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| Product DetailsОсновная информация | |
| ISBN-13Номер книги | 9781243983107 |
| Authorавтор | Vasileios Paschalidis |
| FormatВерсия | Оплата в мягкой обложке |
| Pages NumberКоличество страниц | Страницы 188 |
| PublisherИздатель | Proquest, Umi Dissertation Publishing |
| Publication DateДата публикации | 10 сентября 2011 г. |
| Product DimensionsРазмер товара | 24.6 x 18.9 x 1 cm |
| Shipping WeightТоварный вес | 345 g |
| LanguageЯзык | Английский |
Book Descriptionкраткое введение
In this thesis we carry out a theoretical and numerical study of different 3+1 formulations of General Relativity (GR) which have direct applications to numerical relativity. In particular, we introduce a method to analyze the well-posedness of constrained evolution of the Einstein equations and show that the well-posedness of constrained evolution of the Arnowitt-Deser-Misner (ADM), Baumgarte-Shapiro-Shibata-Nakamura (BSSN) and formulations which resemble the Kidder-Scheel-Teukolsky (KST) one, depends entirely on the properties of the gauge. Driven by this result, we introduce two new well-posed formulations of GR. The first one is a parabolization of the ADM formulation, which we call the PADM formulation, and is derived by addition of combinations of the constraints and their derivatives to the RHS of the ADM evolution equations. The desirable property of PADM is that it turns the surface of constraints into a local attractor because its constraint propagation system becomes second-order parabolic independently of the gauge conditions employed. The PADM system may be classified as mixed hyperbolic---second-order parabolic (MHSP). The second formulation is a parabolization of the KST formulation, which we call the PKST formulation, and is a manifestly MHSP set of equations. We carry out a stability analysis of flat space and demonstrate that the PADM system exponentially damps and smoothes all constraint violating modes. Finally, we describe a numerical implementation of the PADM formulation and study its accuracy and stability in a series of standard numerical tests. We show that the PADM scheme is numerically stable, convergent and second-order accurate, and we compare its numerical properties with those of standard ADM and its hyperbolic KST extension. We demonstrate that PADM has better control of the constraint-violating modes than ADM and KST.