A Multigrid Preconditioner for Jacobian-free Newton–Krylov Methods

Multigrid Preconditioning Methods for an Implicit Jacobian-Free Newton-Krylov Two-Fluid Kinetic Plasma Solver

Plasma is a state of matter in which a collection of atoms have dissociated into their constituent ions and electrons. The availability of this free charge allows the plasma to interact with electromagnetic fields. The fields dictate the motion of the particles and, simultaneously, the motion of the particles alter the fields. This strongly coupled, self-consistent interaction supports a large ...

A Multigrid Preconditioner for the Semiconductor Equations

A multigrid preconditioned conjugate gradient algorithm is introduced into a semiconductor device modeling code DANCIR This code simulates a wide variety of semiconductor devices by numerically solving the drift di usion equations The most time consuming aspect of the simulation is the solution of three linear systems within each iteration of the Gummel method The original version of DANCIR use...

A Frozen Jacobian Multiscale Mortar Preconditioner for Nonlinear Interface Operators

We present an efficient approach for preconditioning systems arising in multiphase flow in a parallel domain decomposition framework known as the mortar mixed finite element method. Subdomains are coupled together with appropriate interface conditions using mortar finite elements. These conditions are enforced using an inexact Newton–Krylov method, which traditionally required the solution of n...

A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems

A Block-Diagonal Algebraic Multigrid Preconditioner for the Brinkman Problem

The Brinkman model is a unified law governing the flow of a viscous fluid in cavity (Stokes equations) and in porous media (Darcy equations). In this work, we explore a novel mixed formulation of the Brinkman problem by introducing the flow’s vorticity as an additional unknown. This formulation allows for a uniformly stable and conforming discretization by standard finite element (Nédélec, Ravi...