78 citations · 734 across the 47 of their papers we have counts for
5 papers · 1 filter
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…