10 citations · 17 across the 8 of their papers we have counts for
8 papers
A Particle-In-Cell Method for Plasmas with a Generalized Momentum Formulation, Part III: A Family of Gauge Conserving Methods
Andrew J. Christlieb, William A. Sands, Stephen R. White
In this paper, we introduce a new family of spatially co-located field solvers for particle-in-cell applications which evolve the potential formulation of Maxwell's equations under…
A Particle-in-cell Method for Plasmas with a Generalized Momentum Formulation, Part II: Enforcing the Lorenz Gauge Condition
Andrew J. Christlieb, William A. Sands, Stephen White
In a previous paper, we developed a new particle-in-cell method for the Vlasov-Maxwell system in which the electromagnetic fields and the equations of motion for the particles were…
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…
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…
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…
Split-facets for Balanced Minimal Evolution Polytopes and the Permutoassociahedron
Stefan Forcey, Logan Keefe, William Sands
Understanding the face structure of the balanced minimal evolution (BME) polytope, especially its top-dimensional facets, is crucially important to phylogenetic applications. We sh…
Facets of the Balanced Minimal Evolution Polytope
Stefan Forcey, Logan Keefe, William Sands
A phylogenetic tree is a way to organize a finite set of species, individuals or other sources of related data. The species for which we have existing DNA data make up the set of l…