High Order Numerical Methods For Problems In Wave Scattering

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High Order Numerical Methods for Problems in Wave Scattering

Author : Dane Scott Grundvig
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (134 download)

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Book Synopsis High Order Numerical Methods for Problems in Wave Scattering by : Dane Scott Grundvig

Download or read book High Order Numerical Methods for Problems in Wave Scattering written by Dane Scott Grundvig and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arbitrary high order numerical methods for time-harmonic acoustic scattering problems originally defined on unbounded domains are constructed. This is done by coupling recently developed high order local absorbing boundary conditions (ABCs) with finite difference methods for the Helmholtz equation. These ABCs are based on exact representations of the outgoing waves by means of farfield expansions. The finite difference methods, which are constructed from a deferred-correction (DC) technique, approximate the Helmholtz equation and the ABCs to any desired order. As a result, high order numerical methods with an overall order of convergence equal to the order of the DC schemes are obtained. A detailed construction of these DC finite difference schemes is presented. Details and results from an extension to heterogeneous media are also included. Additionally, a rigorous proof of the consistency of the DC schemes with the Helmholtz equation and the ABCs in polar coordinates is also given. The results of several numerical experiments corroborate the high order convergence of the proposed method. A novel local high order ABC for elastic waves based on farfield expansions is constructed and preliminary results applying it to elastic scattering problems are presented.

Higher-Order Numerical Methods for Transient Wave Equations

Author : Gary Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 366204823X
Total Pages : 355 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Higher-Order Numerical Methods for Transient Wave Equations by : Gary Cohen

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 2013-04-17 with total page 355 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

Topics in Computational Wave Propagation

Author : Mark Ainsworth
Publisher : Springer Science & Business Media
ISBN 13 : 3642554830
Total Pages : 408 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Topics in Computational Wave Propagation by : Mark Ainsworth

Download or read book Topics in Computational Wave Propagation written by Mark Ainsworth and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: These ten detailed and authoritative survey articles on numerical methods for direct and inverse wave propagation problems are written by leading experts. Researchers and practitioners in computational wave propagation, from postgraduate level onwards, will find the breadth and depth of coverage of recent developments a valuable resource. The articles describe a wide range of topics on the application and analysis of methods for time and frequency domain PDE and boundary integral formulations of wave propagation problems. Electromagnetic, seismic and acoustic equations are considered. Recent developments in methods and analysis ranging from finite differences to hp-adaptive finite elements, including high-accuracy and fast methods are described with extensive references.

Numerical Methods and Algorithms for High Frequency Wave Scattering Problems in Homogeneous and Random Media

Author : Cody Samuel Lorton
Publisher :
ISBN 13 :
Total Pages : 226 pages
Book Rating : 4.:/5 (119 download)

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Book Synopsis Numerical Methods and Algorithms for High Frequency Wave Scattering Problems in Homogeneous and Random Media by : Cody Samuel Lorton

Download or read book Numerical Methods and Algorithms for High Frequency Wave Scattering Problems in Homogeneous and Random Media written by Cody Samuel Lorton and published by . This book was released on 2014 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of four integral parts with a unified objective of developing efficient numerical methods for high frequency time-harmonic wave equations defined on both homogeneous and random media. The first part investigates the generalized weak coercivity of the acoustic Helmholtz, elastic Helmholtz, and time-harmonic Maxwell wave operators. We prove that such a weak coercivity holds for these wave operators on a class of more general domains called generalized star-shape domains. As a by-product, solution estimates for the corresponding Helmholtz-type problems are obtained. The second part of the dissertation develops an absolutely stable (i.e. stable in all mesh regimes) interior penalty discontinuous Galerkin (IP-DG) method for the elastic Helmholtz equations. A special mesh-dependent sesquilinear form is proposed and is shown to be weakly coercive in all mesh regimes. We prove that the proposed IP-DG method converges with optimal rate with respect to the mesh size. Numerical experiments are carried out to demonstrate the theoretical results and compare this method to the standard finite element method. The third part of the dissertation develops a Monte Carlo interior penalty discontinuous Galerkin (MCIP-DG) method for the acoustic Helmholtz equation defined on weakly random media. We prove that the solution to the random Helmholtz problem has a multi-modes expansion (i.e., a power series in a medium- related small parameter). Using this multi-modes expansion an efficient and accurate numerical method for computing moments of the solution to the random Helmholtz problem is proposed. The proposed method is also shown to converge optimally. Numerical experiments are carried out to compare the new multi-modes MCIP-DG method to a classical Monte Carlo method. The last part of the dissertation develops a theoretical framework for Schwarz pre- conditioning methods for general nonsymmetric and indefinite variational problems which are discretized by Galerkin-type discretization methods. Such a framework has been missing in the literature and is of great theoretical and practical importance for solving convection-diffusion equations and Helmholtz-type wave equations. Condition number estimates for the additive and hybrid Schwarz preconditioners are established under some structure assumptions. Numerical experiments are carried out to test the new framework.

Fast Numerical Methods for High Frequency Wave Scattering

Author : Khoa Dang Tran
Publisher :
ISBN 13 :
Total Pages : 306 pages
Book Rating : 4.:/5 (798 download)

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Book Synopsis Fast Numerical Methods for High Frequency Wave Scattering by : Khoa Dang Tran

Download or read book Fast Numerical Methods for High Frequency Wave Scattering written by Khoa Dang Tran and published by . This book was released on 2012 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer simulation of wave propagation is an active research area as wave phenomena are prevalent in many applications. Examples include wireless communication, radar cross section, underwater acoustics, and seismology. For high frequency waves, this is a challenging multiscale problem, where the small scale is given by the wavelength while the large scale corresponds to the overall size of the computational domain. Research into wave equation modeling can be divided into two regimes: time domain and frequency domain. In each regime, there are two further popular research directions for the numerical simulation of the scattered wave. One relies on direct discretization of the wave equation as a hyperbolic partial differential equation in the full physical domain. The other direction aims at solving an equivalent integral equation on the surface of the scatterer. In this dissertation, we present three new techniques for the frequency domain, boundary integral equations.

Numerical Methods for Inverse Scattering Problems

Author : Jingzhi Li
Publisher : Springer Nature
ISBN 13 : 9819937728
Total Pages : 373 pages
Book Rating : 4.8/5 (199 download)

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Book Synopsis Numerical Methods for Inverse Scattering Problems by : Jingzhi Li

Download or read book Numerical Methods for Inverse Scattering Problems written by Jingzhi Li and published by Springer Nature. This book was released on 2023-09-07 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the latest developments on the numerical methods for inverse scattering problems associated with acoustic, electromagnetic, and elastic waves. Inverse scattering problems are concerned with identifying unknown or inaccessible objects by wave probing data, which makes possible many industrial and engineering applications including radar and sonar, medical imaging, nondestructive testing, remote sensing, and geophysical exploration. The mathematical study of inverse scattering problems is an active field of research. This book presents a comprehensive and unified mathematical treatment of various inverse scattering problems mainly from a numerical reconstruction perspective. It highlights the collaborative research outputs by the two groups of the authors yet surveys and reviews many existing results by global researchers in the literature. The book consists of three parts respectively corresponding to the studies on acoustic, electromagnetic, and elastic scattering problems. In each part, the authors start with in-depth theoretical and computational treatments of the forward scattering problems and then discuss various numerical reconstruction schemes for the associated inverse scattering problems in different scenarios of practical interest. In addition, the authors provide an overview of the existing results in the literature by other researchers. This book can serve as a handy reference for researchers or practitioners who are working on or implementing inverse scattering methods. It can also serve as a graduate textbook for research students who are interested in working on numerical algorithms for inverse scattering problems.

High-order Numerical Methods for Scattering Problems

Author : Abinand Gopal
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (127 download)

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Book Synopsis High-order Numerical Methods for Scattering Problems by : Abinand Gopal

Download or read book High-order Numerical Methods for Scattering Problems written by Abinand Gopal and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Numerical Methods for Solving Wave Scattering Problems

Author : Nhan Thanh Tran
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (95 download)

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Book Synopsis Numerical Methods for Solving Wave Scattering Problems by : Nhan Thanh Tran

Download or read book Numerical Methods for Solving Wave Scattering Problems written by Nhan Thanh Tran and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Wave and Scattering Methods for Numerical Simulation

Author : Stefan Bilbao
Publisher : John Wiley & Sons
ISBN 13 : 0470870184
Total Pages : 380 pages
Book Rating : 4.4/5 (78 download)

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Book Synopsis Wave and Scattering Methods for Numerical Simulation by : Stefan Bilbao

Download or read book Wave and Scattering Methods for Numerical Simulation written by Stefan Bilbao and published by John Wiley & Sons. This book was released on 2004-10-22 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering-based numerical methods are increasingly applied to the numerical simulation of distributed time-dependent physical systems. These methods, which possess excellent stability and stability verification properties, have appeared in various guises as the transmission line matrix (TLM) method, multidimensional wave digital (MDWD) filtering and digital waveguide (DWN) methods. This text provides a unified framework for all of these techniques and addresses the question of how they are related to more standard numerical simulation techniques. Covering circuit/scattering models in electromagnetics, transmission line modelling, elastic dynamics, as well as time-varying and nonlinear systems, this book highlights the general applicability of this technique across a variety of disciplines, as well as the inter-relationships between simulation techniques and digital filter design. provides a comprehensive overview of scattering-based numerical integration methods. reviews the basics of classical electrical network theory, wave digital filters, and digital waveguide networks. discusses applications for time-varying and nonlinear systems. includes an extensive bibliography containing over 250 references. Mixing theory and application with numerical simulation results, this book will be suitable for both experts and readers with a limited background in signal processing and numerical techniques.

Direct and Inverse Problems in Wave Propagation and Applications

Author : Ivan Graham
Publisher : Walter de Gruyter
ISBN 13 : 3110282283
Total Pages : 328 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Direct and Inverse Problems in Wave Propagation and Applications by : Ivan Graham

Download or read book Direct and Inverse Problems in Wave Propagation and Applications written by Ivan Graham and published by Walter de Gruyter. This book was released on 2013-10-14 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the third volume of three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" taking place in Linz, Austria, October 3-7, 2011. This book surveys recent developments in the analysis of wave propagation problems. The topics covered include aspects of the forward problem and problems in inverse problems, as well as applications in the earth sciences. Wave propagation problems are ubiquitous in environmental applications such as seismic analysis, acoustic and electromagnetic scattering. The design of efficient numerical methods for the forward problem, in which the scattered field is computed from known geometric configurations is very challenging due to the multiscale nature of the problems. Even more challenging are inverse problems where material parameters and configurations have to be determined from measurements in conjunction with the forward problem. This book contains review articles covering several state-of-the-art numerical methods for both forward and inverse problems. This collection of survey articles focusses on the efficient computation of wave propagation and scattering is a core problem in numerical mathematics, which is currently of great research interest and is central to many applications in energy and the environment. Two generic applications which resonate strongly with the central aims of the Radon Special Semester 2011 are forward wave propagation in heterogeneous media and seismic inversion for subsurface imaging. As an example of the first application, modelling of absorption and scattering of radiation by clouds, aerosol and precipitation is used as a tool for interpretation of (e.g.) solar, infrared and radar measurements, and as a component in larger weather/climate prediction models in numerical weather forecasting. As an example of the second application, inverse problems in wave propagation in heterogeneous media arise in the problem of imaging the subsurface below land or marine deposits. The book records the achievements of Workshop 3 "Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment". It brings together key numerical mathematicians whose interest is in the analysis and computation of wave propagation and scattering problems, and in inverse problems, together with practitioners from engineering and industry whose interest is in the applications of these core problems.

Mathematical Methods for Wave Phenomena

Author : Norman Bleistein
Publisher : Academic Press
ISBN 13 : 0080916953
Total Pages : 360 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Mathematical Methods for Wave Phenomena by : Norman Bleistein

Download or read book Mathematical Methods for Wave Phenomena written by Norman Bleistein and published by Academic Press. This book was released on 2012-12-02 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer Science and Applied Mathematics: Mathematical Methods for Wave Phenomena focuses on the methods of applied mathematics, including equations, wave fronts, boundary value problems, and scattering problems. The publication initially ponders on first-order partial differential equations, Dirac delta function, Fourier transforms, asymptotics, and second-order partial differential equations. Discussions focus on prototype second-order equations, asymptotic expansions, asymptotic expansions of Fourier integrals with monotonic phase, method of stationary phase, propagation of wave fronts, and variable index of refraction. The text then examines wave equation in one space dimension, as well as initial boundary value problems, characteristics for the wave equation in one space dimension, and asymptotic solution of the Klein-Gordon equation. The manuscript offers information on wave equation in two and three dimensions and Helmholtz equation and other elliptic equations. Topics include energy integral, domain of dependence, and uniqueness, scattering problems, Green's functions, and problems in unbounded domains and the Sommerfeld radiation condition. The asymptotic techniques for direct scattering problems and the inverse methods for reflector imaging are also elaborated. The text is a dependable reference for computer science experts and mathematicians pursuing studies on the mathematical methods of wave phenomena.

Effective Computational Methods for Wave Propagation

Author : Nikolaos A Kampanis
Publisher : CRC Press
ISBN 13 : 9780367387723
Total Pages : 712 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Effective Computational Methods for Wave Propagation by : Nikolaos A Kampanis

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 2019-08-30 with total page 712 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 computational methods used to describe wave propagation phenomena in selected areas of physics and technology. Featuring contributions from internationally known experts, the book is divided into four parts. It begins with the simulation of nonlinear dispersive waves from nonlinear optics and the theory and numerical analysis of Boussinesq systems. The next section focuses on computational approaches, including a finite element method and parabolic equation techniques, for mathematical models of underwater sound propagation and scattering. The book then offers a comprehensive introduction to modern numerical methods for time-dependent elastic wave propagation. The final part supplies an overview of high-order, low diffusion numerical methods for complex, compressible flows of aerodynamics. Concentrating on physics and technology, this volume provides the necessary computational methods to effectively tackle the sources of problems that involve some type of wave motion.

High-order Wave Tracking Strategy for Solving High-frequency Scattering Problems

Author : Inga Girshfeld
Publisher :
ISBN 13 :
Total Pages : 53 pages
Book Rating : 4.:/5 (132 download)

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Book Synopsis High-order Wave Tracking Strategy for Solving High-frequency Scattering Problems by : Inga Girshfeld

Download or read book High-order Wave Tracking Strategy for Solving High-frequency Scattering Problems written by Inga Girshfeld and published by . This book was released on 2021 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wave equations effectively model physical phenomena, applying but not limited to earthquake engineering, geophysical exploration, medical imaging, nondestructive testing, underwater acoustics, electromagnetics, etc. Extensively studied for over a century, the mathematics of wave propagation problems are relatively well-understood, but their computation poses substantial issues, especially for high-frequency regime [3]. Traditional FEM techniques require fine discretization or high order elements, resulting in the pollution effect [1] and numerical instabilities. Over the last few decades, significant efforts have been dedicated toward developing alternative techniques, including a least-squares method, plane wave discontinuous Galerkin methods, etc. Helmholtz problems, which describe time harmonic wave propagation, are well understood mathematically [3], but difficult to solve numerically in the high-frequency regime [1]. Moreover, practical applications of the Helmholtz equation demand solving systems with more than ten million complex unknowns in the mid-frequency range. Thus, reducing the computational cost and the complexity of implementation while preserving the level of accuracy and expanding the frequency regime would have far-reaching effects in the area of real-world application as well as in the computationally important infrastructure. We propose a numerical method to efficiently solve the Helmholtz problem in the high-frequency wave regime by implementing oscillating basis functions, along with a wave tracking strategy to align the basis functions with the direction of the propagating field. Thus, we are able to reduce the number of basis functions which grants access to the high-frequency regime. We use an adaptive local wave tracking strategy that implements a least-squares method. On each element of the mesh, shape functions are rotated until one aligns with the direction of the propagated wave, determined by solving a nonlinear minimization problem using Newton's method. This method is an extended effort from [2], where the distinguishing difference is the choice of basis functions. Moreover, the computation of Jacobians and Hessians that arise in the iterations of Newton's method is based on the exact characterization of the Fréchet derivatives of the field with respect to the propagation directions. Such a characterization is crucial for the stability, fast convergence, and computational efficiency of the Newton algorithm.

Numerical Analysis for Electromagnetic Integral Equations

Author : Karl F. Warnick
Publisher : Artech House
ISBN 13 : 1596933348
Total Pages : 234 pages
Book Rating : 4.5/5 (969 download)

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Book Synopsis Numerical Analysis for Electromagnetic Integral Equations by : Karl F. Warnick

Download or read book Numerical Analysis for Electromagnetic Integral Equations written by Karl F. Warnick and published by Artech House. This book was released on 2008 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction -- Surface integral equation formulations and the method of moments -- Error analysis of the EFIE / with W.C. Chew -- Error analysis of the MFIE and CFIE / with C.P. Davis -- Geometrical singularities and the flat strip -- Resonant structures -- Error analysis for 3D problems -- Higher-order basis functions / with A.F. Peterson -- Operator spectra and iterative solution methods.

Qualitative Methods in Inverse Scattering Theory

Author : Fioralba Cakoni
Publisher : Springer Science & Business Media
ISBN 13 : 3540312307
Total Pages : 232 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Qualitative Methods in Inverse Scattering Theory by : Fioralba Cakoni

Download or read book Qualitative Methods in Inverse Scattering Theory written by Fioralba Cakoni and published by Springer Science & Business Media. This book was released on 2005-12-29 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse scattering theory has been a particularly active and successful field in applied mathematics and engineering for the past twenty years. The increasing demands of imaging and target identification require new powerful and flexible techniques besides the existing weak scattering approximation or nonlinear optimization methods. One class of such methods comes under the general description of qualitative methods in inverse scattering theory. This textbook is an easily-accessible "class-tested" introduction to the field. It is accessible also to readers who are not professional mathematicians, thus making these new mathematical ideas in inverse scattering theory available to the wider scientific and engineering community.

The Nystrom Method in Electromagnetics

Author : Mei Song Tong
Publisher : John Wiley & Sons
ISBN 13 : 1119284880
Total Pages : 528 pages
Book Rating : 4.1/5 (192 download)

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Book Synopsis The Nystrom Method in Electromagnetics by : Mei Song Tong

Download or read book The Nystrom Method in Electromagnetics written by Mei Song Tong and published by John Wiley & Sons. This book was released on 2020-06-29 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, step-by-step reference to the Nyström Method for solving Electromagnetic problems using integral equations Computational electromagnetics studies the numerical methods or techniques that solve electromagnetic problems by computer programming. Currently, there are mainly three numerical methods for electromagnetic problems: the finite-difference time-domain (FDTD), finite element method (FEM), and integral equation methods (IEMs). In the IEMs, the method of moments (MoM) is the most widely used method, but much attention is being paid to the Nyström method as another IEM, because it possesses some unique merits which the MoM lacks. This book focuses on that method—providing information on everything that students and professionals working in the field need to know. Written by the top researchers in electromagnetics, this complete reference book is a consolidation of advances made in the use of the Nyström method for solving electromagnetic integral equations. It begins by introducing the fundamentals of the electromagnetic theory and computational electromagnetics, before proceeding to illustrate the advantages unique to the Nyström method through rigorous worked out examples and equations. Key topics include quadrature rules, singularity treatment techniques, applications to conducting and penetrable media, multiphysics electromagnetic problems, time-domain integral equations, inverse scattering problems and incorporation with multilevel fast multiple algorithm. Systematically introduces the fundamental principles, equations, and advantages of the Nyström method for solving electromagnetic problems Features the unique benefits of using the Nyström method through numerical comparisons with other numerical and analytical methods Covers a broad range of application examples that will point the way for future research The Nystrom Method in Electromagnetics is ideal for graduate students, senior undergraduates, and researchers studying engineering electromagnetics, computational methods, and applied mathematics. Practicing engineers and other industry professionals working in engineering electromagnetics and engineering mathematics will also find it to be incredibly helpful.

A Review of High-order and Optimized Finite-difference Methods for Simulating Linear Wave Phenomena

Author : David W. Zingg
Publisher :
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.:/5 (317 download)

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Book Synopsis A Review of High-order and Optimized Finite-difference Methods for Simulating Linear Wave Phenomena by : David W. Zingg

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."