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General Framework For Achieving Textbook Multigrid Efficiency
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Book Synopsis General Framework for Achieving Textbook Multigrid Efficiency by :
Download or read book General Framework for Achieving Textbook Multigrid Efficiency written by and published by . This book was released on 2000 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general multigrid framework is discussed for obtaining textbook efficiency to solutions of the compressible Euler and Navier-Stokes equations in conservation law form. The general methodology relies on a distributed relaxation procedure to reduce errors in regular (smoothly varying) flow regions; separate and distinct treatments for each of the factors (elliptic and/or hyperbolic) are used to attain optimal reductions of errors. Near boundaries and discontinuities (shocks) additional local relaxations of the conservative equations are necessary. Example calculations are made for the quasi-one-dimensional Euler equations; the calculations illustrate the general procedure.
Download or read book Multigrid written by Ulrich Trottenberg and published by Elsevier. This book was released on 2000-11-20 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multigrid presents both an elementary introduction to multigrid methods for solving partial differential equations and a contemporary survey of advanced multigrid techniques and real-life applications.Multigrid methods are invaluable to researchers in scientific disciplines including physics, chemistry, meteorology, fluid and continuum mechanics, geology, biology, and all engineering disciplines. They are also becoming increasingly important in economics and financial mathematics.Readers are presented with an invaluable summary covering 25 years of practical experience acquired by the multigrid research group at the Germany National Research Center for Information Technology. The book presents both practical and theoretical points of view. * Covers the whole field of multigrid methods from its elements up to the most advanced applications* Style is essentially elementary but mathematically rigorous* No other book is so comprehensive and written for both practitioners and students
Book Synopsis Multiscale and Multiresolution Methods by : Timothy J. Barth
Download or read book Multiscale and Multiresolution Methods written by Timothy J. Barth and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many computionally challenging problems omnipresent in science and engineering exhibit multiscale phenomena so that the task of computing or even representing all scales of action is computationally very expensive unless the multiscale nature of these problems is exploited in a fundamental way. Some diverse examples of practical interest include the computation of fluid turbulence, structural analysis of composite materials, terabyte data mining, image processing, and a multitude of others. This book consists of both invited and contributed articles which address many facets of efficient multiscale representation and scientific computation from varied viewpoints such as hierarchical data representations, multilevel algorithms, algebraic homogeni- zation, and others. This book should be of particular interest to readers interested in recent and emerging trends in multiscale and multiresolution computation with application to a wide range of practical problems.
Book Synopsis Frontiers of Computational Fluid Dynamics 2002 by : Robert William MacCormack
Download or read book Frontiers of Computational Fluid Dynamics 2002 written by Robert William MacCormack and published by World Scientific. This book was released on 2002 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This series of volumes on the OC Frontiers of Computational Fluid DynamicsOCO was introduced to honor contributors who have made a major impact on the field. The first volume was published in 1994 and was dedicated to Prof Antony Jameson; the second was published in 1998 and was dedicated to Prof Earl Murman. The volume is dedicated to Prof Robert MacCormack. The twenty-six chapters in the current volume have been written by leading researchers from academia, government laboratories, and industry. They present up-to-date descriptions of recent developments in techniques for numerical analysis of fluid flow problems, and applications of these techniques to important problems in industry, as well as the classic paper that introduced the OC MacCormack schemeOCO to the world. Contents: The Effect of Viscosity in Hypervelocity Impact Cratering (R W MacCormack); The MacCormack Method OCo Historical Perspective (C M Hung et al.); Numerical Solutions of Cauchy-Riemann Equations for Two and Three Dimensional Flows (M M Hafez & J Houseman); Extension of Efficient Low Dissipation High Order Schemes for 3-D Curvilinear Moving Grids (M Vinokur & H C Yee); Scalable Parallel Implicit Multigrid Solution of Unsteady Incompressible Flows (R Pankajakshan et al.); Lattice Boltzmann Simulation of Incompressible Flows (N Satofuka & M Ishikura); Numerical Simulation of MHD Effects on Hypersonic Flow of a Weakly Ionized Gas in an Inlet (R K Agarwal & P Deb); Development of 3D DRAGON Grid Method for Complex Geometry (M-S Liou & Y Zheng); Advances in Algorithms for Computing Aerodynamic Flows (D W Zingg et al.); Selected CFD Capabilities at DLR (W Kordulla); CFD Applications to Space Transportation Systems (K Fujii); Information Science OCo A New Frontier of CFD (K Oshima & Y Oshima); Integration of CFD into Aerodynamics Education (E M Murman & A Rizzi); and other papers. Readership: Researchers and graduate students in numerical and computational mathematics."
Book Synopsis Recent Advances in Achieving Textbook Multigrid Efficiency for Computational Fluid Dynamics Simulations by : Achi Brandt
Download or read book Recent Advances in Achieving Textbook Multigrid Efficiency for Computational Fluid Dynamics Simulations written by Achi Brandt and published by . This book was released on 2002 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent advances in achieving textbook multigrid efficiency for fluid simulations are presented. Textbook multigrid efficiency is defined as attaining the solution to the governing system of equations in a computational work which is a small multiple of the operation counts associated with discretizing the system. Strategies are reviewed to attain this efficiency by exploiting the factorizability properties inherent to a range of fluid simulations, including the compressible Navier-Stokes equations. factorizability is used to separate the elliptic and hyperbolic factors contributing to the target system; each of the factors can then be treated individually and optimally. Boundary regions and discontinuities are addressed with separate (local) treatments. New formulations and recent calculations demonstrating the attainment of textbook efficiency for aerodynamic simulations are shown.
Book Synopsis SIAM Journal on Scientific Computing by :
Download or read book SIAM Journal on Scientific Computing written by and published by . This book was released on 2004 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Analysis of Boundary Conditions for Factorizable Discretizations of the Euler Equations by : Boris Diskin
Download or read book Analysis of Boundary Conditions for Factorizable Discretizations of the Euler Equations written by Boris Diskin and published by . This book was released on 2002 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article, several sets of boundary conditions or factorizable schemes corresponding to the steady-state compressible Euler equations are evaluated. The analyzed model is a one-dimensional constant-coefficient problem. Numerical tests have been performed for a fully subsonic quasi-one-dimensional flow in a convergent/divergent channel. This paper focuses on the effect of boundary-condition equations on stability and accuracy of the discrete solutions. Explicit correspondence between solutions and boundary conditions is established through a boundary-condition-sensitivity (BCS) matrix. The following new findings are reported: (1) Examples of stable discrete problems contradicting a wide-spread belief that employment of a one-order-lower approximation schemes in an O(h)-small region does not affect the overall accuracy order of the solution have been found and explained. Such counterexamples can only be constructed for systems of differential equations. For scalar equations, the conventional wisdom is correct. (2) A negative effect of overspecified (although, exact) boundary conditions on accuracy and stability of the solution has been observed and explained. (3) Sets of practical boundary conditions for factorizable schemes providing stable second-order accurate solutions have been formulated. These schemes belong to a family of second-order schemes requiring second-order accuracy for some numerical-closure boundary conditions.
Author :National Aeronautics and Space Administration (NASA) Publisher :Createspace Independent Publishing Platform ISBN 13 :9781721014828 Total Pages :50 pages Book Rating :4.0/5 (148 download)
Book Synopsis Textbook Multigrid Efficiency for Leading Edge Stagnation by : National Aeronautics and Space Administration (NASA)
Download or read book Textbook Multigrid Efficiency for Leading Edge Stagnation written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-06-11 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: A multigrid solver is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work which is a small (less than 10) multiple of the operation count in evaluating the discrete residuals. TME in solving the incompressible inviscid fluid equations is demonstrated for leading- edge stagnation flows. The contributions of this paper include (1) a special formulation of the boundary conditions near stagnation allowing convergence of the Newton iterations on coarse grids, (2) the boundary relaxation technique to facilitate relaxation and residual restriction near the boundaries, (3) a modified relaxation scheme to prevent initial error amplification, and (4) new general analysis techniques for multigrid solvers. Convergence of algebraic errors below the level of discretization errors is attained by a full multigrid (FMG) solver with one full approximation scheme (F.4S) cycle per grid. Asymptotic convergence rates of the F.4S cycles for the full system of flow equations are very fast, approaching those for scalar elliptic equations.Diskin, Boris and Thomas, James L. and Mineck, Raymond E.Langley Research CenterFLOW EQUATIONS; INCOMPRESSIBLE FLUIDS; INVISCID FLOW; STAGNATION FLOW; BOUNDARY CONDITIONS; LEADING EDGES; ITERATION
Book Synopsis NASA Langley Scientific and Technical Information Output 2000 by :
Download or read book NASA Langley Scientific and Technical Information Output 2000 written by and published by . This book was released on 2001 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Activities of Institute for Computer Applications in Science and Engineering (ICASE) by :
Download or read book Activities of Institute for Computer Applications in Science and Engineering (ICASE) written by and published by . This book was released on 2001 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 888 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Activities of ICASE written by and published by . This book was released on 2002 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis New Factorizable Discretizations for the Euler Equations by : Boris Diskin
Download or read book New Factorizable Discretizations for the Euler Equations written by Boris Diskin and published by . This book was released on 2002 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: A multigrid method is defined as having textbook multigrid efficiency (TME) if solutions to the governing system of equations are attained in a computational work that is a small (less than 10) multiple of the operation count in one target-grid residual evaluation. Away to achieve TME for the Euler and Navier-Stokes equations is to apply the distributed relaxation method thereby separating the elliptic and hyperbolic partitions of the equations. Design of a distributed relaxation scheme can be significantly simplified if the target discretization possesses two properties: (1) factorizability, and (2) consistent approximations for the separate factors. The first property implies that the discrete system determinant can be represented as a product of discrete factors, each of them approximating a corresponding factor of the determinant of the differential equations. The second property requires that the discrete factors reflect the physical anisotropies, be stable, and be easily solvable. In this paper, discrete schemes for the nonconservative Euler equations possessing properties (1) and (2) have been derived and analyzed. The accuracy of these scheme has been tested for subsonic flow regimes and is comparable with the accuracy of standard schemes. TME has been demonstrated in solving fully subsonic quasi-one-dimensional flow in a convergent/divergent channel.
Book Synopsis A Multigrid Tutorial by : William L. Briggs
Download or read book A Multigrid Tutorial written by William L. Briggs and published by SIAM. This book was released on 2000-07-01 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Book Synopsis Numerical Mathematics and Advanced Applications 2009 by : Gunilla Kreiss
Download or read book Numerical Mathematics and Advanced Applications 2009 written by Gunilla Kreiss and published by Springer Science & Business Media. This book was released on 2010-10-19 with total page 900 pages. Available in PDF, EPUB and Kindle. Book excerpt: xxx
Book Synopsis Opportunities for Breakthroughs in Large-Scale Computational Simulation and Design by :
Download or read book Opportunities for Breakthroughs in Large-Scale Computational Simulation and Design written by and published by . This book was released on 2002 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Opportunities for breakthroughs in the large-scale computational simulation and design of aerospace vehicles are presented. Computational fluid dynamics tools to be used within multidisciplinary analysis and design methods are emphasized. The opportunities stem from speedups and robustness improvements in the underlying unit operations associated with simulation (geometry modeling, grid generation, physical modeling, analysis, etc.). Further, an improved programming environment can synergistically integrate these unit operations to leverage the gains. The speedups result from reducing the problem setup time through geometry modeling and grid generation operations, and reducing the solution time through the operation counts associated with solving the discretized equations to a sufficient accuracy. The opportunities are addressed only at a general level here, but an extensive list of references containing further details is included.
Book Synopsis Modern Circuit Placement by : Gi-Joon Nam
Download or read book Modern Circuit Placement written by Gi-Joon Nam and published by Springer Science & Business Media. This book was released on 2007-08-26 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers advanced techniques in modern circuit placement. It details all of most recent placement techniques available in the field and analyzes the optimality of these techniques. Coverage includes all the academic placement tools that competed against one another on the same industrial benchmark circuits at the International Symposium on Physical Design (ISPD), these techniques are also extensively being used in industrial tools as well. The book provides significant amounts of analysis on each technique such as trade-offs between quality-of-results (QoR) and runtime.
