Implicit solvers for unstructured meshes
Journal of Computational Physics
Multigrid strategies for viscous flow solvers on anisotropic unstructured meshes
Journal of Computational Physics
Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Journal of Computational Physics
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
High-order discontinuous Galerkin methods using an hp-multigrid approach
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Preconditioning methods for discontinuous Galerkin solutions of the Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
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The relative performance of a nonlinear full approximation storage multigrid algorithm and an equivalent linear multigrid algorithm for solving two different nonlinear problems is investigated. The first case consists of a transient radiation diffusion problem for which an exact linearization is available, while the second problem involves the solution of the steady-state Navier-Stokes equations, where a first-order discrete Jacobian is employed as an approximation to the Jacobian of a second-order-accurate discretization. When an exact linearization is employed, the linear and nonlinear multigrid methods asymptotically converge at identical rates and the linear method is found to be more efficient due to its lower cost per cycle. When an approximate linearization is employed, as in the Navier-Stokes cases, the relative efficiency of the linear approach versus the nonlinear approach depends both on the degree to which the linear system approximates the full Jacobian as well as on the relative cost of linear versus nonlinear multigrid cycles. For cases where convergence is limited by a poor Jacobian approximation, substantial speedup can be obtained using either multigrid method as a preconditioner to a Newton-Krylov method.