45 citations · 173 across the 28 of their papers we have counts for
14 papers · 1 filter
Boundary Integral Methods for Particle Diffusion in Complex Geometries: Shielding, Confinement, and Escape
Jesse Cherry, Alan E. Lindsay, Bryan D. Quaife
We present a numerical method for the solution of diffusion problems in unbounded planar regions with complex geometries of absorbing and reflecting bodies. Our numerical method ap…
Trapping of Planar Brownian Motion: Full First Passage Time Distributions by Kinetic Monte-Carlo, Asymptotic and Boundary Integral Methods
Jake Cherry, Alan E. Lindsay, Adrian Navarro Hernandez +1
We consider the problem of determining the arrival statistics of unbiased planar random walkers to complex target configurations. In contrast to problems posed in finite domains, s…
On the Spatial and Temporal Order of Convergence of Hyperbolic PDEs
Siddhartha Bishnu, Mark Petersen, Bryan Quaife
In this work, we determine the full expression for the global truncation error of hyperbolic partial differential equations (PDEs). In particular, we use theoretical analysis and s…
Stable and contact-free time stepping for dense rigid particle suspensions
Lukas Bystricky, Sachin Shanbhag, Bryan D. Quaife
We consider suspensions of rigid bodies in a two-dimensional viscous fluid. Even with high-fidelity numerical methods, unphysical contact between particles occurs because of spatia…
A boundary integral equation method for mode elimination and vibration confinement in thin plates with clamped points
Alan E. Lindsay, Bryan Quaife, Laura Wendelberger
We consider the bi-Laplacian eigenvalue problem for the modes of vibration of a thin elastic plate with a discrete set of clamped points. A high-order boundary integral equation me…
An efficient preconditioner for the fast simulation of a 2D Stokes flow in porous media
Pieter Coulier, Bryan Quaife, Eric Darve
We consider an efficient preconditioner for boundary integral equation (BIE) formulations of the two-dimensional Stokes equations in porous media. While BIEs are well-suited for re…
High-order adaptive time stepping for vesicle suspensions with viscosity contrast
Bryan Quaife, George Biros
We construct a high-order adaptive time stepping scheme for vesicle suspensions with viscosity contrast. The high-order accuracy is achieved using a spectral deferred correction (S…
Integral equation methods for the Yukawa-Beltrami equation on the sphere
Nilima Nigam, Mary-Catherine Kropinski, Bryan Quaife
An integral equation method for solving the Yukawa-Beltrami equation on a multiply-connected sub-manifold of the unit sphere is presented. A fundamental solution for the Yukawa-Bel…
A New Family of Regularized Kernels for the Harmonic Oscillator
Benjamin Ong, Andrew Christlieb, Bryan Quaife
In this paper, a new two-parameter family of regularized kernels is introduced, suitable for applying high-order time stepping to N-body systems. These high-order kernels are deriv…
Adaptive Time Stepping for Vesicle Suspensions
Bryan Quaife, George Biros
We present an adaptive arbitrary-order accurate time-stepping numerical scheme for the flow of vesicles suspended in Stokesian fluids. Our scheme can be summarized as an approximat…
High-volume fraction simulations of two-dimensional vesicle suspensions
Bryan Quaife, George Biros
We consider numerical algorithms for the simulation of the rheology of two-dimensional vesicles suspended in a viscous Stokesian fluid. The vesicle evolution dynamics is governed b…
On preconditioners for the Laplace double-layer in 2D
Bryan Quaife, George Biros
The discretization of the double-layer potential integral equation for the interior Dirichlet Laplace problem in a domain with smooth boundary results in a linear system that has a…
Fast integral equation methods for the heat equation and the modified Helmholtz equation in two dimensions
Mary-Catherine Kropinski, Bryan Quaife
We present an efficient integral equation approach to solve the heat equation, $u_t (\x) - Δu(\x) = F(\x,t)$, in a two-dimensional, multiply connected domain, and with Dirichlet bo…
Fast integral equation methods for the modified Helmholtz equation
Mary-Catherine Kropinski, Bryan Quaife
We present a collection of integral equation methods for the solution to the two-dimensional, modified Helmholtz equation, $u(\x) - α^2 Δu(\x) = 0$, in bounded or unbounded multipl…