164 citations · 215 across the 7 of their papers we have counts for
9 papers
Multigrid Primer: Basic Principles
Stephen F. McCormick, Rasmus Tamstorf
The goal of this primer is to provide a relatively short exposition of the basics of multigrid methods, simplified by focusing on fundamental concepts in a variational setting. Thi…
Rounding-Error Analysis of Multigrid V-Cycles
Stephen F. McCormick, Rasmus Tamstorf
This paper provides a rounding-error analysis for two-grid methods that use one relaxation step both before and after coarsening. The analysis is based on floating point arithmetic…
Multigrid Methods using Block Floating Point Arithmetic
Nils Kohl, Stephen F. McCormick, Rasmus Tamstorf
Block Floating Point (BFP) arithmetic is currently seeing a resurgence in interest because it requires less power, less chip area, and is less complicated to implement in hardware…
Discretization-error-accurate mixed-precision multigrid solvers
Rasmus Tamstorf, Joseph Benzaken, Stephen F. McCormick
This paper builds on the algebraic theory in the companion paper [Algebraic Error Analysis for Mixed-Precision Multigrid Solvers] to obtain discretization-error-accurate solutions…
Algebraic error analysis for mixed-precision multigrid solvers
Stephen F. McCormick, Joseph Benzaken, Rasmus Tamstorf
This paper establishes the first theoretical framework for analyzing the rounding-error effects on multigrid methods using mixed-precision iterative-refinement solvers. While motiv…
Weak Boundary Condition Enforcement for Linear Kirchhoff-Love Shells: Formulation, Error Analysis, and Verification
Joseph Benzaken, John A. Evans, Stephen McCormick +1
Stable and accurate modeling of thin shells requires proper enforcement of all types of boundary conditions. Unfortunately, for Kirchhoff-Love shells, strong enforcement of Dirichl…