265 citations · 601 across the 26 of their papers we have counts for
29 papers
Planar Curve Registration using Bayesian Inversion
Andreas Bock, Colin J. Cotter, Robert C. Kirby
We study parameterisation-independent closed planar curve matching as a Bayesian inverse problem. The motion of the curve is modelled via a curve on the diffeomorphism group acting…
On the convergence of monolithic multigrid for implicit Runge-Kutta time stepping of finite element problems
Robert C. Kirby
Finite element discretization of time dependent problems also require effective time-stepping schemes. While implicit Runge-Kutta methods provide favorable accuracy and stability p…
Exact domain truncation for the Morse-Ingard equations
Robert C. Kirby, Xiaoyu Wei, Andreas Kloeckner
Morse and Ingard give a coupled system of time-harmonic equations for the temperature and pressure of an excited gas. These equations form a critical aspect of modeling trace gas s…
Integral Equation Methods for the Morse-Ingard Equations
Xiaoyu Wei, Andreas Klöckner, Robert C. Kirby
We present two (a decoupled and a coupled) integral-equation-based methods for the Morse-Ingard equations subject to Neumann boundary conditions on the exterior domain. Both method…
Weighted-norm preconditioners for a multi-layer tide model
Colin J. Cotter, Robert C. Kirby, Hunter Morris
We derive a linearized rotating shallow water system modeling tides, which can be discretized by mixed finite elements. Unlike previous models, this model allows for multiple layer…
Transformations for Piola-mapped elements
Francis Aznaran, Robert Kirby, Patrick Farrell
The Arnold-Winther element successfully discretizes the Hellinger-Reissner variational formulation of linear elasticity; its development was one of the key early breakthroughs of t…
Full waveform inversion using triangular waveform adapted meshes
Keith J. Roberts, Alexandre Olender, Lucas Franceschini +3
In this article, continuous Galerkin finite elements are applied to perform full waveform inversion (FWI) for seismic velocity model building. A time-domain FWI approach is detaile…
Bringing Trimmed Serendipity Methods to Computational Practice in Firedrake
Justin Crum, Cyrus Cheng, David A. Ham +4
We present an implementation of the trimmed serendipity finite element family, using the open source finite element package Firedrake. The new elements can be used seamlessly withi…
Additive Schwarz methods for serendipity elements
Jorge Marchena-Menendez, Robert C. Kirby
While solving Partial Differential Equations (PDEs) with finite element methods (FEM), serendipity elements allow us to obtain the same order of accuracy as rectangular tensor-prod…
Bounds-constrained polynomial approximation using the Bernstein basis
Larry Allen, Robert C. Kirby
A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforc…
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…
Optimal-order preconditioners for the Morse-Ingard equations
Peter Coogan, Robert C. Kirby
The Morse-Ingard equations of thermoacoustics are a system of coupled time-harmonic equations for the temperature and pressure of an excited gas. They form a critical aspect of mod…
Structured inversion of the Bernstein mass matrix
Larray 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…
Code generation for generally mapped finite elements
Robert C. Kirby, Lawrence Mitchell
Many classical finite elements such as the Argyris and Bell elements have long been absent from high-level PDE software. Building on recent theoretical work, we describe how to imp…
Exposing and exploiting structure: optimal code generation for high-order finite element methods
Miklós Homolya, Robert C. Kirby, David A. Ham
Code generation based software platforms, such as Firedrake, have become popular tools for developing complicated finite element discretisations of partial differential equations.…
A general approach to transforming finite elements
Robert C. Kirby
The use of a reference element on which a finite element basis is constructed once and mapped to each cell in a mesh greatly expedites the structure and efficiency of finite elemen…
Mixed finite elements for global tide models with nonlinear damping
Colin J. Cotter, P. Jameson Graber, Robert C. Kirby
We study mixed finite element methods for the rotating shallow water equations with linearized momentum terms but nonlinear drag. By means of an equivalent second-order formulation…
Solver composition across the PDE/linear algebra barrier
Robert C. Kirby, Lawrence Mitchell
The efficient solution of discretisations of coupled systems of partial differential equations (PDEs) is at the core of much of numerical simulation. Significant effort has been ex…
Efficient discontinuous Galerkin finite element methods via Bernstein polynomials
Robert C. Kirby
We consider the discontinuous Galerkin method for hyperbolic conservation laws, with some particular attention to the linear acoustic equation, using Bernstein polynomials as local…
Mixed finite elements for global tide models
Colin J. Cotter, Robert C. Kirby
We study mixed finite element methods for the linearized rotating shallow water equations with linear drag and forcing terms. By means of a strong energy estimate for an equivalent…
Delocalization for the 3-D discrete random Schroedinger operator at weak disorder
Westin King, Robert C. Kirby, Constanze Liaw
We apply a recently developed approach (Liaw 2013) to study the existence of extended states for the three dimensional discrete random Schroedinger operator at small disorder. The…