Solving the Einstein constraint equations on multi-block triangulations using finite element methods

Details Solving the Einstein constraint equations on multi-block triangulations using finite element methods Solving the Einstein constraint equations on multi-block triangulations using finite element methods

2008-01-11

arxiv.org/abs/0801.1823v3

Class. Quantum Grav. 26, 145007 (2009)

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Changes made to match the version to appear in Classical and Quantum Gravity

Scientific paper

In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these equations on three-dimensional multi-block domains using finite element methods. We illustrate our approach on a simple example of Brill wave initial data, with the constraints reducing to a single linear elliptic equation for the conformal factor $\psi$. We use quadratic Lagrange elements on semi-structured simplicial meshes, obtained by triangulation of multi-block grids. In the case of uniform refinement the scheme is superconvergent at most mesh vertices, due to local symmetry of the finite element basis with respect to local spatial inversions. We show that in the superconvergent case subsequent unstructured mesh refinements do not improve the quality of our initial data. As proof of concept that this approach is feasible for generating multi-block initial data in three dimensions, after constructing the initial data we evolve them in time using a high order finite-differencing multi-block approach and extract the gravitational waves from the numerical solution.

Affiliated with

Also associated with

No associations

Rating

Solving the Einstein constraint equations on multi-block triangulations using finite element methods does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Solving the Einstein constraint equations on multi-block triangulations using finite element methods, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Solving the Einstein constraint equations on multi-block triangulations using finite element methods will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-548390