78 citations · 734 across the 47 of their papers we have counts for
9 papers · 1 filter
Arbitrarily high order Convected Scheme solution of the Vlasov-Poisson system
Yaman Güçlü, Andrew J. Christlieb, William N. G. Hitchon
The Convected Scheme (CS) is a `forward-trajectory' semi-Lagrangian method for solution of transport equations, which has been most often applied to the kinetic description of plas…
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…
A High Order Time Splitting Method Based on Integral Deferred Correction for Semi-Lagrangian Vlasov Simulations
Andrew Christlieb, Wei Guo, Maureen Morton +1
Semi-Lagrangian schemes with various splitting methods, and with different reconstruction/interpolation strategies have been applied to kinetic simulations. For example, the order…
Finite Difference Weighted Essentially Non-Oscillatory Schemes with Constrained Transport for Ideal Magnetohydrodynamics
Andrew J. Christlieb, James A. Rossmanith, Qi Tang
In this work we develop a class of high-order finite difference weighted essentially non-oscillatory (FD-WENO) schemes for solving the ideal magnetohydrodynamic (MHD) equations in…
Higher order A-stable schemes for the wave equation using a recursive convolution approach
Matthew F. Causley, Andrew J. Christlieb
In several recent works \cite{Causley2013a}, \cite{Causley2013}, we developed a new second order, A-stable approach to wave propagation problems based on the method of lines transp…
Method of Lines Transpose: A Fast Implicit Wave Propagator
Matthew F. Causley, Andrew J. Christlieb, Yaman Guclu +1
As a follow up to \cite{Causley2013}, we provide a detailed description of the numerical implementation of an O(N), A-stable, second order accurate solution of the wave equation, c…
Energy-conserving discontinuous Galerkin methods for the Vlasov-Ampère system
Yingda Cheng, Andrew J. Christlieb, Xinghui Zhong
In this paper, we propose energy-conserving numerical schemes for the Vlasov-Ampère (VA) systems. The VA system is a model used to describe the evolution of probability density fun…
A Multiscale Sub-linear Time Fourier Algorithm for Noisy Data
Andrew Christlieb, David Lawlor, Yang Wang
We extend the recent sparse Fourier transform algorithm of (Lawlor, Christlieb, and Wang, 2013) to the noisy setting, in which a signal of bandwidth N is given as a superposition o…
High-order multiderivative time integrators for hyperbolic conservation laws
David C. Seal, Yaman Güçlü, Andrew J. Christlieb
Multiderivative time integrators have a long history of development for ordinary differential equations, and yet to date, only a small subset of these methods have been explored as…