The evolution of hyperboloidal data with the dual foliation formalism: Mathematical analysis and wave equation tests
| Autor: | Hannes R. Rüter, Marcus Bugner, Bernd Brügmann, Enno Harms, David Hilditch |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Physics
Physics and Astronomy (miscellaneous) 010308 nuclear & particles physics Eikonal equation Mathematical analysis FOS: Physical sciences General Relativity and Quantum Cosmology (gr-qc) Wave equation 01 natural sciences Central region General Relativity and Quantum Cosmology Nonlinear system Formalism (philosophy of mathematics) Theory of relativity 0103 physical sciences Boundary value problem 010306 general physics |
| Popis: | A long-standing problem in numerical relativity is the satisfactory treatment of future null-infinity. We propose an approach for the evolution of hyperboloidal initial data in which the outer boundary of the computational domain is placed at infinity. The main idea is to apply the `dual foliation' formalism in combination with hyperboloidal coordinates and the generalized harmonic gauge formulation. The strength of the present approach is that, following the ideas of Zenginoglu, a hyperboloidal layer can be naturally attached to a central region using standard coordinates of numerical relativity applications. Employing a generalization of the standard hyperboloidal slices, developed by Calabrese et. al., we find that all formally singular terms take a trivial limit as we head to null-infinity. A byproduct is a numerical approach for hyperboloidal evolution of nonlinear wave equations violating the null-condition. The height-function method, used often for fixed background spacetimes, is generalized in such a way that the slices can be dynamically `waggled' to maintain the desired outgoing coordinate lightspeed precisely. This is achieved by dynamically solving the eikonal equation. As a first numerical test of the new approach we solve the 3D flat space scalar wave equation. The simulations, performed with the pseudospectral bamps code, show that outgoing waves are cleanly absorbed at null-infinity and that errors converge away rapidly as resolution is increased. 29 pages, 5 figures, 2 tables |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|