Topic
Finite difference method
About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.
Papers published on a yearly basis
Papers
More filters
TL;DR: The flux-corrected transport (FCT) as discussed by the authors algorithm, adapted from hydrodynamics, reduces the numerical dispersion in finite-difference wavefield continuation by incorporating diffusion into the wave field continuation process.
Abstract: Finite-difference acoustic-wave modeling and reverse-time depth migration based on the full wave equation are general approaches that can take into account arbitrary variations in velocity and density and can handle turning waves as well. However, conventional finite-difference methods for solving the acoustic- or elastic-wave equation suffer from numerical dispersion when too few samples per wavelength are used. The flux-corrected transport (FCT) algorithm, adapted from hydrodynamics, reduces the numerical dispersion in finite-difference wavefield continuation. The flux-correction procedure endeavors to incorporate diffusion into the wavefield continuation process only where needed to suppress the numerical dispersion. Incorporating the flux-correction procedure in conventional finite-difference modeling or reverse-time migration can provide finite-difference solutions with no numerical dispersion even for impulsive sources. The FCT correction, which can be applied to finite-difference approximations of any order in space and time, is an efficient alternative to use for finite-difference approximations of increasing order. Through demonstrations of modeling and migration on both synthetic and field data, we show the benefits of the FCT algorithm, as well as its inability to fully recover resolution lost when the spatial sampling becomes too coarse.
89 citations
TL;DR: In this paper, the singular forces are computed implicitly by solving a small system of equations at each time step, which is derived from a second order projection method and then distributed to nearby Cartesian grid points using the immersed boundary method.
89 citations
TL;DR: In this article, a new elastic finite-difference (FD) method for spatially irregular grids is presented, which is simple and, at the same time, saves considerable memory and computing time.
Abstract: Finite‐difference (FD) modeling of complicated structures requires simple algorithms. This paper presents a new elastic FD method for spatially irregular grids that is simple and, at the same time, saves considerable memory and computing time. Features like faults, low‐velocity layers, cavities, and/or nonplanar surfaces are treated on a fine grid, while the remaining parts of the model are, with equal accuracy, represented on a coarse grid. No interpolation is needed between the fine and coarse parts due to the rectangular grid cells. Relatively abrupt transitions between the small and large grid steps produce no numerical artifacts in the present method. Planar or nonplanar free surfaces, including underground cavities, are treated in a way similar to internal grid points but with consideration of the zero‐valued elastic parameters and density outside the free surface (vacuum formalism). A theoretical proof that vacuum formalism fullfills the free‐surface conditions is given. Numerical validation is per...
89 citations
Book•
01 Jan 2001
TL;DR: This book offers a straightforward presentation of the sophisticated techniques used in waveguide analysis and enables a quick grasp of modern numerical methods with easy mathematics.
Abstract: A complete survey of modern design and analysis techniques for optical waveguides This volume thoroughly details modern and widely accepted methods for designing the optical waveguides used in telecommunications systems. It offers a straightforward presentation of the sophisticated techniques used in waveguide analysis and enables a quick grasp of modern numerical methods with easy mathematics. The book is intended to guide the reader to a comprehensive understanding of optical waveguide analysis through self-study. This comprehensive presentation includes: An extensive and exhaustive list of mathematical manipulations Detailed explanations of common design methods: finite element method (FEM), finite difference method (FDM), beam propagation method (BPM), and finite difference time-domain method (FD-TDM) Explanations for numerical solutions of optical waveguide problems with sophisticated techniques used in modern computer-aided design (CAD) software Solutions to Maxwell's equations and the Schrodinger equation The authors provide excellent self-study material for practitioners, researchers, and students, while also presenting detailed mathematical manipulations that can be easily understood by readers who are unfamiliar with them. Introduction to Optical Waveguide Analysis presents modern design methods in a comprehensive and easy-to-understand format.
89 citations