50 citations · 117 across the 9 of their papers we have counts for
10 papers
Dimensions of exactly divergence-free finite element spaces in 3D
L. Ridgway Scott, Tabea Tscherpel
We examine the dimensions of various inf-sup stable mixed finite element spaces on tetrahedral meshes in 3D with exact divergence constraints. More precisely, we compare the standa…
Two conjectures on the Stokes complex in three dimensions on Freudenthal meshes
Patrick E. Farrell, Lawrence Mitchell, L. Ridgway Scott
In recent years a great deal of attention has been paid to discretizations of the incompressible Stokes equations that exactly preserve the incompressibility constraint. These are…
Extrapolating the Arnoldi Algorithm To Improve Eigenvector Convergence
Sara Pollock, L. Ridgway Scott
We consider extrapolation of the Arnoldi algorithm to accelerate computation of the dominant eigenvalue/eigenvector pair. The basic algorithm uses sequences of Krylov vectors to fo…
Robust multigrid methods for nearly incompressible elasticity using macro elements
Patrick E. Farrell, Lawrence Mitchell, L. Ridgway Scott +1
We present a mesh-independent and parameter-robust multigrid solver for the Scott-Vogelius discretisation of the nearly incompressible linear elasticity equations on meshes with a…
Point Movement in a DSL for Higher-Order FEM Visualization
Teodoro Collin, Charisee Chiw, L. Ridgway Scott +2
Scientific visualization tools tend to be flexible in some ways (e.g., for exploring isovalues) while restricted in other ways, such as working only on regular grids, or only on un…
An Adaptive Savitsky-Golay Filter for Smoothing Finite Element Computation
Teodoro Collin, Gordon Kindlmann, L. Ridgway Scott
The smoothing technique of Savitzky and Golay is extended to data defined on multidimensional meshes. A smoothness-increasing accuracy-conserving (SIAC) filter is defined that is s…
A Nonlocal Poisson-Fermi Model for Ionic Solvent
Dexuan Xie, Jinn-Liang Liu, Bob Eisenberg +1
We propose a nonlocal Poisson-Fermi model for ionic solvent that includes ion size effects and polarization correlations among water molecules in the calculation of electrostatic p…
Topological Optimization of the Evaluation of Finite Element Matrices
Robert C. Kirby, Anders Logg, L. Ridgway Scott +1
We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over…
Optimizing the Evaluation of Finite Element Matrices
Robert C. Kirby, Matthew Knepley, Anders Logg +1
Assembling stiffness matrices represents a significant cost in many finite element computations. We address the question of optimizing the evaluation of these matrices. By finding…
Unstructured Geometric Multigrid in Two and Three Dimensions on Complex and Graded Meshes
Peter R. Brune, Matthew G. Knepley, L. Ridgway Scott
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially wh…