This paper introduces an automated approach for generating a finite element (FE)
discretization of a multi-compartment human head model for electroencephalographic (EEG) …

The magnetohydrodynamics (MHD) equations are continuum models used in the study of a
wide range of plasma physics systems, including the evolution of complex plasma dynamics …

We develop a universally applicable embedded boundary finite difference method, which
results in a symmetric positive definite linear system and does not suffer from small cell …

Abstract Application of a Discontinuous Petrov-Galerkin (DPG) method for simulation of
compressible viscous flows in three dimensions is presented. The approach enables …

Equilibriums in magnetic confinement devices result from force balancing between the
Lorentz force and the plasma pressure gradient. In an axisymmetric configuration like a …

A parallel cut-cell algorithm is described to solve the free-boundary problem of the Grad--
Shafranov equation. The algorithm reformulates the free-boundary problem in an irregular …

In this work we consider a relativistic drift-kinetic model for runaway electrons along with a
Fokker–Planck operator for small-angle Coulomb collisions, a radiation damping operator …

I provide an introduction to the application of deep learning and neural networks for solving
partial differential equations (PDEs). The approach, known as physics-informed neural …

A pointwise error estimation of the form O (ρ h^ 8), O (ρ h 8), h is the mesh size, for the
approximate solution of the Dirichlet problem for Laplace's equation on a rectangular …

The shallow-water equations are a set of nonlinear partial differential equations with many
applications including storm surge, oceanic circulation, dam failures, and landslides. The …