Hyperbolic Methods for Einstein’s Equations

Hyperbolic Methods for Einstein’s Equations

I review evolutionary aspects of general relativity, in particular those related to the hyperbolic character of the field equations and to the applications or consequences that this property entails. I look at several approaches to obtaining symmetric hyperbolic systems of equations out of Einstein' equations by either removing some gauge freedoms from them, or by considering certain linear com...

Multistep-Galerkin Methods for Hyperbolic Equations

Multistep methods for firstand second-order ordinary differential equations are used for the full discretizations of standard Galerkin approximations to the initial-periodic boundary value problem for first-order linear hyperbolic equations in one space dimension and to the initial-boundary value problem for second-order lin2 ear selfadjoint hyperbolic equations in many space dimensions. L -err...

Additive Schwarz Methods for Hyperbolic Equations 5153

Additive Schwarz Methods for Hyperbolic Equations

In recent years there has been gratifying progress in the development of domain decomposition algorithms for symmetric and nonsymmetric elliptic problems and even some inde nite problems Many methods possess the attractive property that the convergence rate is optimal i e independent of the size of the discrete problem and of the number of subdomains or within a polylog factor of optimal There ...

Semi-Lagrangian Particle Methods for Hyperbolic Equations

Particle methods with remeshing of particles at each time-step can be seen as forward semi-lagrangian conservative methods for advection-dominated problems, and must be analyzed as such. In this article we investigate the links between these methods and finite-difference methods and present convergence results as well as techniques to control their oscillations. We emphasize the role of the siz...