Download or read book Local Space time Adaptive Finite Element Methods for the Wave Equation on Unbounded Domains written by Dantong He and published by . This book was released on 2003 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Element and Discontinuous Galerkin Methods for Transient Wave Equations written by Gary Cohen and published by Springer. This book was released on 2016-08-05 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem of its spurious-free approximations. Treatment of unbounded domains by Absorbing Boundary Conditions (ABC) and Perfectly Matched Layers (PML) is described and analyzed in a separate chapter. The two last chapters deal with time approximation including local time-stepping and with the study of some complex models, i.e. acoustics in flow, gravity waves and vibrating thin plates. Throughout, emphasis is put on the accuracy and computational efficiency of the methods, with attention brought to their practical aspects.This monograph also covers in details the theoretical foundations and numerical analysis of these methods. As a result, this monograph will be of interest to practitioners, researchers, engineers and graduate students involved in the numerical simulationof waves.
Download or read book A Local Refinement Finite Element Method for Time Dependent Partial Differential Equations written by J. E. Flaherty and published by . This book was released on 1984 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors discuss an adaptive local refinement finite element method for solving initial-boundary value problems for vector systems of partial differential equations in one space dimension and time. The method ues piecewise bilinear rectangular space-time finite elements. For each time step, grids are automatically added to regions where the local discretization error is estimated as being larger than a prescribed tolerance. The authors discuss several aspects oof their algorithm, including the tree structure that is used to represent the finite element solution and grids, an error estimation technique, and initial boundary conditions at coarse-fine mesh interfaces. The authors also present computational results for a simple linear hyperbolic problem, a problem involving Burger's equation, and a model combustion problem. Originator-supplied keywords include: Adaptive methods, Finite element methods, Local refinement, and Time dependent problems.
Download or read book Higher Order Numerical Methods for Transient Wave Equations written by Gary Cohen and published by Springer Science & Business Media. This book was released on 2001-11-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: "To my knowledge [this] is the first book to address specifically the use of high-order discretizations in the time domain to solve wave equations. [...] I recommend the book for its clear and cogent coverage of the material selected by its author." --Physics Today, March 2003
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.
Download or read book Computational Methods for Acoustics Problems written by Frédéric Magoulès and published by . This book was released on 2008 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This volume presents in eleven chapters key computational methods for acoustics and vibro-acoustics problems. Each chapter, written by different authors, presents a state of the art of well-established or innovative methods, techniques or algorithms. A bibliography is included at the end of each chapter."--BOOK JACKET.
Download or read book Proceedings of the ASME Noise Control and Acoustics Division written by and published by . This book was released on 2004 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Space Time Discretization of Elasto Acoustic Wave Equation in Polynomial Trefftz DG Bases written by Elvira Shishenina and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discontinuous Finite Element Methods (DG FEM) have proven flexibility and accuracy for solving wave problems in complex media. However, they require a large number of degrees of freedom, which increases the corresponding computational cost compared with that of continuous finite element methods. Among the different variational approaches to solve boundary value problems, there exists a particular family of methods, based on the use of trial functions in the form of exact local solutions of the governing equations. The idea was first proposed by Trefftz in 1926, and since then it has been further developed and generalized. A Trefftz-DG variational formulation applied to wave problems reduces to surface integrals that should contribute to decreasing the computational costs.Trefftz-type approaches have been widely used for time-harmonic problems, while their implementation for time-dependent simulations is still limited. The feature of Trefftz-DG methods applied to time-dependent problems is in the use of space-time meshes. Indeed, standard DG methods lead to the construction of a semi-discrete system of ordinary differential equations in time which are integrated by using an appropriate scheme. But Trefftz-DG methods applied to wave problems lead to a global matrix including time and space discretizations which is huge and sparse. This significantly hampers the deployment of this technology for solving industrial problems.In this work, we develop a Trefftz-DG framework for solving mechanical wave problems including elasto-acoustic equations. We prove that the corresponding formulations are well-posed and we address the issue of solving the global matrix by constructing an approximate inverse obtained from the decomposition of the global matrix into a block-diagonal one. The inversion is then justified under a CFL-type condition. This idea allows for reducing the computational costs but its accuracy is limited to small computational domains. According to the limitations of the method, we have investigated the potential of Tent Pitcher algorithms following the recent works of Gopalakrishnan et al. It consists in constructing a space-time mesh made of patches that can be solved independently under a causality constraint. We have obtained very promising numerical results illustrating the potential of Tent Pitcher in particular when coupled with a Trefftz-DG method involving only surface terms. In this way, the space-time mesh is composed of elements which are 3D objects at most. It is also worth noting that this framework naturally allows for local time-stepping which is a plus to increase the accuracy while decreasing the computational burden.
Download or read book The Scaled Boundary Finite Element Method written by John P. Wolf and published by John Wiley & Sons. This book was released on 2003-03-14 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: A novel computational procedure called the scaled boundary finite-element method is described which combines the advantages of the finite-element and boundary-element methods : Of the finite-element method that no fundamental solution is required and thus expanding the scope of application, for instance to anisotropic material without an increase in complexity and that singular integrals are avoided and that symmetry of the results is automatically satisfied. Of the boundary-element method that the spatial dimension is reduced by one as only the boundary is discretized with surface finite elements, reducing the data preparation and computational efforts, that the boundary conditions at infinity are satisfied exactly and that no approximation other than that of the surface finite elements on the boundary is introduced. In addition, the scaled boundary finite-element method presents appealing features of its own : an analytical solution inside the domain is achieved, permitting for instance accurate stress intensity factors to be determined directly and no spatial discretization of certain free and fixed boundaries and interfaces between different materials is required. In addition, the scaled boundary finite-element method combines the advantages of the analytical and numerical approaches. In the directions parallel to the boundary, where the behaviour is, in general, smooth, the weighted-residual approximation of finite elements applies, leading to convergence in the finite-element sense. In the third (radial) direction, the procedure is analytical, permitting e.g. stress-intensity factors to be determined directly based on their definition or the boundary conditions at infinity to be satisfied exactly. In a nutshell, the scaled boundary finite-element method is a semi-analytical fundamental-solution-less boundary-element method based on finite elements. The best of both worlds is achieved in two ways: with respect to the analytical and numerical methods and with respect to the finite-element and boundary-element methods within the numerical procedures. The book serves two goals: Part I is an elementary text, without any prerequisites, a primer, but which using a simple model problem still covers all aspects of the method and Part II presents a detailed derivation of the general case of statics, elastodynamics and diffusion.
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2003 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Design and Analysis of Space time and Galerkin least squares Finite Element Methods for Fluid structure Interaction in Exterior Domains written by Stanford University. Division of Applied Mechanics. Division of Applied Mechanics and published by . This book was released on 1994 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Encyclopedia of Computational Mechanics written by Erwin Stein and published by . This book was released on 2004 with total page 870 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Encyclopedia of Computational Mechanics provides a comprehensive collection of knowledge about the theory and practice of computational mechanics.
Download or read book The Wave Finite Element Method written by Boris F. Shorr and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational mechanics, as a science employed for the numerical model ing of processes in nature and engineering, has over the last few decades developed two strands. The first concerns the putting of more and more powerful software packages into computational practice, using increas ingly high-performance computers with increasingly large memory. The traditional finite element and finite difference approaches are still preva lent. Over the years however, researchers have met with new problems; their solutions on the basis of traditional methods are at best difficult and at worst impossible to obtain. Such problems provided a powerful impetus in the development of the second strand, resulting in the development of es sentially new approaches for numerical modeling, for example meshless methods, "molecular" dynamics, neuron networks. The current state of the art formed the basis of many papers presented at the Fifth World Congress on Computational Mechanics, Vienna 2002. It is within the framework of the second strand that this book has been written.
Download or read book A Space time Finite Element Method for the Second Order Wave Equation written by Donald A. French and published by . This book was released on 1991 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Adaptive Finite Element Method I Solution Algorithm and Computational Examples written by and published by . This book was released on 1994 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: An adaptive finite element method is developed to solve initial boundary value problems for vector systems of parabolic partial differential equations in one space dimension and time. The differential equations are discretized in space using piecewise linear finite element approximations. Superconvergence properties and quadratic polynomials are used to derive a computation ally inexpensive approximation to the spatial component of the error. This technique is coupled with time integration schemes of successively higher orders to obtain an approximation of the temporal and total discretization errors. These approximate errors are used to control an adaptive mesh refinement strategy. Refinement is performed in space, time, or both space and time depending on the dominant component of the error estimate. A computer code coupling this refinement strategy and stable mesh movement has been written and applied to a number of problems. These computations confirm that proper mesh movement can reduce the computational efforts associated with mesh refinement.
Download or read book Analysis of Some Higher Order Space Time Moving Finite Element Methods written by Maximilian Sloan Metti and published by . This book was released on 2013 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a study of an application of finite element methods designed for convection-dominated, time-dependent partial differential equations. Specifically, this work analyzes finite element discretizations that employ moving meshes in order to solve linear differential equations over space-time domains. These methods can lead to significant savings in computation costs for problems having solutions that develop steep moving fronts, as moving meshes have the ability to track these fronts continuously with a high concentration of nodes; this flexibility allows for much larger time steps than standard tensor product finite elements, while maintaining high resolution of fine structures that sweep through the spatial domain. The main results are a priori and a posteriori error bounds for some moving finite element methods of high order and general time-stepping schemes. These finite element methods follow a method of lines approach for propagating the solution in time, though the error analysis places a strong emphasis on the properties inherited by the finite element aspects of the discrete problem. Another focus of this work is to determine practical and efficient schemes for adaptive meshing and mesh motion. As a result of this research, a solver has been written in C++ that is applicable to time-dependent linear convection-diffusion-reaction equations with a single dimension for the spatial.
Download or read book Local mesh local order adaptive finite element methods with a posteriori error estimators for elliptic partial differential equations v written by Alan Weiser and published by . This book was released on 1981 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt:
