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Finite difference

About: Finite difference is a research topic. Over the lifetime, 19693 publications have been published within this topic receiving 408603 citations.


Papers
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Journal ArticleDOI
TL;DR: In this paper, a new rotated staggered grid where all medium parameters are defined at appropriate positions within an elementary cell for the essential operations is proposed to simulate the propagation of elastic waves in a medium containing cracks, pores or free surfaces.

584 citations

Book
01 Jan 1999
TL;DR: The purpose of this monograph is to discuss models for optimization and search, as well as some of the principles used in computer programming, which have been used in the design of search engines and mobile devices.
Abstract: Preface 1. Introduction Part I. Analytical Models: 2. Ordinary differential and difference equations 3. Partial differential equations 4. Variational principles 5. Random systems Part II. Numerical Models: 6. Finite differences: ordinary difference equations 7. Finite differences: partial differential equations 8. Finite elements 9. Cellular automata and lattice gases Part III. Observational Models: 10. Function fitting 11. Transforms 12. Architectures 13. Optimization and search 14. Clustering and density estimation 15. Filtering and state estimation 16. Linear and nonlinear time series Appendix 1. Graphical and mathematical software Appendix 2. Network programming Appendix 3. Benchmarking Appendix 4. Problem solutions Bibliography.

574 citations

Journal ArticleDOI
TL;DR: A procedure for constructing solutions to the Riemann problem for gas dynamics with a general convex equation of state is given in this paper, where approximate procedures involving a local parametrization of the EO of state are introduced in order to calculate numerical fluxes in conservative finite difference schemes.

569 citations

Journal ArticleDOI
TL;DR: In this article, the use of high speed, high capacity vector computers allows the resultant finite-difference equations to be factored in-place, allowing inversions to be generated using data from a very large number of source positions.
Abstract: Frequency-domain methods are well suited to the imaging of wide-aperture cross-hole data. However, although the combination of the frequency domain with the wavenumber domain has facilitated the development of rapid algorithms, such as diffraction tomography, this has also required linearization with respect to homogeneous reference media. This restriction, and association restrictions on source-receiver geometries, are overcome by applying inverse techniques that operate in the frequency-space domain. In order to incorporate the rigorous modelling technique of finite differences into the inverse procedure a nonlinear approach is used. To reduce computational costs the method of finite differences is applied directly to the frequency-domain wave equation. The use of high speed, high capacity vector computers allow the resultant finite-difference equations to be factored in-place. In this way wavefields can be computed for additional source positions at minimal extra cost, allowing inversions to be generated using data from a very large number of source positions. Synthetic studies show that where weak scatter approximations are valid, diffraction tomography performs slightly better than a single iteration of non-linear inversion. However, if the background velocities increase systematically with depth, diffraction tomography is ineffective whereas non-linear inversion yields useful images from one frequency component of the data after a single iteration. Further synthetic studies indicate the efficacy of the method in the time-lapse monitoring of injection fluids in tertiary hydrocarbon recovery projects.

567 citations

Book
25 Jun 2004
TL;DR: In this article, Quasilinear systems and conservation laws are discussed, including conservative schemes and non-conservative schemes, and a numerical test with source is proposed. But the test is based on a finite volume.
Abstract: Introduction.- 1. Quasilinear systems and conservation laws.- 2. Conservative schemes.- 3. Source terms.- 4. Nonconservative schemes.- 5. Multidimensional finite volumes with sources.- 6. Numerical test with source.- Bibliography

561 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023153
2022411
2021722
2020679
2019678
2018708