A spectral solver for evolution problems with spatial S3-topology
arXiv:0804.4222 · doi:10.1016/j.jcp.2009.05.037
Abstract
We introduce a single patch collocation method in order to compute solutions of initial value problems of partial differential equations whose spatial domains are 3-spheres. Besides the main ideas, we discuss issues related to our implementation and analyze numerical test applications. Our main interest lies in cosmological solutions of Einstein's field equations. Motivated by this, we also elaborate on problems of our approach for general tensorial evolution equations when certain symmetries are assumed. We restrict to U(1)- and Gowdy symmetry here.
29 pages, 11 figures, uses psfrag and hyperref, large parts rewritten in order to match to the requirements of the journal, conclusions unchanged; J. Comput. Phys. (2009)
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Cited by in corpus (15)
- Continuum and Discrete Initial-Boundary-Value Problems and Einstein's Field Equations
- Black holes in a box: towards the numerical evolution of black holes in AdS
- Numerical evolutions of fields on the 2-sphere using a spectral method based on spin-weighted spherical harmonics
- Smooth Gowdy symmetric generalized Taub-NUT solutions
- Numerical solutions of Einstein's equations for cosmological spacetimes with spatial topology S3 and symmetry group U(1)
- Numerical space-times near space-like and null infinity. The spin-2 system on Minkowski space
- Investigations of solutions of Einstein's field equations close to lambda-Taub-NUT
- Non-genericity of the Nariai solutions: I. Asymptotics and spatially homogeneous perturbations
- The numerical initial boundary value problem for the generalized conformal field equations
- Non-genericity of the Nariai solutions: II. Investigations within the Gowdy class
- Asymptotically flat vacuum initial data sets from a modified parabolic-hyperbolic formulation of the Einstein vacuum constraint equations
- Spectral methods for the spin-2 equation near the cylinder at spatial infinity
- Regularity of Cauchy horizons in S2xS1 Gowdy spacetimes
- Numerical construction of initial data sets of binary black hole type using a parabolic-hyperbolic formulation of the vacuum constraint equations
- Asymptotically hyperboloidal initial data sets from a parabolic-hyperbolic formulation of the Einstein vacuum constraints