New efficient algorithm for the isometric embedding of 2-surface metrics in 3 dimensional Euclidean space
arXiv:1411.0975 · doi:10.1088/0264-9381/32/1/015002
Abstract
We present a new numerical method for the isometric embedding of 2-geometries specified by their 2-metrics in three dimensional Euclidean space. Our approach is to directly solve the fundamental embedding equation supplemented by six conditions that fix translations and rotations of the embedded surface. This set of equations is discretized by means of a pseudospectral collocation point method. The resulting nonlinear system of equations are then solved by a Newton-Raphson scheme. We explain our numerical algorithm in detail. By studying several examples we show that our method converges provided we start the Newton-Raphson scheme from a suitable initial guess. Our novel method is very efficient for smooth 2-metrics.
arXiv comment17 pages, 10 figures, accepted for publication by Class. Quantum Grav
References in corpus (9)
- Numerical Relativity: A review
- Quasilocal mass in general relativity
- Isometric embeddings into the Minkowski space and new quasi-local mass
- Constructing quasi-equilibrium initial data for binary neutron stars with arbitrary spins
- A new numerical method to construct binary neutron star initial data
- Black hole evolution with the BSSN system by pseudo-spectral methods
- Long term black hole evolution with the BSSN system by pseudospectral methods
- Embedding initial data for black hole collisions
- Isometric embeddings of black hole horizons in three-dimensional flat space