14 citations · 15 across the 11 of their papers we have counts for
14 papers
Automated Galerkin time stepping in Irksome
Boris D. Andrews, Pablo Brubeck, Patrick E. Farrell +2
As the study of temporal and spatial discretization schemes continues to advance, recent work has focused on the use of Galerkin-in-time discretization schemes that enable broader…
Cohomology of Finite Element Stokes Complexes on Alfeld Splits
Pablo D. Brubeck, Yizhou Liang, Charles Parker
We show that the cohomology of the finite element Stokes complex consisting of piecewise polynomials spaces on an Alfeld split mesh from Fu, Guzmán, & Neilan (2020, Math. Comp., 89…
Achieving Material Robustness via Symmetric Stress Finite Element Discretizations
Pablo Brubeck, Charles Parker, Umberto Zerbinati
When discretizing symmetric stress tensors in variational problems arising in continuum mechanics, one has to choose how to enforce the symmetry of the stress tensor: (i) strongly…
Accelerated implicitization: Robust fixed-point iterations arising from an explicit scheme
Nicolas A. Barnafi, Felipe Galarce, Pablo Brubeck
This work proposes a general strategy for solving possibly nonlinear problems arising from implicit time discretizations as a sequence of explicit solutions. The resulting sequence…
Automated Runge-Kutta-Nyström time stepping for finite element methods in Irksome
Robert C. Kirby, Scott P. MacLachlan, Pablo D. Brubeck
Irksome is a library based on the Unified Form Language (UFL) that automates the application of Runge-Kutta time-stepping methods for finite element spatial discretizations of part…
DefElement: an encyclopedia of finite element definitions
Matthew W. Scroggs, Pablo D. Brubeck, Joseph P. Dean +2
DefElement is an online encyclopedia of finite element definitions that was created and is maintained by the authors of this paper. DefElement aims to make information about elemen…
Fast solvers for the high-order FEM simplicial de Rham complex: Extended edition
Pablo D. Brubeck, Patrick E. Farrell, Robert C. Kirby +1
We present new finite elements for solving the Riesz maps of the de Rham complex on triangular and tetrahedral meshes at high order. The finite elements discretize the same spaces…
FIAT: enabling classical and modern macroelements
Pablo D. Brubeck, Robert C. Kirby
Many classical and modern finite element spaces are derived by dividing each computational cell into finer pieces. Such \emph{macroelements} frequently enable the enforcement of ma…
FIAT: improving performance and accuracy for high-order finite elements
Pablo D. Brubeck, Robert C. Kirby, Fabian Laakmann +1
FIAT (the FInite element Automatic Tabulator) provides a powerful Python library for the generation and evaluation of finite element basis functions on a reference element. This re…
Multigrid solvers for the de Rham complex with optimal complexity in polynomial degree
Pablo D. Brubeck, Patrick E. Farrell
The Riesz maps of the de Rham complex frequently arise as subproblems in the construction of fast preconditioners for more complicated problems. In this work we present multi…
Lightning Stokes solver
Pablo D. Brubeck, Lloyd N. Trefethen
Gopal and Trefethen recently introduced "lightning solvers" for the 2D Laplace and Helmholtz equations, based on rational functions with poles exponentially clustered near singular…
A scalable and robust vertex-star relaxation for high-order FEM
Pablo D. Brubeck, Patrick E. Farrell
Pavarino proved that the additive Schwarz method with vertex patches and a low-order coarse space gives a -robust solver for symmetric and coercive problems. However, for very h…
Vandermonde with Arnoldi
Pablo D. Brubeck, Yuji Nakatsukasa, Lloyd N. Trefethen
Vandermonde matrices are exponentially ill-conditioned, rendering the familiar "polyval(polyfit)" algorithm for polynomial interpolation and least-squares fitting ineffective at hi…
Time-symmetry, symplecticity and stability of Euler-Maclaurin and Lanczos-Dyche integration
Charalampos M. Markakis, Michael F. O'Boyle, Derek Glennon +5
Numerical evolution of time-dependent differential equations via explicit Runge-Kutta or Taylor methods typically fails to preserve symmetries of a system. It is known that there e…