78 citations · 734 across the 47 of their papers we have counts for
48 papers
A Semi-Lagrangian Adaptive-Rank (SLAR) Method for Linear Advection and Nonlinear Vlasov-Poisson System
Nanyi Zheng, Daniel Hayes, Andrew Christlieb +1
High-order semi-Lagrangian methods for kinetic equations have been under rapid development in the past few decades. In this work, we propose a semi-Lagrangian adaptive rank (SLAR)…
On the rotational invariance and hyperbolicity of shallow water moment equations in two dimensions
Matthew Bauerle, Andrew J. Christlieb, Mingchang Ding +1
In this paper, we investigate the two-dimensional extension of a recently introduced set of shallow water models based on a regularized moment expansion of the incompressible Navie…
A Particle-in-cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation
Andrew J. Christlieb, William A. Sands, Stephen White
This paper formulates a new particle-in-cell method for the Vlasov-Maxwell system. Under the Lorenz gauge condition, Maxwell's equations for the electromagnetic fields can be writt…
Machine learning moment closure models for the radiative transfer equation III: enforcing hyperbolicity and physical characteristic speeds
Juntao Huang, Yingda Cheng, Andrew J. Christlieb +1
This is the third paper in a series in which we develop machine learning (ML) moment closure models for the radiative transfer equation (RTE). In our previous work \cite{huang2021g…
Machine learning moment closure models for the radiative transfer equation II: enforcing global hyperbolicity in gradient based closures
Juntao Huang, Yingda Cheng, Andrew J. Christlieb +2
This is the second paper in a series in which we develop machine learning (ML) moment closure models for the radiative transfer equation (RTE). In our previous work \cite{huang2021…
Machine learning moment closure models for the radiative transfer equation I: directly learning a gradient based closure
Juntao Huang, Yingda Cheng, Andrew J. Christlieb +1
In this paper, we take a data-driven approach and apply machine learning to the moment closure problem for radiative transfer equation in slab geometry. Instead of learning the unc…
Parallel Scaling of the Regionally-Implicit Discontinuous Galerkin Method with Quasi-Quadrature-Free Matrix Assembly
Andrew J. Christlieb, Pierson T. Guthrey, James A. Rossmanith
In this work we investigate the parallel scalability of the numerical method developed in Guthrey and Rossmanith [The regionally implicit discontinuous Galerkin method: Improving t…
Superconvergent Non-Polynomial Approximations
Andrew Christlieb, William Sands, Hyoseon Yang
In this paper, we introduce a superconvergent approximation method that employs radial basis functions (RBFs) in the numerical solution of conservation laws. The use of RBFs for in…
Parallel Algorithms for Successive Convolution
Andrew J. Christlieb, Pierson T. Guthrey, William A. Sands +1
In this work, we consider alternative discretizations for PDEs which use expansions involving integral operators to approximate spatial derivatives. These constructions use explici…
Benchmark Computation of Morphological Complexity in the Functionalized Cahn-Hilliard Gradient Flow
Andrew Christlieb, Keith Promislow, Zengqiang Tan +3
Reductions of the self-consistent mean field theory model of amphiphilic molecules in solvent can lead to a singular family of functionalized Cahn-Hilliard energies. We modify thes…
A Kernel-Based Explicit Unconditionally Stable Scheme for Hamilton-Jacobi Equations on Nonuniform Meshes
Andrew Christlieb, William Sands, Hyoseon Yang
In \cite{christlieb2019kernel}, the authors developed a class of high-order numerical schemes for the Hamilton-Jacobi (H-J) equations, which are unconditionally stable, yet take th…
A Kernel Based Unconditionally Stable Scheme for Nonlinear Parabolic Partial Differential Equations
Kaipeng Wang, Andrew Christlieb, Yan Jiang +1
In this paper, a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients. This method is based on our previous work…
A Kernel Based High Order "Explicit" Unconditionally Stable Constrained Transport Method for Ideal Magnetohydrodynamics
Firat Cakir, Andrew Christlieb, Yan Jiang
The ideal Magnetohydrodynamics (MHD) equations are challenging because one needs to maintain the divergence free condition, $\nabla \cdot \Bv = 0$. Many numerical methods have been…
Multiscale High-Dimensional Sparse Fourier Algorithms for Noisy Data
Bosu Choi, Andrew Christlieb, Yang Wang
We develop an efficient and robust high-dimensional sparse Fourier algorithm for noisy samples. Earlier in the paper ``Multi-dimensional sublinear sparse Fourier algorithm" (2016),…
A Kernel Based High Order "Explicit" Unconditionally Stable Scheme for Time Dependent Hamilton-Jacobi Equations
Andrew Christlieb, Wei Guo, Yan Jiang
In this paper, a class of high order numerical schemes is proposed for solving Hamilton-Jacobi (H-J) equations. This work is regarded as an extension of our previous work for nonli…
A high-order finite difference WENO scheme for ideal magnetohydrodynamics on curvilinear meshes
Andrew J. Christlieb, Xiao Feng, Yan Jiang +1
A high-order finite difference numerical scheme is developed for the ideal magnetohydrodynamic equations based on an alternative flux formulation of the weighted essentially non-os…
Competition and Complexity in Amphiphilic Polymer Morphology
Andrew Christlieb, Noa Kraitzman, Keith Promislow
We analyze the competitive evolution of codimension one and two morphologies within the gradient flow of the strong Functionalized Cahn-Hilliard equation. On a slow time s…
Kernel Based High Order "Explicit" Unconditionally-Stable Scheme for Nonlinear Degenerate Advection-Diffusion Equations
Andrew Christlieb, Wei Guo, Yan Jiang
In this paper, we present a novel numerical scheme for solving a class of nonlinear degenerate parabolic equations with non-smooth solutions. The proposed method relies on a specia…
A New Class of Fully Discrete Sparse Fourier Transforms: Faster Stable Implementations with Guarantees
Sami Merhi, Ruochuan Zhang, Mark A. Iwen +1
In this paper we consider Sparse Fourier Transform (SFT) algorithms for approximately computing the best -term approximation of the Discrete Fourier Transform (DFT) $\mathbf{\ha…
Energy transfer in compressible magnetohydrodynamic turbulence
Philipp Grete, Brian W. O'Shea, Kris Beckwith +2
Magnetic fields, compressibility and turbulence are important factors in many terrestrial and astrophysical processes. While energy dynamics, i.e. how energy is transferred within…
Method of lines transpose: Energy gradient flows using direct operator inversion for phase field models
Matthew Causley, Hana Cho, Andrew Christlieb
In this work, we develop an implicit real space method in 1D and 2D for the Cahn Hilliard (CH) and vector Cahn Hilliard (VCH) equations, based on the Method Of Lin…
A WENO-based Method of Line Transpose Approach for Vlasov Simulations
Andrew Christlieb, Wei Guo, Yan Jiang
In this paper, a high order implicit Method of Line Transpose (MOL ) method based on a weighted essentially non-oscillatory (WENO) methodology is developed for one-dimensional…
An Asymptotic Preserving Maxwell Solver Resulting in the Darwin Limit of Electrodynamics
Yingda Cheng, Andrew J. Christlieb, Wei Guo +1
In plasma simulations, where the speed of light divided by a characteristic length is at a much higher frequency than other relevant parameters in the underlying system, such as th…
High-Dimensional Sparse Fourier Algorithms
Bosu Choi, Andrew Christlieb, Yang Wang
In this paper, we discuss the development of a sublinear sparse Fourier algorithm for high-dimensional data. In ``Adaptive Sublinear Time Fourier Algorithm" by D. Lawlor, Y. Wang a…