Sparse Diagonal Forms for Translation Operators for the Helmholtz Equation in Two Dimensions,

1995 ◽  
Author(s):  
Vladimir Rokhlin
Keyword(s):  
Helmholtz Equation ◽  
Two Dimensions ◽  
Diagonal Forms ◽  
Translation Operators

scholarly journals On reconstruction of the coefficient in complex Helmholtz’s equation

2021 ◽  
Vol 2056 (1) ◽  
pp. 012015
Author(s):  
M Malovichko ◽  
A Orazbayev ◽  
Yu Kloss ◽  
N Khokhlov
Keyword(s):  
Helmholtz Equation ◽  
Waveform Inversion ◽  
Theory Of Elasticity ◽  
Two Dimensions ◽  
Seismic Exploration ◽  
Research Areas ◽  
Full Waveform ◽  
Early Results ◽  
Fast Solution ◽  
Primary Focus

Abstract This note summarizes some preliminary results on the fast solution of the coefficient inverse problem for the Helmholtz equation, given measured pressure in a set of observation points. The Helmholtz equation is the model PDE for the harmonic problem of the linear theory of elasticity, and this work is a move in that direction. The problem has been the primary focus for several research areas, most notably seismic exploration. Still, practical problems are very challenging because they are non-linear and large. In this paper, we develop a novel numerical method for seismic full-waveform inversion based on Newton iterations. Its distinctive future is that it does not require the Jacobian of the target functional. Thus, in certain scenarios, it will perform only a fraction of computations comparing to the conventional Gauss-Newton algorithm. We present some early results on the Helmholtz equation in two dimensions.

A smoothed finite element method for exterior Helmholtz equation in two dimensions

2017 ◽  
Vol 84 ◽  
pp. 237-252 ◽  
Author(s):  
Yingbin Chai ◽  
Zhixiong Gong ◽  
Wei Li ◽  
Tianyun Li ◽  
Qifan Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Helmholtz Equation ◽  
Two Dimensions ◽  
Smoothed Finite Element Method ◽  
Element Method

Remarks on the implementation of the wideband FMM for the Helmholtz equation in two dimensions

2006 ◽  
pp. 99-110 ◽  
Author(s):  
H. Cheng ◽  
W. Crutchfield ◽  
Z. Gimbutas ◽  
L. Greengard ◽  
J. Huang ◽  
...  
Keyword(s):  
Helmholtz Equation ◽  
Two Dimensions
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