Related papers: Variational derivation and compatible discretizati…
In this paper we propose an extension of the generalized Lagrangian multiplier method (GLM) of Munz et al. (JCP 2000, JCP 2002), which was originally conceived for the numerical solution of the Maxwell and MHD equations with divergence-type…
In this paper we present three different numerical approaches to account for curl-type involution constraints in hyperbolic partial differential equations for continuum physics. All approaches have a direct analogy to existing and…
We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence…
In this paper, we develop a structure-preserving discretization of the Lagrangian framework for electromagnetism, combining techniques from variational integrators and discrete differential forms. This leads to a general family of…
Chew, Goldberger & Low (CGL) equations are a set of hyperbolic PDEs with non-conservative products used to model the plasma flows, when the assumption of local thermodynamic equilibrium is not valid, and the pressure tensor is assumed to be…
This paper aims at developing exactly energy-conservative and structure-preserving finite volume schemes for the discretisation of first-order symmetric-hyperbolic and thermodynamically compatible (SHTC) systems of partial differential…
This paper proposes a semi-implicit arbitrary Lagrangian-Eulerian (ALE) method for the solution of the unified Godunov-Peshkov-Romenski (GPR) model of continuum mechanics. To handle the curl free involutions arising in the solid limit of…
We propose a new technique to generate reasonable systems of partial differential equations (PDE) that could be potential candidates for depicting models in natural sciences related to quasi-linear equations. Such systems appear within…
We consider multi-dimensional extensions of Maxwell's seminal rheo-logical equation for 1D viscoelastic flows. We aim at a causal model for compressible flows, defined by semi-group solutions given initial conditions , and such that…
We propose a finite element discretisation approach for the incompressible Euler equations which mimics their geometric structure and their variational derivation. In particular, we derive a finite element method that arises from a…
In recent years, two important techniques for geometric numerical discretization have been developed. In computational electromagnetics, spatial discretization has been improved by the use of mixed finite elements and discrete differential…
One- and multi-dimensional stochastic Maxwell equations with additive noise are considered in this paper. It is known that such system can be written in the multi-symplectic structure, and the stochastic energy increases linearly in time.…
A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of Discrete Exterior Calculus, the field solver, interpolation scheme and…
This paper discusses the computation of derivatives for optimization problems governed by linear hyperbolic systems of partial differential equations (PDEs) that are discretized by the discontinuous Galerkin (dG) method. An efficient and…
This paper proposes a charge-conserving, variational, spatio-temporal discretization for the drift-kinetic Vlasov-Maxwell system, utilizing finite-elements for the electromagnetic fields and the particle-in-cell approach for the Vlasov…
In this work we present a novel structure-preserving scheme for the discretization of the Godunov-Peshkov-Romenski (GPR) model of continuum mechanics written in Lagrangian form. This model admits an extra conservation law for the total…
In this paper, we generalize the idea in our previous work for the Vlasov-Amp\`{e}re (VA) system \cite{cheng_va} and develop energy-conserving discontinuous Galerkin (DG) methods for the Vlasov-Maxwell (VM) system. The VM system is a…
We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different…
We develop a finite volume method for Maxwell's equations in materials whose electromagnetic properties vary in space and time. We investigate both conservative and non-conservative numerical formulations. High-order methods accurately…
This paper applies the gradient discretisation method (GDM) for fourth order elliptic variational inequalities. The GDM provides a new formulation of error estimates and a complete convergence analysis of several numerical methods. We show…