164 citations · 223 across the 10 of their papers we have counts for
11 papers
On Compatible Transfer Operators in Nonsymmetric Algebraic Multigrid
Ben S. Southworth, Thomas A. Manteuffel
The standard goal for an effective algebraic multigrid (AMG) algorithm is to develop relaxation and coarse-grid correction schemes that attenuate complementary error modes. In the…
Mixed and least-squares finite element methods with application to linear hyperbolic problems
Delyan Z. Kalchev, Thomas A. Manteuffel, Steffen Münzenmaier
In this paper, a few dual least-squares finite element methods and their application to scalar linear hyperbolic problems are studied. The purpose is to obtain -norm approxima…
A Least-Squares Finite Element Method Based on the Helmholtz Decomposition for Hyperbolic Balance Laws
Delyan Z. Kalchev, Thomas A. Manteuffel
In this paper, a least-squares finite element method for scalar nonlinear hyperbolic balance laws is proposed and studied. The approach is based on a formulation that utilizes an a…
Parallel Approximate Ideal Restriction Multigrid for Solving the S Transport Equations
Joshua Hanophy, Ben S. Southworth, Ruipeng Li +2
The computational kernel in solving the transport equations is the parallel sweep, which corresponds to directly inverting a block lower triangular linear system that arises…
Advances in Implementation, Theoretical Motivation, and Numerical Results for the Nested Iteration with Range Decomposition Algorithm
Wayne Mitchell, Tom Manteuffel
This paper studies a low-communication algorithm for solving elliptic partial differential equations (PDE's) on high-performance machines, the nested iteration with range decomposi…
Convergence in Norm of Nonsymmetric Algebraic Multigrid
Ben S. Southworth, Thomas A. Manteuffel
Algebraic multigrid (AMG) is one of the fastest numerical methods for solving large sparse linear systems. For SPD matrices, convergence of AMG is well motivated in the -norm, a…
Nonsymmetric Reduction-based Algebraic Multigrid
Thomas A. Manteuffel, Steffen Munzenmaier, John Ruge +1
Algebraic multigrid (AMG) is often an effective solver for symmetric positive definite (SPD) linear systems resulting from the discretization of general elliptic PDEs, or the spati…
A Root-Node Based Algebraic Multigrid Method
Thomas A. Manteuffel, Luke N. Olson, Jacob B. Schroder +1
This paper provides a unified and detailed presentation of root-node style algebraic multigrid (AMG). Algebraic multigrid is a popular and effective iterative method for solving la…
Constrained Optimization for Liquid Crystal Equilibria: Extended Results
J. H. Adler, D. B. Emerson, S. P. MacLachlan +1
This paper investigates energy-minimization finite-element approaches for the computation of nematic liquid crystal equilibrium configurations. We compare the performance of these…
First-Order System Least Squares and the Energetic Variational Approach for Two-Phase Flow
J. H. Adler, J. Brannick, C. Liu +2
This paper develops a first-order system least-squares (FOSLS) formulation for equations of two-phase flow. The main goal is to show that this discretization, along with numerical…
Adaptive multigrid algorithm for the lattice Wilson-Dirac operator
R. Babich, J. Brannick, R. C. Brower +5
We present an adaptive multigrid solver for application to the non-Hermitian Wilson-Dirac system of QCD. The key components leading to the success of our proposed algorithm are the…