43 citations · 292 across the 26 of their papers we have counts for
6 papers · 1 filter
Computing the Dirichlet-Neumann Operator on a Cylinder
Saad Qadeer, Jon Wilkening
The computation of the Dirichlet-Neumann operator for the Laplace equation is the primary challenge for the numerical simulation of the ideal fluid equations. The techniques used c…
Convergence of a mass-lumped finite element method for the Landau-Lifshitz equation
Eugenia Kim, Jon Wilkening
The dynamics of the magnetic distribution in a ferromagnetic material is governed by the Landau-Lifshitz equation, which is a nonlinear geometric dispersive equation with a nonconv…
Comparison of five methods of computing the Dirichlet-Neumann operator for the water wave problem
Jon Wilkening, Vishal Vasan
We compare the effectiveness of solving Dirichlet-Neumann problems via the Craig-Sulem (CS) expansion, the Ablowitz-Fokas-Musslimani (AFM) implicit formulation, the dual AFM formul…
Boltzmann Equation Solver Adapted to Emergent Chemical Non-equilibrium
Jeremiah Birrell, Jon Wilkening, Johann Rafelski
We present a novel method to solve the spatially homogeneous and isotropic relativistic Boltzmann equation. We employ a basis set of orthogonal polynomials dynamically adapted to a…
Accurate Spectral Numerical Schemes for Kinetic Equations with Energy Diffusion
Jon Wilkening, Antoine Cerfon, Matt Landreman
We examine the merits of using a family of polynomials that are orthogonal with respect to a non-classical weight function to discretize the speed variable in continuum kinetic cal…
Variational Particle Schemes for the Porous Medium Equation and for the System of Isentropic Euler Equations
Michael Westdickenberg, Jon Wilkening
Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework o…