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Showing 1 to 12 of 12 for “"Newton-Krylov"”.
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Hessian Matrix-Free Lagrange-Newton-Krylov-Schur-Schwarz Methods for Elliptic Inverse Problems
… we develop a parallel preconditioned Newton-Krylov method employed in a Hessian-free manner. The preconditioners have an inner-outer structure, taking the form of a Schur complement (block factorization) at the outer level and Schwarz projections at the inner level. However, building …
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A preconditioned Newton-Krylov method for computing steady-state pulse solutions of mode-locked lasers
… using a specially preconditioned matrix-implicit Newton-Krylov solver. Solutions are obtained at least an order of magnitude faster than with dynamic simulation, the standard method. Our method is demonstrated experimentally on a one-dimensional temporal model of an eight femtosecond mode-locked …
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Innovative Methods for Solving Multicomponent Biogeochemical Groundwater Transport on Supercomputers
To evaluate the performance of the Jacobian-Free Newton-Krylov method, PARTRAN was used to simulate enhanced in situ bioremediation of subsurface NAPL (non-aqueous phase liquid) contamination on the ASCI Q supercomputer at Los Alamos National Laboratory, on which a study of parallel …
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Robust computational methods to simulate slow-fast dynamical systems governed by predator-prey models
… convergence, such as the Jacobian-Free Newton-Krylov (JFNK) and the Anderson’s Acceleration (AA) fixed point methods.
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A linear multigrid preconditioner for the solution of the Navier-Stokes equations using a discontinuous Galerkin discretization
A Newton-Krylov method is developed for the solution of the steady compressible Navier-Stokes equations using a Discontinuous Galerkin (DG) discretization on unstructured meshes. An element Line-Jacobi preconditioner is presented which solves a block tridiagonal system along lines of maximum …
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Iterative solvers in implicit time integration for compressible flows
… equations in each time step which is solved by a Newton-Krylov method. Therein one applies a linearization technique combined with a preconditioned Krylov subspace algorithm for solving the resulting linear problems. Our inexact Newton method uses a first order approximation of the Jacobian. The …
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Discontinuous Galerkin solutions of the Boltzmann equation: spectral collocation and moment methods
… to mitigate stiffness concerns. A Jacobian-Free Newton—Krylov method is presented, accelerated with a sweeping preconditioner. The method is tested on 1D and 2D problems in order to validate its convergence behavior and investigate its efficiency. The second method uses DG for moment equations, …
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Development of a Multifluid Magnetohydrodynamic Model for Anisotropic, Partially Ionized Plasmas
… one-dimension and a parallel scheme utilizing a Newton-Krylov-Schwarz (NKS) implicit algorithm for the two-dimensional solution procedure. The numerical fluxes in the Godunov-type scheme are solved using HLLE and Godunov numerical flux functions. The two-dimensional solution procedure includes …
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Nonlinear deformations of a thick-walled hyperelastic tube under external pressure
… The weighted residual-Galerkin method and the Newton-Krylov nonlinear solver are adopted for solving the governing equations. Since the nonlinear problem is highly sensitive to small changes in the numerical scheme, convergence was obtained only when the analytical Jacobian matrix was used. A …
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A fast and efficient solver for viscous-plastic sea ice dynamics
… in solving these equations with a Jacobian-Free Newton- Krylov (JFNK) solver. We present an improved JFNK solver, where a fully second order discretization is achieved via the Crank Nicolson scheme and consistency is improved via a novel approach to the rheology term. More importantly, we present …
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Unstructured h-adaptive finite volume schemes for compressible viscous fluid flow
… Time integration is based on a fully implicit Newton-Krylov type approach, which is suitable for stationary and non-stationary flows. A local preconditioning technique is employed in conjunction with the AUSMDV(P) upwind method to operate effectively within the quasi-incompressible low Mach …
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Stochastic methods for uncertainty quantification in radiation transport
… such as block Gauss-Seidel or block Jacobi, or a Krylov iterative method, which can be preconditioned using these splittings. When multiplication is present, the SFEM system is non-linear and a Newton-Krylov method is employed to solve it. The SCM utilizes a suitable quadrature rule to compute the …