Firedrake is a new tool for automating the numerical solution of partial differential equations.
Firedrake adopts the domain-specific language for the finite element method of the FEniCS …

In this paper, we present a series of mathematical abstractions for seismologically relevant
wave equations discretized using finite-element methods, and demonstrate how these …

PetscSF, the communication component of the Portable, Extensible Toolkit for Scientific
Computation (PETSc), is designed to provide PETSc's communication infrastructure suitable …

Most research on preconditioners for time-dependent PDEs has focused on implicit multi-
step or diagonally-implicit multi-stage temporal discretizations. In this paper, we consider …

We present a dynamically load-balanced parallel p-adaptive implicit high-order flux
reconstruction method for under-resolved turbulence simulation. The high-order explicit first …

We present a generic algorithm for numbering and then efficiently iterating over the data
values attached to an extruded mesh. An extruded mesh is formed by replicating an existing …

The magnetohydrodynamics equations model a wide range of plasma physics applications
and are characterized by a nonlinear system of partial differential equations that strongly …

Large-scale PDE simulations using high-order finite-element methods on unstructured
meshes are an indispensable tool in science and engineering. The widely used open …

Particle-in-cell methods employ particle representations of unknown fields but also employ
continuum fields for other parts of the problem. Thus projection between particle and …

While implicit Runge–Kutta (RK) methods possess high order accuracy and important
stability properties, implementation difficulties and the high expense of solving the coupled …