Search Results - "Kirby, Robert C"

High-order bounds-satisfying approximation of partial differential equations via finite element variational inequalities by Kirby, Robert C., Shapero, Daniel

“…Solutions to many important partial differential equations satisfy bounds constraints, but approximations computed by finite element or finite difference…”
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Bounds-constrained polynomial approximation using the Bernstein basis by Allen, Larry, Kirby, Robert C.

“…A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent…”
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Fast inversion of the simplicial Bernstein mass matrix by Kirby, Robert C.

“…We consider the mass matrix arising from Bernstein polynomials as finite element shape functions. In particular, we give an explicit formula for its…”
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Finite element approximation and preconditioners for a coupled thermal–acoustic model by Brennan, Brian, Kirby, Robert C.

“…We consider a time-harmonic mathematical model for a coupled thermal–acoustic model. We demonstrate coercivity of the PDE system and hence well-posedness and…”
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From Functional Analysis to Iterative Methods by Kirby, Robert C.

“…We examine condition numbers, preconditioners, and iterative methods for finite element discretizations of coercive PDEs in the context of the fundamental…”
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Fast simplicial finite element algorithms using Bernstein polynomials by Kirby, Robert C.

“…Fast algorithms for applying finite element mass and stiffness operators to the B-form of polynomials over d -dimensional simplices are derived. These rely on…”
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Mixed finite elements for global tide models with nonlinear damping by Cotter, Colin J., Graber, P. Jameson, Kirby, Robert C.

“…We study mixed finite element methods for the rotating shallow water equations with linearized momentum terms but nonlinear drag. By means of an equivalent…”
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Mixed finite elements for global tide models by Cotter, Colin J., Kirby, Robert C.

“…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…”
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spyro: a Firedrake-based wave propagation and full-waveform-inversion finite-element solver by Roberts, Keith J, Olender, Alexandre, Franceschini, Lucas, Kirby, Robert C, Gioria, Rafael S, Carmo, Bruno S

“…In this article, we introduce spyro, a software stack to solve wave propagation in heterogeneous domains and perform full waveform inversion (FWI) employing…”
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Preconditioning mixed finite elements for tide models by Kirby, Robert C., Kernell, Tate

“…We describe a fully discrete mixed finite element method for the linearized rotating shallow water model, possibly with damping. While Crank–Nicolson…”
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Integral equation methods for the Morse-Ingard equations by Wei, Xiaoyu, Klöckner, Andreas, Kirby, Robert C.

“…We present two (a decoupled and a coupled) integral-equation-based methods for the Morse-Ingard equations subject to Neumann boundary conditions on the…”
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Exact domain truncation for the Morse-ingard equations by Kirby, Robert C., Wei, Xiaoyu, Klöckner, Andreas

“…Morse and Ingard [1] give a coupled system of time-harmonic equations for the temperature and pressure of an excited gas. These equations form a critical…”
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A nonlocal boundary condition for domain truncation in frequency-domain Helmholtz problems by Kirby, Robert C., Kloeckner, Andreas, Sepanski, Ben

“…Numerical resolution of exterior Helmholtz problems requires some approach to domain truncation. As an alternative to approximate nonreflecting boundary…”
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Planar curve registration using Bayesian inversion by Bock, Andreas, Cotter, Colin J., Kirby, Robert C.

“…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…”
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Automated FEM discretizations for the Stokes equation by Terrel, A.R., Scott, L.R., Knepley, M.G., Kirby, R.C.

“…Current FEM software projects have made significant advances in various automated modeling techniques. We present some of the mathematical abstractions…”
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Symplectic-mixed finite element approximation of linear acoustic wave equations by Kirby, Robert C., Kieu, Thinh Tri

“…We apply mixed finite element approximations to the first-order form of the acoustic wave equation. The semidiscrete method exactly conserves the system…”
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Transformations for Piola-mapped elements by Aznaran, Francis R. A., Farrell, Patrick E., Kirby, Robert C.

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Block preconditioners for finite element discretization of incompressible flow with thermal convection by Howle, Victoria E., Kirby, Robert C.

“…SUMMARY We derive block preconditioners for a finite element discretization of incompressible flow coupled to heat transport by the Boussinesq approximation…”
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Fast simplicial quadrature-based finite element operators using Bernstein polynomials by Kirby, Robert C., Thinh, Kieu Tri

“…We derive low-complexity matrix-free finite element algorithms for simplicial Bernstein polynomials on simplices. Our techniques, based on a sparse…”
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On the convergence of monolithic multigrid for implicit Runge-Kutta time stepping of finite element problems by Kirby, Robert C

“…Finite element discretization of time dependent problems also require effective time-stepping schemes. While implicit Runge-Kutta methods provide favorable…”
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