I’ve just finished Jörg Frauendiener’s, “On the applicability of constrained symplectic integrators in general relativity”. It’s a readable paper (the necessary background is given in the paper) about numerical integration in Hamiltonian systems. The idea here is that if we have a symplectic manifold modelling the states of some system of ODE’s, along with a …
Tag Archive: Numerical Relativity
Hyperbolicity of BSSN
So, from what I understand it seems that strong and symmetric hyperbolicity of equations is only defined for systems with first order derivatives. The significance is that strong or symmetric hyperbolic systems of differential equations are “well posed” that is, roughly speaking, that they have unique solutions that depend continuously on the initial data (i.e. …
Analytic work on constraint quantities lacking?
The paper provides a general introduction to how to perform analysis of the attractors of some dynamical system (with specified initial conditions) and then applies this to a particular initial value formulation of Einstein’s equations.
Is general relativity “essential understood”?
Predictably the papers answer is no. Why? Because current numerical methods in general relativity are limited. The paper implies that these limitations are Inability to compute global solutions Inability to evolve initial data for strongly gravitating and very dynamic systems. In any case Friedrich then divides the field equations to four classes the system of …
Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. I. The conformal field equations.
It a long title for a small paper that provides a decent overview. I’ll be honest, I’m struggling to get a grip on the PDE side of GR. Oh I don’t have much of a problem with the notation, the concepts, or the methods. What I do have a problem with is the motivation. I …