Algebraic multigrid theory: The symmetric case
Applied Mathematics and Computation - Second Copper Mountain conference on Multigrid methods Copper Mountain, Colorado
First-order system least squares for second-order partial differential equations: part I
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
First-Order System Least Squares for Second-Order Partial Differential Equations: Part II
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
A multigrid tutorial (2nd ed.)
A multigrid tutorial (2nd ed.)
An implicit, nonlinear reduced resistive MHD solver
Journal of Computational Physics
Analysis of Velocity-Flux Least-Squares Principles for the Navier--Stokes Equations: Part II
SIAM Journal on Numerical Analysis
On Mesh-Independent Convergence of an Inexact Newton--Multigrid Algorithm
SIAM Journal on Scientific Computing
Multilevel First-Order System Least Squares for Nonlinear Elliptic Partial Differential Equations
SIAM Journal on Numerical Analysis
Multilevel first-order system least squares for quasilinear elliptic partial differential equations
Multilevel first-order system least squares for quasilinear elliptic partial differential equations
Implicit adaptive mesh refinement for 2D reduced resistive magnetohydrodynamics
Journal of Computational Physics
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Magnetohydrodynamics (MHD) is a fluid theory that describes plasma physics by treating the plasma as a fluid of charged particles. Hence, the equations that describe the plasma form a nonlinear system that couples Navier-Stokes equations with Maxwell's equations. This paper shows that the first-order system least squares (FOSLS) finite element method is a viable discretization for these large MHD systems. To solve this system, a nested-iteration-Newton-FOSLS-AMG approach is taken. Most of the work is done on the coarse grid, including most of the linearizations. We show that at most one Newton step and a few V-cycles are all that are needed on the finest grid. Here, we describe how the FOSLS method can be applied to incompressible resistive MHD and how it can be used to solve these MHD problems efficiently. A 3D steady state and a reduced 2D time-dependent test problem are studied. The latter equations can simulate a “large aspect-ratio” tokamak. The goal is to resolve as much physics from the test problems with the least amount of computational work. We show that this is achieved in a few dozen work units or fine grid residual evaluations.