Journal ArticleDOI
Higher-Order Numerical Methods for Transient Wave Equations
TLDR
This book surveys higher-order finite difference methods and develops various mass-lumped finite element methods for the transient wave equations, and presents the most efficient methods, respecting both accuracy and stability for each sort of problem.Abstract:
Solving efficiently the wave equations involved in modeling acoustic, elastic or electromagnetic wave propagation remains a challenge both for research and industry. To attack the problems coming from the propagative character of the solution, the author constructs higher-order numerical methods to reduce the size of the meshes, and consequently the time and space stepping, dramatically improving storage and computing times. This book surveys higher-order finite difference methods and develops various mass-lumped finite (also called spectral) element methods for the transient wave equations, and presents the most efficient methods, respecting both accuracy and stability for each sort of problem. A central role is played by the notion of the dispersion relation for analyzing the methods. The last chapter is devoted to unbounded domains which are modeled using perfectly matched layer (PML) techniques. Numerical examples are given.read more
Citations
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Journal ArticleDOI
Reverse time migration with optimal checkpointing
TL;DR: This paper describes optimal checkpointing in a form which applies both to RTM and other applications of the adjoint state method, such as construction of velocity updates from prestack wave equation migration.
Journal ArticleDOI
Propagation, Observation, and Control of Waves Approximated by Finite Difference Methods
TL;DR: This paper surveys several topics related to the observation and control of wave propagation phenomena modeled by finite difference methods, focusing on the property of observability, corresponding to the question of whether the total energy of solutions can be estimated from partial measurements on a subregion of the domain or boundary.
Book ChapterDOI
The finite-difference time-domain method for modeling of seismic wave propagation
TL;DR: In this article, a review of the recent development in finite-difference time-domain modeling of seismic wave propagation and earthquake motion is presented, which is a robust numerical method applicable to structurally complex media.
Journal ArticleDOI
Forward and adjoint simulations of seismic wave propagation on fully unstructured hexahedral meshes
Daniel Peter,Dimitri Komatitsch,Dimitri Komatitsch,Yang Luo,Roland Martin,Nicolas Le Goff,Emanuele Casarotti,Pieyre Le Loher,Federica Magnoni,Qinya Liu,Céline Blitz,Tarje Nissen-Meyer,Piero Basini,Jeroen Tromp +13 more
TL;DR: This work presents various examples of fully unstructured meshes, snapshots of wavefields and finite-frequency kernels generated by Version 2.0 'Sesame' of the widely used open source spectral-element package SPECFEM3D, and benchmarked for a layercake model.
Journal ArticleDOI
Discrete Dispersion Relation for hp -Version Finite Element Approximation at High Wave Number
TL;DR: The dispersive properties of high order finite element schemes are analyzed in the setting of the Helmholtz equation, and an explicit form of the discrete dispersion relation is obtained for elements of arbitrary order.