相关论文: A Multigrid Preconditioner for Jacobian-free Newto…
A Jacobian free Newton Krylov (JFNK) method with a globalization scheme is introduced to solve large and complex nonlinear systems of equations that arise in groundwater flow models of multi-layer aquifer systems. We explore the advantages…
This work extends the application of Jacobian-free Newton-Krylov (JFNK) methods to higher-order cell-centred finite-volume formulations for solid mechanics. While conventional schemes are typically limited to second-order accuracy, we…
We present a comparison of different multigrid approaches for the solution of systems arising from high-order continuous finite element discretizations of elliptic partial differential equations on complex geometries. We consider the…
Jacobian-Free Newton-Krylov (JFNK) methods avoid forming the full Jacobian, but still require Jacobian-vector products, i.e., Gateaux derivatives of the nonlinear residual along Krylov directions. In standard Finite Differences (FD)…
This study investigates the efficacy of Jacobian-free Newton-Krylov methods in finite-volume solid mechanics. Traditional Newton-based approaches require explicit Jacobian matrix formation and storage, which can be computationally expensive…
A high-order Newton multigrid method is proposed for steady-state shallow water flows in open channels with regular and irregular geometries. The method integrates a finite volume discretization with third-order weighted essentially…
The focus of this work is on the construction and analysis of optimal-order multigrid preconditioners to be used in the Newton-Krylov method for a distributed optimal control problem constrained by the stationary Navier-Stokes equations. As…
We present a first step towards a multigrid method for solving the min-cost flow problem. Specifically, we present a strategy that takes advantage of existing black-box fast iterative linear solvers, i.e. algebraic multigrid methods. We…
In this paper we study a monolithic Newton-Krylov solver with exact Jacobian for the solution of incompressible FSI problems. A main focus of this work is on the use of geometric multigrid preconditioners with modified Richardson smoothers…
This work presents a set of preconditioning strategies able to significantly accelerate the performance of fully implicit energy-conserving Particle-in-Cell methods to a level that becomes competitive with semi-implicit methods. We compare…
We propose a convenient matrix-free neural architecture for the multigrid method. The architecture is simple enough to be implemented in less than fifty lines of code, yet it encompasses a large number of distinct multigrid solvers. We…
Challenging aspects of large-scale turbulent edge simulations in plasma physics include robust nonlinear solvers and efficient preconditioners. This paper presents recent advances in the scalable solution of nonlinear partial differential…
In this work, we propose a robust and easily implemented algebraic multigrid method as a stand-alone solver or a preconditioner in Krylov subspace methods for solving either symmetric and positive definite or saddle point linear systems of…
We consider a family of steady free-surface flow problems in two dimensions, concentrating on the effect of nonlinearity on the train of gravity waves that appear downstream of a disturbance. By exploiting standard complex variable…
Numerical solution of discrete PDEs corresponding to saddle point problems is highly relevant to physical systems such as Stokes flow. However, scaling up numerical solvers for such systems is often met with challenges in efficiency and…
Within the framework of $ p $-adaptive flux reconstruction, we aim to construct efficient polynomial multigrid ($p$MG) preconditioners for implicit time integration of the Navier--Stokes equations using Jacobian-free Newton--Krylov (JFNK)…
A preconditioning framework for the coupled problem of frictional contact mechanics and fluid flow in the fracture network is presented. The porous medium is discretized using low-order continuous finite elements, with cell-centered…
We propose an alternative implementation of preconditioning techniques for the solution of non-linear problems. Within the framework of Newton-Krylov methods, preconditioning techniques are needed to improve the performance of the solvers.…
Phase-field fracture models lead to variational problems that can be written as a coupled variational equality and inequality system. Numerically, such problems can be treated with Galerkin finite elements and primal-dual active set…
The calculation of the emerging radiation from a model atmosphere requires knowledge of the emissivity and absorption coefficients, which are proportional to the atomic level population densities of the levels involved in each transition.…