Download or read book Adaptive Mesh Refinement for Pseudospectral Methods in Numerical Relativity written by Sarah Renkhoff and published by . This book was released on 2023* with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Across all of computational physics, a central problem is that of discretization, from the choice of resolution in simple finite difference approaches, to the details of more intricate discretization schemes such as spectral elements. The choice of discretization decides the numerical solution space, as well as the properties of numerical methods, such as their convergence and stability. For this reason, the effective use of any numerical scheme requires a proper understanding of the underlying discretization scheme and its parameters. In particular, modern numerical methods often incorporate adaptive discretization schemes, utilizing heterogeneous meshes that change with time. In this work, we will explore one such method in the form of a state-of-the-art numerical relativity code, and the implementation of an adaptive mesh refinement (AMR) scheme within it. We describe in detail its features, and the resulting properties as it is used to solve physical problems in the form of hyperbolic partial differential equations, and we examine the scaling behavior of the resulting method. We also present results obtained using this scheme, in the form of simulations of the critical collapse of gravitational waves, that were made possible by the AMR system, showing some evidence of both self-similarity and universality in this system. Finally, we study a suite of several challenging test cases, beginning with a simple two-dimensional wave equation with an added nonlinearity, which results in critical behavior for certain choices of initial data, then moving on to the collapse of a real scalar field minimally coupled to general relativity in spherical symmetry. Finally, we use the collapse of gravitational waves in vacuum in axisymmetry as our third test case. We use these example problems to evaluate the gains in terms of accuracy, as well as efficiency, that are obtained through the use of adaptive resolutions.
Download or read book Adaptive Mesh Refinement in Numerical Relativity written by Lee Ashton Wild and published by . This book was released on 1996 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Frontiers in Numerical Relativity written by Charles R. Evans and published by Cambridge University Press. This book was released on 1989-04-13 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1989 text will be of value to those who wish to understand developments in computer studies of general relativity at the time of publication.
Download or read book Numerical Relativity written by Masaru Shibata and published by World Scientific. This book was released on 2015-11-05 with total page 844 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is composed of two parts: First part describes basics in numerical relativity, that is, the formulations and methods for a solution of Einstein's equation and general relativistic matter field equations. This part will be helpful for beginners of numerical relativity who would like to understand the content of numerical relativity and its background. The second part focuses on the application of numerical relativity. A wide variety of scientific numerical results are introduced focusing in particular on the merger of binary neutron stars and black holes."--
Download or read book Adaptive Mesh Refinement Theory and Applications written by Tomasz Plewa and published by Springer Science & Business Media. This book was released on 2005-12-20 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced numerical simulations that use adaptive mesh refinement (AMR) methods have now become routine in engineering and science. Originally developed for computational fluid dynamics applications these methods have propagated to fields as diverse as astrophysics, climate modeling, combustion, biophysics and many others. The underlying physical models and equations used in these disciplines are rather different, yet algorithmic and implementation issues facing practitioners are often remarkably similar. Unfortunately, there has been little effort to review the advances and outstanding issues of adaptive mesh refinement methods across such a variety of fields. This book attempts to bridge this gap. The book presents a collection of papers by experts in the field of AMR who analyze past advances in the field and evaluate the current state of adaptive mesh refinement methods in scientific computing.
Download or read book General Relativistic Numerical Simulations with Adaptive Mesh Refinement written by Jian Tao and published by . This book was released on 2008 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scalar Fields in Numerical General Relativity written by Katy Clough and published by Springer. This book was released on 2018-06-16 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the use of numerical relativity (NR) methods to solve cosmological problems, and describes one of the first uses of NR to study inflationary physics. NR consists in the solution of Einstein’s Equation of general relativity, which governs the evolution of matter and energy on cosmological scales, and in systems where there are strong gravitational effects, such as around black holes. To date, NR has mainly been used for simulating binary black hole and neutron star mergers like those detected recently by LIGO. Its use as a tool in fundamental problems of gravity and cosmology is novel, but rapidly gaining interest. In this thesis, the author investigates the initial condition problem in early universe cosmology – whether an inflationary expansion period could have “got going” from initially inhomogeneous conditions – and identifies criteria for predicting the robustness of particular models. State-of-the-art numerical relativity tools are developed in order to address this question, which are now publicly available.
Download or read book General Relativity and Gravitation written by Abhay Ashtekar and published by Cambridge University Press. This book was released on 2015-06-01 with total page 697 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore spectacular advances in cosmology, relativistic astrophysics, gravitational wave science, mathematics, computational science, and the interface of gravitation and quantum physics with this unique celebration of the centennial of Einstein's discovery of general relativity. Twelve comprehensive and in-depth reviews, written by a team of world-leading international experts, together present an up-to-date overview of key topics at the frontiers of these areas, with particular emphasis on the significant developments of the last three decades. Interconnections with other fields of research are also highlighted, making this an invaluable resource for both new and experienced researchers. Commissioned by the International Society on General Relativity and Gravitation, and including accessible introductions to cutting-edge topics, ample references to original research papers, and informative colour figures, this is a definitive reference for researchers and graduate students in cosmology, relativity, and gravitational science.
Download or read book Adaptive Mesh Strategies for the Spectral Element Method written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1992 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: An adaptive spectral element method has been developed for the efficient solution of time dependent partial differential equations. Adaptive mesh strategies that include resolution refinement and coarsening by three different methods are illustrated on solutions to the one-dimensional viscous Burgers equation and the two-dimensional Navier-Stokes equations for driven flow in a cavity. Sharp gradients, singularities and regions of poor resolution are resolved optimally as they develop in time using error estimators which indicate the choice of refinement to be used. The adaptive formulation presents significant increases in efficiency, flexibility and general capabilities for high order spectral methods.
Download or read book An Adaptive Mesh Refinement Method for the Korteweg de Vries Equation written by E. S. Fraga and published by . This book was released on 1987 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Physics Briefs written by and published by . This book was released on 1992 with total page 1434 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Adaptive Mesh Methods and Software for Time dependent Partial Differential Equations written by Shengtai Li and published by . This book was released on 1998 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Physics of the Early Universe written by Eleftherios Papantonopoulos and published by Springer Science & Business Media. This book was released on 2005-01-07 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Physics of the Early Universe is an edited and expanded version of the lectures given at a recent summer school of the same name. Its aim is to present an advanced multi-authored textbook that meets the needs of both postgraduate students and young researchers interested in, or already working on, problems in cosmology and general relativity, with emphasis on the early universe. A particularly strong feature of the present work is the constructive-critical approach to the present mainstream theories, the careful assessment of some alternative approaches, and the overall balance between theoretical and observational considerations. As such, this book will also benefit experienced scientists and nonspecialists from related areas of research.
Download or read book An Adaptive Mesh Moving and Local Refinement Method for Time Dependent Partial Differential Equations written by and published by . This book was released on 1990 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: We discuss mesh-moving, static mesh regeneration, and local mesh-refinement algorithms that can be used with a finite difference or finite element scheme to solve initial boundary value problems for vector systems of time-dependent partial differential equations in two space dimensions and time. A coarse based mesh of quadrilateral cells is moved by an algebraic mesh-movement function so as to follow and isolate spatially distinct phenomena. The local mesh-refinement method recursively divides the time step and spatial cells of the moving base mesh in regions where error indicators are high until a prescribed tolerance is satisfied. The static mesh-regeneration procedure is used to create a new base mesh when the existing one becomes to distorted. The adaptive methods have been combined with a MacCormack finite difference scheme for hyperbolic systems and an error indicator based upon estimates of the local discretization error obtained by Richardson extrapolation. Results are presented for several computational examples.
Download or read book Special Issue on Adaptive Mesh Refinement Methods for CFD Applications written by Rupak Biswas and published by . This book was released on 1996 with total page 2 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Relativistic Hydrodynamics written by Luciano Rezzolla and published by Oxford University Press, USA. This book was released on 2013-09-26 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an up-to-date, lively and approachable introduction to the mathematical formalism, numerical techniques and applications of relativistic hydrodynamics. The topic is presented here in a form which will be appreciated both by students and researchers in the field.
Download or read book General Relativity Cosmology and Astrophysics written by Jiří Bičák and published by Springer. This book was released on 2014-06-12 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles included in this Volume represent a broad and highly qualified view on the present state of general relativity, quantum gravity, and their cosmological and astrophysical implications. As such, it may serve as a valuable source of knowledge and inspiration for experts in these fields, as well as an advanced source of information for young researchers. The occasion to gather together so many leading experts in the field was to celebrate the centenary of Einstein's stay in Prague in 1911-1912. It was in fact during his stay in Prague that Einstein started in earnest to develop his ideas about general relativity that fully developed in his paper in 1915. Approaching soon the centenary of his famous paper, this volume offers a precious overview of the path done by the scientific community in this intriguing and vibrant field in the last century, defining the challenges of the next 100 years. The content is divided into four broad parts: (i) Gravity and Prague, (ii) Classical General Relativity, (iii) Cosmology and Quantum Gravity, and (iv) Numerical Relativity and Relativistic Astrophysics.
