相关论文: Geometric Computational Electrodynamics with Varia…

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…

Variational integrators for Lagrangian dynamical systems provide a systematic way to derive geometric numerical methods. These methods preserve a discrete multisymplectic form as well as momenta associated to symmetries of the Lagrangian…

Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. Variational integrators are an important class of geometric integrators. The general idea…

Numerical methods that preserves geometric invariants of the system such as energy, momentum and symplectic form, are called geometric integrators. These include variational integrators as an important subclass of geometric integrators. The…

This paper presents a method to construct variational integrators for time-dependent lagrangian systems. The resulting algorithms are symplectic, preserve the momentum map associated with a Lie group of symmetries and also describe the…

A novel finite element method for the approximation of Maxwell's equations over hybrid two-dimensional grids is studied. The choice of appropriate basis functions and numerical quadrature leads to diagonal mass matrices which allow for…

Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. In this paper we present a method to construct symplectic-momentum integrators for…

Variational symplectic algorithms have recently been developed for carrying out long-time simulation of charged particles in magnetic fields. As a direct consequence of their derivation from a discrete variational principle, these…

Symplectic integrators offer many advantages for the numerical solution of Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two of the central Hamiltonian systems encountered in…

This paper presents a geometric-variational approach to continuous and discrete mechanics and field theories. Using multisymplectic geometry, we show that the existence of the fundamental geometric structures as well as their preservation…

Compatible discretizations, such as finite element exterior calculus, provide a discretization framework that respect the cohomological structure of the de Rham complex, which can be used to systematically construct stable mixed finite…

Yee's finite-difference method preserves two crucial properties of Maxwell's equations -- locality and symplecticity -- and thereby enjoys two computational advantages: scalability on high-performance architectures and long-time numerical…

Lagrangian multiform theory is a variational framework for integrable systems. In this article we introduce a new formulation which is based on symplectic geometry and which treats position, momentum and time coordinates of a…

This paper is a summary of the theory of discrete embeddings introduced in [5]. A discrete embedding is an algebraic procedure associating a numerical scheme to a given ordinary differential equation. Lagrangian systems possess a…

A semi-implicit finite difference time domain (FDTD) numerical Maxwell solver is developed for full electromagnetic Particle-in-Cell (PIC) codes for the simulations of plasma-based acceleration. The solver projects the volumetric Yee…

A novel finite element scheme is studied for solving the time-dependent Maxwell's equations on unstructured grids efficiently. Similar to the traditional Yee scheme, the method has one degree of freedom for most edges and a sparse inverse…

An efficient finite-difference time-domain (FDTD) algorithm is built to solve the transverse electric 2D Maxwell's equations with inhomogeneous dielectric media where the electric fields are discontinuous across the dielectric interface.…

Taking advantage of the flexibility of the variational method with coordinate transformations, we derive a self-consistent set of equations of motion from a discretized Lagrangian to study kinetic plasmas using a Fourier decomposed…

We present a discretisation of the 3+1 formulation of the Yang-Mills equations in the temporal gauge, using a Lie algebra-valued extension of the discrete de Rham (DDR) sequence, that preserves the non-linear constraint exactly. In contrast…

We present a structure preserving discretization of the fundamental spacetime geometric structures of fluid mechanics in the Lagrangian description in 2D and 3D. Based on this, multisymplectic variational integrators are developed for…