Higher-Order Numerical Methods for Transient Wave Equations

By G. Cohen. 2001

725 citations recorded by the source corpus.

Subfields: Electrical and Electronic Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/560c9170b581091cd54eb16a49ccd3b905690cf5

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In Electrical and Electronic Engineering

In Numerical Analysis

Citations in the corpus

Influence of Gauss and Gauss‐Lobatto quadrature rules on the accuracy of a quadrilateral finite element method in the time domain (2009, methodology): “The mass lumping technique consists of replacing the exact non-diagonal mass matrix by an approximate diagonal one [14],[7], which leads to a truly explicit scheme after time discretization.”
A Stable Finite Difference Method for the Elastic Wave Equation on Complex Geometries with Free Surfaces (2007, neutral): “As for finite difference methods, the formal order of these methods will be reduced to first order if material discontinuities are not aligned with element boundaries, see [6, 9].”
Reverse time migration with optimal checkpointing (2007, methodology): “The code uses Perfectly Matched Layer absorbing boundary conditions to simulate unbounded domain wave propagation (Cohen, 2001), which actually augments the systems (3) and (4) with additional fields and evolution laws which absorb energy near the boundary.”
Forward and adjoint simulations of seismic wave propagation on fully unstructured hexahedral meshes (2011, methodology): “D) elements (Wingate & Boyd 1996; Taylor & Wingate 2000; Komatitsch et al. 2001; Cohen 2002; Mercerat et al. 2006), as well as mixed meshes, although with increased cost and reduced accuracy in these non-tensorized elements, as in the discontinuous Galerkin method.”
UNIFORM STABILIZATION OF A VISCOUS NUMERICAL APPROXIMATION FOR A LOCALLY DAMPED WAVE EQUATION (2007, methodology): “From the Lax theorem (see [5]), we conclude that the scheme (89) is convergent.”
Stable Grid Refinement and Singular Source Discretization for Seismic Wave Simulations (2009, positive): “The main challenge is clearly to develop a stable fourth order spatial discretization, because the temporal accuracy can easily be matched by using a modified equation approach, see for example [8].”
Locking‐free continuum displacement finite elements with nodal integration (2008, background): “The crucial distinction between the above approaches and the present work lies in the use to which the so-called variational consistency condition is being put (our Equation (18), and Equation (34) of Reference [20]); we construct the assumed-strain operators from this condition, whereas in the abov”
Propagation, Observation, and Control of Waves Approximated by Finite Difference Methods (2005, methodology): “We refer to the book by Cohen [24] for the analysis of reflection and transmission indices for numerical schemes for wave equations with interfaces.”
Coercive space-time finite element methods for initial boundary value problems (2020, background): “, [42] for parabolic partial differential equations and [7, 8] for hyperbolic problems.”
The Wave Equation: Control and Numerics (2012, background): “, of the curve in the dispersion diagram (see Figure 5), is a natural consequence of the classical properties of the superposition of linear harmonic oscillators with close but not identical phases (see [21]).”
A uniformly controllable and implicit scheme for the 1-D wave equation (2005, background): “This by now well known phenomenon is due to the fact that (Sh,∆t) and, in general any discrete dynamics, generates spurious high-frequency oscillations that do not exist at the continuous level [7].”