krylov methods and Krylov Schwarz domain decomposition methods have begun to become established in computational uid dynamics CFD over the past decade The former employ a Krylov method inside of Newton s method in a Jacobian free manner through directional di erencing The latter employ an overlapping Schwarz domain decomposition to derive a preconditioner for the Krylov accelerator that ...

Nonlinear Overlapping Domain Decomposition Methods

We discuss some overlapping domain decomposition algorithms for solving sparse nonlinear system of equations arising from the discretization of partial differential equations. All algorithms are derived using the three basic algorithms: Newton for local or global nonlinear systems, Krylov for the linear Jacobian system inside Newton, and Schwarz for linear and/or nonlinear preconditioning. The ...

A 738

New nonlinear FETI-DP (dual-primal finite element tearing and interconnecting) and BDDC (balancing domain decomposition by constraints) domain decomposition methods are introduced. In all these methods, in each iteration, local nonlinear problems are solved on the subdomains. The new approaches can significantly reduce communication and show a significantly improved performance, especially for ...

Aerodynamic Applications of Newton-krylov-schwarz Solvers

Parallel implicit solution methods are increasingly important in aerodynamics , since reliable low-residual solutions at elevated CFL number are prerequisite to such large-scale applications of aerodynamic analysis codes as aeroelasticity and optimization. In this chapter, a class of nonlinear implicit methods and a class of linear implicit methods are deened and illustrated. Their composition ...