87 citations · 270 across the 12 of their papers we have counts for
14 papers
The Closest Point Method for Surface PDEs with General Boundary Conditions
Tony Wong, Colin B. Macdonald, Byungjoon Lee
We generalize the closest point method (CPM) to solve surface partial differential equations with general boundary conditions. The proposed extrapolation method provides a unified…
A fast solver for the pseudo-two-dimensional model of lithium-ion batteries
Rachel Han, Colin Macdonald, Brian Wetton
The pseudo-two-dimensional (P2D) model is a complex mathematical model that can capture the electrochemical processes in Li-ion batteries. However, the model also brings a heavy co…
Optimization of the Mean First Passage Time in Near-Disk and Elliptical Domains in 2-D with Small Absorbing Traps
Sarafa A. Iyaniwura, Tony Wong, Colin B. Macdonald +1
The determination of the mean first passage time (MFPT) for a Brownian particle in a bounded 2-D domain containing small absorbing traps is a fundamental problem with biophysical a…
Simulation and Optimization of Mean First Passage Time Problems in 2-D using Numerical Embedded Methods and Perturbation Theory
Sarafa Iyaniwura, Tony Wong, Michael J. Ward +1
We develop novel numerical methods and perturbation approaches to determine the mean first passage time (MFPT) for a Brownian particle to be captured by either small stationary or…
Nearest Neighbor Sampling of Point Sets using Rays
Liangchen Liu, Louis Ly, Colin Macdonald +1
We propose a new framework for the sampling, compression, and analysis of distributions of point sets and other geometric objects embedded in Euclidean spaces. Our approach involve…
Anisotropic Diffusion on Curved Surfaces
Emma Naden, Thomas März, Colin B. Macdonald
We demonstrate a method for filtering images defined on curved surfaces embedded in 3D. Applications are noise removal and the creation of artistic effects. Our approach relies on…
Revisionist Integral Deferred Correction with Adaptive Stepsize Control
Andrew J. Christlieb, Colin B. Macdonald, Benjamin W. Ong +1
Adaptive stepsize control is a critical feature for the robust and efficient numerical solution of initial-value problems in ordinary differential equations. In this paper, we show…
An embedded method-of-lines approach to solving partial differential equations on surfaces
Ingrid von Glehn, Thomas März, Colin B. Macdonald
We introduce a method-of-lines formulation of the closest point method, a numerical technique for solving partial differential equations (PDEs) defined on surfaces. This is an embe…
The Closest Point Method and multigrid solvers for elliptic equations on surfaces
Yujia Chen, Colin B. Macdonald
Elliptic partial differential equations are important both from application and analysis points of views. In this paper we apply the Closest Point Method to solving elliptic equati…
Spatially partitioned embedded Runge-Kutta methods
David I. Ketcheson, Colin B. Macdonald, Steven J. Ruuth
We study spatially partitioned embedded Runge--Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different p…
Strong stability preserving explicit Runge-Kutta methods of maximal effective order
Yiannis Hadjimichael, Colin B. Macdonald, David I. Ketcheson +1
We apply the concept of effective order to strong stability preserving (SSP) explicit Runge-Kutta methods. Relative to classical Runge-Kutta methods, methods with an effective orde…
Calculus on Surfaces with General Closest Point Functions
Thomas März, Colin B. Macdonald
The Closest Point Method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys. 2008] and successfully…
Solving eigenvalue problems on curved surfaces using the Closest Point Method
Colin B. Macdonald, Jeremy Brandman, Steven J. Ruuth
Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace--Beltrami operator on ra…
Strong stability preserving two-step Runge-Kutta methods
David I. Ketcheson, Sigal Gottlieb, Colin B. Macdonald
We investigate the strong stability preserving (SSP) property of two-step Runge-Kutta (TSRK) methods. We prove that all SSP TSRK methods belong to a particularly simple subclass of…