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Unstructured Space Time Finite Element Methods In Four Dimensions
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Book Synopsis Unstructured Space-Time Finite Element Methods in Four Dimensions by : David Charles Lenz
Download or read book Unstructured Space-Time Finite Element Methods in Four Dimensions written by David Charles Lenz and published by . This book was released on 2020 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large-scale simulations of time-dependent partial differential equations are, at present, largely reliant on massively parallel computers. As a result, the parallel scalability of numerical methods for partial differential equations is of crucial importance. In recent years, continuous space-time finite element methods have emerged as a promising technique for approximating these equations in a scalable, flexible way. In a space-time finite element method, the space and time variables of a time-dependent equation are treated as a single unified variable in higher-dimensional space. The higher-dimensional space-time domain is discretized into a collection of simplices and finite element methods may then be defined over this discretization. Parallelization is then achieved through domain decomposition techniques. In this dissertation, we extend the theory of space-time finite element methods to a more general class of problems. We prove new theoretical results describing the stability of space-time methods applied to parabolic partial differential equations with nontrivial convection and reaction terms. In particular, we define a streamline-upwind scheme which upwinds in the direction of the space-time convection. The stabilized method is proved to be coercive with respect to an energy norm and asymptotic error bounds are derived. This dissertation also proposes several operations for the construction and refinement of unstructured, conforming four-dimensional simplex meshes. We define a simple algorithm which takes as input any tetrahedral mesh and produces a corresponding four-dimensional, simplicial space-time mesh. Our algorithm always produces conforming triangulations and may be run concurrently for each spatial element. In addition, we describe how four-dimensional simplex elements can be bisected in order to achieve local spatiotemporal refinement.
Book Synopsis Adaptive Unstructured Spacetime Meshing for Four-dimensional Spacetime Discontinuous Galerkin Finite Element Methods by :
Download or read book Adaptive Unstructured Spacetime Meshing for Four-dimensional Spacetime Discontinuous Galerkin Finite Element Methods written by and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Unstructured Space-time Finite Element Method of Heat Conduction by : Chi-Kyung Kim
Download or read book Unstructured Space-time Finite Element Method of Heat Conduction written by Chi-Kyung Kim and published by . This book was released on 1992 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Element Analysis with Error Estimators by : J. E. Akin
Download or read book Finite Element Analysis with Error Estimators written by J. E. Akin and published by Elsevier. This book was released on 2005-06-22 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: This key text is written for senior undergraduate and graduate engineering students. It delivers a complete introduction to finite element methods and to automatic adaptation (error estimation) that will enable students to understand and use FEA as a true engineering tool. It has been specifically developed to be accessible to non-mathematics students and provides the only complete text for FEA with error estimators for non-mathematicians. Error estimation is taught on nearly half of all FEM courses for engineers at senior undergraduate and postgraduate level; no other existing textbook for this market covers this topic. The only introductory FEA text with error estimation for students of engineering, scientific computing and applied mathematics Includes source code for creating and proving FEA error estimators
Book Synopsis Space-Time Methods by : Ulrich Langer
Download or read book Space-Time Methods written by Ulrich Langer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-09-23 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an introduction to modern space-time discretization methods such as finite and boundary elements and isogeometric analysis for time-dependent initial-boundary value problems of parabolic and hyperbolic type. Particular focus is given on stable formulations, error estimates, adaptivity in space and time, efficient solution algorithms, parallelization of the solution pipeline, and applications in science and engineering.
Book Synopsis Mesh-Free and Finite Element-Based Methods for Structural Mechanics Applications by : Nicholas Fantuzzi
Download or read book Mesh-Free and Finite Element-Based Methods for Structural Mechanics Applications written by Nicholas Fantuzzi and published by MDPI. This book was released on 2021-01-27 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of solving complex engineering problems has always been a major topic in all industrial fields, such as aerospace, civil and mechanical engineering. The use of numerical methods has increased exponentially in the last few years, due to modern computers in the field of structural mechanics. Moreover, a wide range of numerical methods have been presented in the literature for solving such problems. Structural mechanics problems are dealt with using partial differential systems of equations that might be solved by following the two main classes of methods: Domain-decomposition methods or the so-called finite element methods and mesh-free methods where no decomposition is carried out. Both methodologies discretize a partial differential system into a set of algebraic equations that can be easily solved by computer implementation. The aim of the present Special Issue is to present a collection of recent works on these themes and a comparison of the novel advancements of both worlds in structural mechanics applications.
Book Synopsis Theoretical And Computational Acoustics '95 by : Ding Lee
Download or read book Theoretical And Computational Acoustics '95 written by Ding Lee and published by World Scientific. This book was released on 1996-08-30 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: This conference provided a forum for active researchers to discuss the state-of-the-art in theoretical and computational acoustics. Topics covered fluid/elastic interface-theoretical and computational aspects with applications, seismic waves and earthquake studies, modeling, theoretical and computational aspects for multidimensional wave propagation, methods for computational acoustics, structural acoustics, scattering and inverse problems, solutions to acoustic problems by supercomputers and parallel processing, and application of neural networks to acoustics.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Methods by : George Em Karniadakis
Download or read book Numerical Methods written by George Em Karniadakis and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-04-15 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This third volume collects authoritative chapters covering several numerical aspects of fractional calculus, including time and space fractional derivatives, finite differences and finite elements, and spectral, meshless, and particle methods.
Book Synopsis Moving Space-time Finite Element Methods for Convection-diffusion Problems by : Rafael Brigham Neves Ferreira Santos
Download or read book Moving Space-time Finite Element Methods for Convection-diffusion Problems written by Rafael Brigham Neves Ferreira Santos and published by . This book was released on 1991 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Two-dimensional, Three-dimensional and Four-dimensional Anisotropic Mesh Adaptation for the Time-continuous Space-time Finite Element Method with Applications to the Incompressible Navier-Stokes Equations by : Pascal Tremblay
Download or read book Two-dimensional, Three-dimensional and Four-dimensional Anisotropic Mesh Adaptation for the Time-continuous Space-time Finite Element Method with Applications to the Incompressible Navier-Stokes Equations written by Pascal Tremblay and published by . This book was released on 2007 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Enhanced Material, Parts Optimization and Process Intensification by : Uwe Reisgen
Download or read book Enhanced Material, Parts Optimization and Process Intensification written by Uwe Reisgen and published by Springer Nature. This book was released on 2021-03-07 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reports on topics at the interface between material processing, product and process optimization. It covers new developments and challenges in welding, brazing, cutting and coating, casting and molding, additive manufacturing, simulation and optimization techniques, as well as functional and structural materials and composites. Gathering authoritative contributions on the latest research and applications, presented at the International Joint Conference on Enhanced Material and Part Optimization and Process Intensification, EMPOrIA 2020, organized by SFB1120 Aachen, SFB814 Erlangen and CCE Darmstadt, on May 19–20, 2020, in Aachen, this book provides academics, students, and professionals with a timely snapshot of the main research trends, and extensive information on cutting-edge methods and technologies in materials, manufacturing and process engineering.
Book Synopsis Large-Scale Scientific Computing by : Ivan Lirkov
Download or read book Large-Scale Scientific Computing written by Ivan Lirkov and published by Springer Nature. This book was released on 2020-02-13 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes revised papers from the 12th International Conference on Large-Scale Scientific Computing, LSSC 2019, held in Sozopol, Bulgaria, in June 2019. The 70 papers presented in this volume were carefully reviewed and selected from 81 submissions. The book also contains two invited talks. The papers were organized in topical sections named as follows: control and optimization of dynamical systems; meshfree and particle methods; fractional diffusion problems: numerical methods, algorithms and applications; pore scale flow and transport simulation; tensors based algorithms and structures in optimization and applications; HPC and big data: algorithms and applications; large-scale models: numerical methods, parallel computations and applications; monte carlo algorithms: innovative applications in conjunctions with other methods; application of metaheuristics to large-scale problems; large scale machine learning: multiscale algorithms and performance guarantees; and contributed papers.
Book Synopsis Proceedings of the ASME Noise Control and Acoustics Division by :
Download or read book Proceedings of the ASME Noise Control and Acoustics Division written by and published by . This book was released on 2003 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Finite Element Method for Initial Value Problems by : Karan S. Surana
Download or read book The Finite Element Method for Initial Value Problems written by Karan S. Surana and published by CRC Press. This book was released on 2017-10-17 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike most finite element books that cover time dependent processes (IVPs) in a cursory manner, The Finite Element Method for Initial Value Problems: Mathematics and Computations focuses on the mathematical details as well as applications of space-time coupled and space-time decoupled finite element methods for IVPs. Space-time operator classification, space-time methods of approximation, and space-time calculus of variations are used to establish unconditional stability of space-time methods during the evolution. Space-time decoupled methods are also presented with the same rigor. Stability of space-time decoupled methods, time integration of ODEs including the finite element method in time are presented in detail with applications. Modal basis, normal mode synthesis techniques, error estimation, and a posteriori error computations for space-time coupled as well as space-time decoupled methods are presented. This book is aimed at a second-semester graduate level course in FEM.
Book Synopsis Proper Orthogonal Decomposition Methods for Partial Differential Equations by : Zhendong Luo
Download or read book Proper Orthogonal Decomposition Methods for Partial Differential Equations written by Zhendong Luo and published by Academic Press. This book was released on 2018-11-26 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proper Orthogonal Decomposition Methods for Partial Differential Equations evaluates the potential applications of POD reduced-order numerical methods in increasing computational efficiency, decreasing calculating load and alleviating the accumulation of truncation error in the computational process. Introduces the foundations of finite-differences, finite-elements and finite-volume-elements. Models of time-dependent PDEs are presented, with detailed numerical procedures, implementation and error analysis. Output numerical data are plotted in graphics and compared using standard traditional methods. These models contain parabolic, hyperbolic and nonlinear systems of PDEs, suitable for the user to learn and adapt methods to their own R&D problems. Explains ways to reduce order for PDEs by means of the POD method so that reduced-order models have few unknowns Helps readers speed up computation and reduce computation load and memory requirements while numerically capturing system characteristics Enables readers to apply and adapt the methods to solve similar problems for PDEs of hyperbolic, parabolic and nonlinear types
Book Synopsis Galerkin Finite Element Methods for Parabolic Problems by : V. Thomee
Download or read book Galerkin Finite Element Methods for Parabolic Problems written by V. Thomee and published by Springer. This book was released on 2006-11-14 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt:
