48 citations · 75 across the 8 of their papers we have counts for
11 papers · 1 filter
Mixed-Precision Computing for Scientific Discovery: Formats, Co-Design, and Responsible Approximation
Emmanuel Agullo, Hartwig Anzt, Daniel Bauer +37
Reduced and mixed precision have moved from a niche optimization to a central design axis in scientific computing and engineering, driven by energy constraints, heterogeneous accel…
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…
Multigrid with Linear Storage Complexity
Daniel Bauer, Nils Kohl, Stephen F. McCormick +1
As the discretization error for the solution of a partial differential equation (PDE) decreases, the precision required to store the corresponding coefficients naturally increases.…
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…
Constructing Nitsche's method for variational problems
Joseph Benzaken, John A. Evans, Rasmus Tamstorf
Nitsche's method is a well-established approach for weak enforcement of boundary conditions for partial differential equations (PDEs). It has many desirable properties, including t…
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…
Asynchronous Variational Contact Mechanics
Etienne Vouga, David Harmon, Rasmus Tamstorf +1
An asynchronous, variational method for simulating elastica in complex contact and impact scenarios is developed. Asynchronous Variational Integrators (AVIs) are extended to handle…
Asynchronous Variational Integration of Interaction Potentials for Contact Mechanics
Etienne Vouga, David Harmon, Rasmus Tamstorf +1
Asynchronous Variational Integrators (AVIs) have demonstrated long-time good energy behavior. It was previously conjectured that this remarkable property is due to their geometric…