Download or read book A Review of High order and Optimized Finite difference Methods for Simulating Linear Wave Phenomena written by David W. Zingg and published by . This book was released on 1996 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "This paper presents a review of high-order and optimized finite-difference methods for numerically simulating the propagation and scattering of linear waves, such as electromagnetic, acoustic, or elastic waves. The spatial operators reviewed include compact schemes, non-compact schemes, schemes on staggered grids, and schemes which are optimized to produce specific characteristics. The time-marching methods discussed include Runge-Kutta methods, Adams-Bashforth methods, and the leapfrog method. In addition, the following fourth-order fully-discrete finite-difference methods are considered: a one-step implicit scheme with a three-point spatial stencil, a one-step explicit scheme with a five-point spatial stencil, and a two-step explicit scheme with a five-point spatial stencil. For each method studied, the number of grid points per wavelength required for accurate simulation of wave propagation over large distances is presented. Recommendations are made with respect to the suitability of the methods for specific problems and practical aspects of their use, such as appropriate Courant numbers and grid densities. Avenues for future research are suggested."
Download or read book Higher Order FDTD Schemes for Waveguides and Antenna Structures written by Nikolaos Kantartzis and published by Springer Nature. This book was released on 2022-06-01 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This publication provides a comprehensive and systematically organized coverage of higher order finite-difference time-domain or FDTD schemes, demonstrating their potential role as a powerful modeling tool in computational electromagnetics. Special emphasis is drawn on the analysis of contemporary waveguide and antenna structures. Acknowledged as a significant breakthrough in the evolution of the original Yee's algorithm, the higher order FDTD operators remain the subject of an ongoing scientific research. Among their indisputable merits, one can distinguish the enhanced levels of accuracy even for coarse grid resolutions, the fast convergence rates, and the adjustable stability. In fact, as the fabrication standards of modern systems get stricter, it is apparent that such properties become very appealing for the accomplishment of elaborate and credible designs.
Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Download or read book Effective Computational Methods for Wave Propagation written by Nikolaos A. Kampanis and published by CRC Press. This book was released on 2008-02-25 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to the increase in computational power and new discoveries in propagation phenomena for linear and nonlinear waves, the area of computational wave propagation has become more significant in recent years. Exploring the latest developments in the field, Effective Computational Methods for Wave Propagation presents several modern, valuable
Download or read book High accuracy Finite difference Schemes for Linear Wave Propagation written by Henry Martin Jurgens and published by . This book was released on 1997 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical simulation of linear wave propagation and scattering cannot be handled effectively using the second-order methods that are in widespread use today. To obtain accurate results these methods require grids with a resolution in the hundreds of points per wavelength to propagate a wave a distance greater than thirty wavelengths. Methods which can obtain accurate solutions without such high grid resolutions are needed for simulating long-range wave propagation. A procedure is presented for developing high-accuracy finite-difference schemes which are optimized in order to minimize the numerical phase and amplitude errors over a given range of frequencies. These high-accuracy schemes are used to solve the two-dimensional time-domain Maxwell equations for electromagnetic wave propagation and scattering. Boundary conditions are presented which preserve the accuracy of these schemes when modeling interfaces between different materials. A stable and accurate far-field boundary treatment is used which allows waves to exit the numerical domain with very little spurious reflection. Numerical experiments are performed which demonstrate the utility of the high-accuracy schemes using Cartesian and curvilinear grids. Two schemes are studied, one which produces the maximum formal order of accuracy, and one which is optimized for propagation distances less than roughly three hundred wavelengths. The high-accuracy schemes are shown to be substantially more efficient, in both computing time and memory, than methods which are second- and fourth-order in space. The optimized scheme can produce significant error reduction relative to the maximum-order scheme, with no additional expense, especially when the number of wavelengths of travel is large.
Download or read book Monthly Catalog of United States Government Publications written by and published by . This book was released on 1999 with total page 892 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Collection of Technical Papers written by American Institute of Aeronautics and Astronautics and published by AIAA (American Institute of Aeronautics & Astronautics). This book was released on 1997 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 13th AIAA Computational Fluid Dynamics Conference. It addresses numerical procedures for the solution of fluid dynamics and interdisciplinary problems. Technical sessions of the conference focus on design optimization, solution adaptive techniques, convergence acceleration methods, high-resolution schemes, parallel computing as well as improved algorithms for the solution of viscous, inviscid, and multi-component flow applications. The programme also includes a panel discussion addressing the evoluting roles of government, industry and academia in future CFD developments.
Download or read book AIAA Journal written by American Institute of Aeronautics and Astronautics and published by . This book was released on 2001 with total page 1304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book International Aerospace Abstracts written by and published by . This book was released on 1998 with total page 980 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advances in Computational Electrodynamics written by Allen Taflove and published by Artech House Publishers. This book was released on 1998 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite-Difference Time-Domain (FD-TD) modeling is arguably the most popular and powerful means available to perform detailed electromagnetic engineering analyses. Edited by the pioneer and foremost authority on the subject, here is the first book to assemble in one resource the latest techniques and results of the leading theoreticians and practitioners of FD-TD computational electromagnetics modeling.
Download or read book Aerospace America written by and published by . This book was released on 1997 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multi dimensional Upwind Leapfrog Schemes and Their Applications written by Cheolwan Kim and published by . This book was released on 1997 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computational Electrodynamics written by Allen Taflove and published by Artech House Publishers. This book was released on 2005 with total page 1050 pages. Available in PDF, EPUB and Kindle. Book excerpt: This extensively revised and expanded third edition of the Artech House bestseller, Computational Electrodynamics: The Finite-Difference Time-Domain Method, offers you the most up-to-date and definitive resource on this critical method for solving Maxwell's equations. There has been considerable advancement in FDTD computational technology over the past few years, and this new edition brings you the very latest details with four new invited chapters on advanced techniques for PSTD, unconditional stability, provably stable FDTD-FETD hybrids, and hardware acceleration. Moreover, you find many completely new sections throughout the book, including major updates on convolutional PML ABCs; dispersive, nonlinear, classical-gain, and quantum-gain materials; and micro-, nano-, and bio- photonics.
Download or read book Higher Order Finite Element Methods written by Pavel Solin and published by CRC Press. This book was released on 2003-07-28 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite element method has always been a mainstay for solving engineering problems numerically. The most recent developments in the field clearly indicate that its future lies in higher-order methods, particularly in higher-order hp-adaptive schemes. These techniques respond well to the increasing complexity of engineering simulations and
Download or read book The Accurate Finite difference Scheme and Finite element Method for some Partial Differential Equations written by Ulziibayar Vandondoo and published by Springer. This book was released on 2023-11-20 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is intended for graduate students, researchers and teachers. It is devoted to the construction of high-order schemes of the finite difference method and the finite element method for the solution of multidimensional boundary value problems for various partial differential equations, in particular, linear Helmholtz and wave equations, and nonlinear Burgers' equation. The finite difference method is a standard numerical method for solving boundary value problems. Recently, considerable attention has been paid to constructing an accurate (or exact) difference approximation for some ordinary and partial differential equations. An exact finite difference method is developed for Helmholtz and wave equations with general boundary conditions (including initial condition for wave equation) on the rectangular domain in R2. The method proposed here comes from [4] and is based on separation of variables method and expansion of one-dimensional three-point difference operators for sufficiently smooth solution. The efficiency and accuracy of the method have been tested on several examples.
Download or read book High Performance Computing of Big Data for Turbulence and Combustion written by Sergio Pirozzoli and published by Springer. This book was released on 2019-05-28 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides state-of-art information on high-accuracy scientific computing and its future prospects, as applicable to the broad areas of fluid mechanics and combustion, and across all speed regimes. Beginning with the concepts of space-time discretization and dispersion relation in numerical computing, the foundations are laid for the efficient solution of the Navier-Stokes equations, with special reference to prominent approaches such as LES, DES and DNS. The basis of high-accuracy computing is rooted in the concept of stability, dispersion and phase errors, which require the comprehensive analysis of discrete computing by rigorously applying error dynamics. In this context, high-order finite-difference and finite-volume methods are presented. Naturally, the coverage also includes fundamental notions of high-performance computing and advanced concepts on parallel computing, including their implementation in prospective hexascale computers. Moreover, the book seeks to raise the bar beyond the pedagogical use of high-accuracy computing by addressing more complex physical scenarios, including turbulent combustion. Tools like proper orthogonal decomposition (POD), proper generalized decomposition (PGD), singular value decomposition (SVD), recursive POD, and high-order SVD in multi-parameter spaces are presented. Special attention is paid to bivariate and multivariate datasets in connection with various canonical flow and heat transfer cases. The book mainly addresses the needs of researchers and doctoral students in mechanical engineering, aerospace engineering, and all applied disciplines including applied mathematics, offering these readers a unique resource.
Download or read book The Finite Difference Modelling of Earthquake Motions written by Peter Moczo and published by Cambridge University Press. This book was released on 2014-04-24 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among all the numerical methods in seismology, the finite-difference (FD) technique provides the best balance of accuracy and computational efficiency. This book offers a comprehensive introduction to FD and its applications to earthquake motion. Using a systematic tutorial approach, the book requires only undergraduate degree-level mathematics and provides a user-friendly explanation of the relevant theory. It explains FD schemes for solving wave equations and elastodynamic equations of motion in heterogeneous media, and provides an introduction to the rheology of viscoelastic and elastoplastic media. It also presents an advanced FD time-domain method for efficient numerical simulations of earthquake ground motion in realistic complex models of local surface sedimentary structures. Accompanied by a suite of online resources to help put the theory into practice, this is a vital resource for professionals and academic researchers using numerical seismological techniques, and graduate students in earthquake seismology, computational and numerical modelling, and applied mathematics.
