Adaptive Mesh Methods and Software for Time-dependent Partial Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Adaptive Mesh Methods and Software for Time-dependent Partial Differential Equations write by Shengtai Li. This book was released on 1998. Adaptive Mesh Methods and Software for Time-dependent Partial Differential Equations available in PDF, EPUB and Kindle.
Adaptive Moving Mesh Methods
Adaptive Moving Mesh Methods - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Adaptive Moving Mesh Methods write by Weizhang Huang. This book was released on 2010-10-26. Adaptive Moving Mesh Methods available in PDF, EPUB and Kindle. This book is about adaptive mesh generation and moving mesh methods for the numerical solution of time-dependent partial differential equations. It presents a general framework and theory for adaptive mesh generation and gives a comprehensive treatment of moving mesh methods and their basic components, along with their application for a number of nontrivial physical problems. Many explicit examples with computed figures illustrate the various methods and the effects of parameter choices for those methods. Graduate students, researchers and practitioners working in this area will benefit from this book.
An adaptive mesh moving and local refinement method for time-dependent partial differential equations
An adaptive mesh moving and local refinement method for time-dependent partial differential equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An adaptive mesh moving and local refinement method for time-dependent partial differential equations write by David C. Arney. This book was released on 1987. An adaptive mesh moving and local refinement method for time-dependent partial differential equations available in PDF, EPUB and Kindle.
Adjoint-guided Adaptive Mesh Refinement for Hyperbolic Systems of Equations
Adjoint-guided Adaptive Mesh Refinement for Hyperbolic Systems of Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Adjoint-guided Adaptive Mesh Refinement for Hyperbolic Systems of Equations write by Brisa N. Davis. This book was released on 2018. Adjoint-guided Adaptive Mesh Refinement for Hyperbolic Systems of Equations available in PDF, EPUB and Kindle. One difficulty in developing numerical methods for time-dependent partial differential equations is the fact that solutions contain time-varying regions where much higher resolution is required than elsewhere in the domain. The open source Clawpack software implements block-structured adaptive mesh refinement to selectively refine around propagating waves in the AMRClaw and GeoClaw packages. In particular, GeoClaw is widely used for tsunami modeling, the application that motivated this work. For problems where the solution must be computed over a large domain but is only of interest in one small area (e.g. one coastal community when doing tsunami modeling, or the location of a pressure gauge when doing acoustics modeling), a method that allows identifying and refining the grid only in regions that influence this target area would significantly reduce the computational cost of finding a solution. The adaptive mesh refinement approach currently implemented in AMRClaw and GeoClaw often refines waves that will not impact the target area. To remedy this, we seek a method that enables the identification and refinement of only the waves that will influence the location of interest. In this work we show that solving the time-dependent adjoint equation and using a suitable inner product with either the forward solution, or the estimated one-step error in the forward solution, allows for a more precise refinement of the relevant waves. We present the adjoint methodology first in one space dimension for illustration and in a broad context since it could also be used in other adaptive software, and for other tsunami applications beyond adaptive mesh refinement. We then show how this adjoint method has been integrated into the adaptive mesh refinement strategy of the open source AMRClaw and GeoClaw software and present linear variable coefficient acoustics and tsunami modeling results showing that the accuracy of the solution is maintained and the computational time required is significantly reduced through the integration of the adjoint method into adaptive mesh refinement. The adjoint method is compared to adaptive mesh refinement methods already available in the AMRClaw software, and the advantages and disadvantages of using the adjoint method are discussed. Other capabilities of the adjoint method such as focusing on specific time ranges of interest, sensitivity analysis, and source impact analysis and design are also presented. The new algorithms are incorporated in Clawpack and code for the examples presented in this work is archived on Github.
Numerical Time-Dependent Partial Differential Equations for Scientists and Engineers
Numerical Time-Dependent Partial Differential Equations for Scientists and Engineers - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Time-Dependent Partial Differential Equations for Scientists and Engineers write by Moysey Brio. This book was released on 2010-09-21. Numerical Time-Dependent Partial Differential Equations for Scientists and Engineers available in PDF, EPUB and Kindle. It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc. The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them. In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability analysis in the presence of the boundaries and interfaces; Treatment of problems with different temporal/spatial scales either explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes. Self contained presentation of key issues in successful numerical simulation Accessible to scientists and engineers with diverse background Provides analysis of the dispersion relation, symmetries, particular solutions and instabilities of the partial differential equations
