265 citations · 601 across the 26 of their papers we have counts for
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Finite elements for Helmholtz equations with a nonlocal boundary condition
Robert C. Kirby, Andreas Klöckner, Ben Sepanski
Numerical resolution of exterior Helmholtz problems requires some approach to domain truncation. As an alternative to approximate nonreflecting boundary conditions and invocation o…
Irksome: Automating Runge--Kutta time-stepping for finite element methods
Patrick E. Farrell, Robert C. Kirby, Jorge Marchena-Menendez
While implicit Runge--Kutta methods possess high order accuracy and important stability properties, implementation difficulties and the high expense of solving the coupled algebrai…
Structured inversion of the Bernstein-Vandermonde Matrix
Larry Allen, Robert C. Kirby
Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. Many fundamental probl…
Preconditioning mixed finite elements for tide models
Tate Kernell, Robert C. Kirby
We describe a fully discrete mixed finite element method for the linearized rotating shallow water model, possibly with damping. While Crank-Nicolson time-stepping conserves energy…