5 papers
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…
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…
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…
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…