Multi-Center Vector Field Methods for Wave Equations

Multi-Symplectic Runge-Kutta Collocation Methods for Hamiltonian Wave Equations

A number of conservative PDEs, like various wave equations, allow for a multi-symplectic formulation which can be viewed as a generalization of the symplectic structure of Hamiltonian ODEs. We show that Gauss-Legendre collocation in space and time leads to multi-symplectic integrators, i.e., to numerical methods that preserve a symplectic conservation law similar to the conservation of symplect...

Multi-symplectic Runge–Kutta-type methods for Hamiltonian wave equations

The non-linear wave equation is taken as a model problem for the investigation. Different multisymplectic reformulations of the equation are discussed. Multi-symplectic Runge–Kutta methods and multi-symplectic partitioned Runge–Kutta methods are explored based on these different reformulations. Some popular and efficient multi-symplectic schemes are collected and constructed. Stability analyses...

Far Field Expansion for Anisotropic Wave Equations

Operator Splitting Methods for Wave Equations

Abstract The motivation for our studies is coming from simulation of earthquakes, that are modelled by elastic wave equations. In our paper we focus on stiff phanomenons for the wave equations. In the course of this article we discuss iterative operator splitting methods for wave equations motivated by realistic problems dealing with seismic sources and waves. The operator splitting methods are...

Neumann–neumann Methods for Vector Field Problems

In this paper, we study some Schwarz methods of Neumann–Neumann type for some vector field problems, discretized with the lowest order Raviart–Thomas and Nédélec finite elements. We consider a hybrid Schwarz preconditioner consisting of a coarse component, which involves the solution of the original problem on a coarse mesh, and local ones, which involve the solution of Neumann problems on the ...