68 citations · 76 across the 6 of their papers we have counts for
6 papers
Linearization Errors in Discrete Goal-Oriented Error Estimation
Brian N. Granzow, D. Thomas Seidl, Stephen D. Bond
This paper is concerned with goal-oriented a posteriori error estimation for nonlinear functionals in the context of nonlinear variational problems solved with continuous Galerkin…
Numerical Integration of the Extended Variable Generalized Langevin Equation with a Positive Prony Representable Memory Kernel
Andrew D. Baczewski, Stephen D. Bond
Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological syst…
Goal-Oriented Adaptivity and Multilevel Preconditioning for the Poisson-Boltzmann Equation
Burak Aksoylu, Stephen Bond, Eric Cyr +1
In this article, we develop goal-oriented error indicators to drive adaptive refinement algorithms for the Poisson-Boltzmann equation. Empirical results for the solvation free ener…
Local Refinement and Multilevel Preconditioning: Implementation and Numerical Experiments
Burak Aksoylu, Stephen Bond, Michael Holst
In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While st…
Generating Initial Data in General Relativity using Adaptive Finite Element Methods
Burak Aksoylu, David Bernstein, Stephen Bond +1
The conformal formulation of the Einstein constraint equations is first reviewed, and we then consider the design, analysis, and implementation of adaptive multilevel finite elemen…
On the approximation of Feynman-Kac path integrals for quantum statistical mechanics
Stephen D. Bond, Brian B. Laird, Benedict J. Leimkuhler
Discretizations of the Feynman-Kac path integral representation of the quantum mechanical density matrix are investigated. Each infinite-dimensional path integral is approximated b…