Solution of Parabolic Equations by Backward Euler-Mixed Finite Element Methods on a Dynamically Changing Mesh. - Clint Dawson 001; Robert C. Kirby (SIAM J. Numer. Anal., 1999)

High Resolution Schemes for Conservation Laws with Locally Varying Time Steps. - Clint Dawson 001; Robert C. Kirby (SIAM J. Sci. Comput., 2001)

A new look at expression templates for matrix computation. - Robert C. Kirby (Comput. Sci. Eng., 2003)

On the convergence of high resolution methods with multiple time scales for hyperbolic conservation laws. - Robert C. Kirby (Math. Comput., 2003)

Algorithm 839: FIAT, a new paradigm for computing finite element basis functions. - Robert C. Kirby (ACM Trans. Math. Softw., 2004)

Optimizing the Evaluation of Finite Element Matrices. - Robert C. Kirby; Matthew G. Knepley; Anders Logg; L. Ridgway Scott (SIAM J. Sci. Comput., 2005)

Topological Optimization of the Evaluation of Finite Element Matrices. - Robert C. Kirby; Anders Logg; L. Ridgway Scott; Andy R. Terrel (SIAM J. Sci. Comput., 2006)

Optimizing FIAT with level 3 BLAS. - Robert C. Kirby (ACM Trans. Math. Softw., 2006)

A compiler for variational forms. - Robert C. Kirby; Anders Logg (ACM Trans. Math. Softw., 2006)

Geometric Optimization of the Evaluation of Finite Element Matrices. - Robert C. Kirby; L. Ridgway Scott (SIAM J. Sci. Comput., 2007)

Efficient compilation of a class of variational forms. - Robert C. Kirby; Anders Logg (ACM Trans. Math. Softw., 2007)

Benchmarking Domain-Specific Compiler Optimizations for Variational Forms. - Robert C. Kirby; Anders Logg (ACM Trans. Math. Softw., 2008)

Efficient Assembly of $H( mathrmdiv) and H( mathrmcurl)$ Conforming Finite Elements. - Marie E. Rognes; Robert C. Kirby; Anders Logg (SIAM J. Sci. Comput., 2009)

From Functional Analysis to Iterative Methods. - Robert C. Kirby (SIAM Rev., 2010)

Unified Embedded Parallel Finite Element Computations via Software-Based Fr[e-acute]chet Differentiation. - Kevin R. Long; Robert C. Kirby; Bart G. van Bloemen Waanders (SIAM J. Sci. Comput., 2010)

Singularity-free evaluation of collapsed-coordinate orthogonal polynomials. - Robert C. Kirby (ACM Trans. Math. Softw., 2010)

Fast simplicial finite element algorithms using Bernstein polynomials. - Robert C. Kirby (Numerische Mathematik, 2011)

Block preconditioners for finite element discretization of incompressible flow with thermal convection. - Victoria E. Howle; Robert C. Kirby (Numer. Linear Algebra Appl., 2012)

Fast simplicial quadrature-based finite element operators using Bernstein polynomials. - Robert C. Kirby; Thinh Tri Kieu (Numerische Mathematik, 2012)

Solving PDEs with Intrepid. - Pavel B. Bochev; H. Carter Edwards; Robert C. Kirby; Kara Peterson; Denis Ridzal (Sci. Program., 2012)

Playa: High-performance programmable linear algebra. - Victoria E. Howle; Robert C. Kirby; Kevin Long; Brian Brennan; Kimberly Kennedy (Sci. Program., 2012)

Block Preconditioners for Coupled Physics Problems. - Victoria E. Howle; Robert C. Kirby; Geoffrey Dillon (SIAM J. Sci. Comput., 2013)

Low-Complexity Finite Element Algorithms for the de Rham Complex on Simplices. - Robert C. Kirby (SIAM J. Sci. Comput., 2014)

High-Performance Evaluation of Finite Element Variational Forms via Commuting Diagrams and Duality. - Robert C. Kirby (ACM Trans. Math. Softw., 2014)

Finite element approximation and preconditioners for a coupled thermal-acoustic model. - Brian Brennan; Robert C. Kirby (Comput. Math. Appl., 2015)

Symplectic-mixed finite element approximation of linear acoustic wave equations. - Robert C. Kirby; Thinh Tri Kieu (Numerische Mathematik, 2015)

Mixed finite elements for global tide models. - Colin J. Cotter; Robert C. Kirby (Numerische Mathematik, 2016)

Exposing and exploiting structure: optimal code generation for high-order finite element methods. - Miklós Homolya; Robert C. Kirby; David A. Ham (CoRR, 2017)

Fast inversion of the simplicial Bernstein mass matrix. - Robert C. Kirby (Numerische Mathematik, 2017)

Mixed finite elements for global tide models with nonlinear damping. - Colin J. Cotter; P. Jameson Graber; Robert C. Kirby (Numerische Mathematik, 2018)

Solver Composition Across the PDE/Linear Algebra Barrier. - Robert C. Kirby; Lawrence Mitchell (SIAM J. Sci. Comput., 2018)

Code Generation for Generally Mapped Finite Elements. - Robert C. Kirby; Lawrence Mitchell (ACM Trans. Math. Softw., 2019)

Optimal-order preconditioners for the Morse-Ingard equations. - Robert C. Kirby; Peter Coogan (Comput. Math. Appl., 2020)

Structured Inversion of the Bernstein Mass Matrix. - Larry Allen; Robert C. Kirby (SIAM J. Matrix Anal. Appl., 2020)

Preconditioning mixed finite elements for tide models. - Robert C. Kirby; Tate Kernell (Comput. Math. Appl., 2021)

Full waveform inversion using triangular waveform adapted meshes. - Keith J. Roberts; Alexandre Olender; Lucas Franceschini; Robert C. Kirby; Rafael dos Santos Gioria; Bruno S. Carmo (CoRR, 2021)

Transformations for Piola-mapped elements. - Francis Aznaran; Robert C. Kirby; Patrick E. Farrell (CoRR, 2021)

Structured Inversion of the Bernstein-Vandermonde Matrix. - Larry Allen; Robert C. Kirby (SIAM J. Matrix Anal. Appl., 2021)

Finite Elements for Helmholtz Equations with a Nonlocal Boundary Condition. - Robert C. Kirby; Andreas Klöckner; Ben Sepanski (SIAM J. Sci. Comput., 2021)

Irksome: Automating Runge-Kutta Time-stepping for Finite Element Methods. - Patrick E. Farrell; Robert C. Kirby; Jorge Marchena-Menendez (ACM Trans. Math. Softw., 2021)

Weighted-norm preconditioners for a multi-layer tide model. - Colin J. Cotter; Robert C. Kirby; Hunter Morris (CoRR, 2022)

Bounds-constrained polynomial approximation using the Bernstein basis. - Larry Allen; Robert C. Kirby (Numerische Mathematik, 2022)

Bringing Trimmed Serendipity Methods to Computational Practice in Firedrake. - Justin Crum; Cyrus Cheng; David A. Ham; Lawrence Mitchell; Robert C. Kirby; Joshua A. Levine; Andrew Gillette (ACM Trans. Math. Softw., 2022)

Additive Schwarz Methods for Serendipity Elements. - Jorge Marchena-Menendez; Robert C. Kirby (SIAM J. Sci. Comput., 2023)

Weighted-Norm Preconditioners for a Multilayer Tide Model. - Colin J. Cotter; Robert C. Kirby; Hunter Morris (SIAM J. Sci. Comput., 2023)

Integral equation methods for the Morse-Ingard equations. - Xiaoyu Wei; Andreas Klöckner; Robert C. Kirby (J. Comput. Phys., 2023)

Planar curve registration using Bayesian inversion. - Andreas A. Bock; Colin J. Cotter; Robert C. Kirby (Comput. Math. Appl., 2024)

Exact domain truncation for the Morse-ingard equations. - Robert C. Kirby; Xiaoyu Wei; Andreas Klöckner (Comput. Math. Appl., 2024)

Extending Irksome: improvements in automated Runge-Kutta time stepping for finite element methods. - Robert C. Kirby; Scott P. MacLachlan (CoRR, 2024)

FIAT: improving performance and accuracy for high-order finite elements. - Pablo D. Brubeck; Robert C. Kirby; Fabian Laakmann; Lawrence Mitchell (CoRR, 2024)

On the Convergence of Monolithic Multigrid for Implicit Runge-Kutta Time Stepping of Finite Element Problems. - Robert C. Kirby (SIAM J. Sci. Comput., 2024)

High-order bounds-satisfying approximation of partial differential equations via finite element variational inequalities. - Robert C. Kirby; Daniel Shapero (Numerische Mathematik, 2024)

FIAT: enabling classical and modern macroelements. - Pablo D. Brubeck; Robert C. Kirby (CoRR, 2025)

Fast solvers for the high-order FEM simplicial de Rham complex. - Pablo D. Brubeck; Patrick E. Farrell; Robert C. Kirby; Charles Parker (CoRR, 2025)

Bounds-constrained finite element approximation of time-dependent partial differential equations. - Robert C. Kirby; John D. Stephens (CoRR, 2025)