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Author: Publisher: ISBN: Category : Languages : en Pages : 13
Book Description
The authors develop software tools for the solution of conservation laws using parallel adaptive discontinuous Galerkin methods. In particular, the Rensselaer Partition Model (RPM) provides parallel mesh structures within an adaptive framework to solve the Euler equations of compressible flow by a discontinuous Galerkin method (LOCO). Results are presented for a Rayleigh-Taylor flow instability for computations performed on 128 processors of an IBM SP computer. In addition to managing the distributed data and maintaining a load balance, RPM provides information about the parallel environment that can be used to tailor partitions to a specific computational environment.
Author: Publisher: ISBN: Category : Languages : en Pages : 13
Book Description
The authors develop software tools for the solution of conservation laws using parallel adaptive discontinuous Galerkin methods. In particular, the Rensselaer Partition Model (RPM) provides parallel mesh structures within an adaptive framework to solve the Euler equations of compressible flow by a discontinuous Galerkin method (LOCO). Results are presented for a Rayleigh-Taylor flow instability for computations performed on 128 processors of an IBM SP computer. In addition to managing the distributed data and maintaining a load balance, RPM provides information about the parallel environment that can be used to tailor partitions to a specific computational environment.
Author: Bernardo Cockburn Publisher: Springer Science & Business Media ISBN: 3642597211 Category : Mathematics Languages : en Pages : 468
Book Description
A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.
Author: Andrew Giuliani Publisher: ISBN: Category : Conservation laws (Mathematics) Languages : en Pages :
Book Description
This thesis is concerned with the parallel, adaptive solution of hyperbolic conservation laws on unstructured meshes. First, we present novel algorithms for cell-based adaptive mesh refinement (AMR) on unstructured meshes of triangles on graphics processing units (GPUs). Our implementation makes use of improved memory management techniques and a coloring algorithm for avoiding race conditions. The algorithm is entirely implemented on the GPU, with negligible communication between device and host. We show that the overhead of the AMR subroutines is small compared to the high-order solver and that the proportion of total run time spent adaptively refining the mesh decreases with the order of approximation. We apply our code to a number of benchmarks as well as more recently proposed problems for the Euler equations that require extremely high resolution. We present the solution to a shock reflection problem that addresses the von Neumann triple point paradox. We also study the problem of shock disappearance and self-similar diffraction of weak shocks around thin films. Next, we analyze the stability and accuracy of second-order limiters for the discontinuous Galerkin method on unstructured triangular grids. We derive conditions for a limiter such that the numerical solution preserves second order accuracy and satisfies the local maximum principle. This leads to a new measure of cell size that is approximately twice as large as the radius of the inscribed circle. It is shown with numerical experiments that the resulting bound on the time step is tight. We also consider various combinations of limiting points and limiting neighborhoods and present numerical experiments comparing the accuracy, stability, and efficiency of the corresponding limiters. We show that the theory for strong stability preserving (SSP) time stepping methods employed with the method of lines-type discretizations of hyperbolic conservation laws may result in overly stringent time step restrictions. We analyze a fully discrete finite volume method with slope reconstruction and a second order SSP Runge-Kutta time integrator to show that the maximum stable time step can be increased over the SSP limit. Numerical examples show that this result extends to two-dimensional problems on triangular meshes. Finally, we propose a moment limiter for the discontinuous Galerkin method applied to hyperbolic conservation laws in two and three dimensions. The limiter works by finding directions in which the solution coefficients can be separated and limits them independently of one another by comparing to forward and backward reconstructed differences. The limiter has a precomputed stencil of constant size, which provides computational advantages in terms of implementation and runtime. We provide examples that demonstrate stability and second order accuracy of solutions.
Author: Jack Dongarra Publisher: Springer ISBN: 354033498X Category : Computers Languages : en Pages : 1195
Book Description
This book constitutes the refereed proceedings of the 7th International Conference on Applied Parallel Computing, PARA 2004, held in June 2004. The 118 revised full papers presented together with five invited lectures and 15 contributed talks were carefully reviewed and selected for inclusion in the proceedings. The papers are organized in topical sections.
Author: Abdalkader Baggag Publisher: ISBN: Category : Computational grids (Computer systems) Languages : en Pages : 14
Book Description
Abstract: "This paper describes a parallel implementation of the discontinuous Galerkin method. Discontinuous Galerkin is a spatially compact method that retains its accuracy and robustness on non-smooth unstructured grids and is well suited for time dependent simulations. Several parallelization approaches are studied and evaluated. The most natural and symmetric of the approaches has been implemented in an object-oriented code used to simulate aeroacoustic scattering. The parallel implementation is MPI-based and has been tested on various parallel platforms such as the SGI Origin, IBM SP2, and clusters of SGI and Sun workstations. The scalability results presented for the SGI Origin show slightly superlinear speedup on a fixed-size problem due to cache effects."
Author: V.S. Sunderam Publisher: Springer Science & Business Media ISBN: 3540260439 Category : Computers Languages : en Pages : 1160
Book Description
The three-volume set LNCS 3514-3516 constitutes the refereed proceedings of the 5th International Conference on Computational Science, ICCS 2005, held in Atlanta, GA, USA in May 2005. The 464 papers presented were carefully reviewed and selected from a total of 834 submissions for the main conference and its 21 topical workshops. The papers span the whole range of computational science, ranging from numerical methods, algorithms, and computational kernels to programming environments, grids, networking, and tools. These fundamental contributions dealing with computer science methodologies and techniques are complemented by papers discussing computational applications and needs in virtually all scientific disciplines applying advanced computational methods and tools to achieve new discoveries with greater accuracy and speed.
Author: Radostina Petrova Publisher: BoD – Books on Demand ISBN: 9535128191 Category : Computers Languages : en Pages : 276
Book Description
The finite element method (FEM) is a numerical technique for finding approximate solutions to different numerical problems. The practical applications of FEM are known as finite element analysis (FEA). FEA is a good choice for analyzing problems over complicated domains. The first three chapters of this book contribute to the development of new FE techniques by examining a few key hurdles of the FEM and proposing techniques to mitigate them. The next four chapters focus on the close connection between the development of a new technique and its implementation. Current state-of-the-art software packages for FEA allow the construction, refinement, and optimization of entire designs before manufacturing. This is convincingly demonstrated in the last three chapters of the book with examples from the field of biomechanical engineering. This book presents a current research by highlighting the vitality and potential of the finite elements for the future development of more efficient numerical techniques, new areas of application, and FEA's important role in practical engineering.
Author: Are Magnus Bruaset Publisher: Springer Science & Business Media ISBN: 3540316191 Category : Mathematics Languages : en Pages : 491
Book Description
Since the dawn of computing, the quest for a better understanding of Nature has been a driving force for technological development. Groundbreaking achievements by great scientists have paved the way from the abacus to the supercomputing power of today. When trying to replicate Nature in the computer’s silicon test tube, there is need for precise and computable process descriptions. The scienti?c ?elds of Ma- ematics and Physics provide a powerful vehicle for such descriptions in terms of Partial Differential Equations (PDEs). Formulated as such equations, physical laws can become subject to computational and analytical studies. In the computational setting, the equations can be discreti ed for ef?cient solution on a computer, leading to valuable tools for simulation of natural and man-made processes. Numerical so- tion of PDE-based mathematical models has been an important research topic over centuries, and will remain so for centuries to come. In the context of computer-based simulations, the quality of the computed results is directly connected to the model’s complexity and the number of data points used for the computations. Therefore, computational scientists tend to ?ll even the largest and most powerful computers they can get access to, either by increasing the si e of the data sets, or by introducing new model terms that make the simulations more realistic, or a combination of both. Today, many important simulation problems can not be solved by one single computer, but calls for parallel computing.
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Author: Bernardo Cockburn
Author: Andrew Giuliani
Author: Jack Dongarra
Author: Abdalkader Baggag
Author: V.S. Sunderam
Author: Radostina Petrova
Author: Are Magnus Bruaset
Author: Arieh Iserles
Author: Willem Hundsdorfer