Sampling method using prefiltered band-limited Green's functions for the solution of electromagnetic integral equations

1993 ◽  
Vol 41 (1) ◽  
pp. 20-24 ◽  
Author(s):  
G.F. Herrmann ◽  
S.M. Strain
Keyword(s):  
Integral Equations ◽  
Green's Functions ◽  
Sampling Method ◽  
Green’S Functions ◽  
Band Limited

scholarly journals On the unique solvability of a class of modified boundary integral equations

1984 ◽  
Vol 27 (3) ◽  
pp. 303-311 ◽  
Author(s):  
R. E. Kleinman ◽  
G. F. Roach
Keyword(s):  
Helmholtz Equation ◽  
Integral Equations ◽  
Unique Solvability ◽  
Green's Functions ◽  
Green’S Functions ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Transmission Problem

In a recent paper the authors considered the transmission problem for the Helmholtz equation by using a reformulation of the problem in terms of a pair of coupled boundary integral equations with modified Green's functions as kernels. In this note we settle the question of the unique solvability of these modified boundary integral equations.

POSITIVITY OF GREEN'S FUNCTIONS TO VOLTERRA INTEGRAL AND HIGHER ORDER INTEGRO-DIFFERENTIAL EQUATIONS

2009 ◽  
Vol 07 (04) ◽  
pp. 405-418 ◽  
Author(s):  
M. I. GIL'
Keyword(s):  
Differential Equations ◽  
Integral Equations ◽  
Green's Functions ◽  
Arbitrary Order ◽  
Green’S Functions ◽  
Higher Order ◽  
Volterra Integral Equations ◽  
Differential Delay

We consider Volterra integral equations and arbitrary order integro-differential equations. We establish positivity conditions and two-sided estimates for Green's functions. These results are then applied to obtain stability and positivity conditions for equations with nonlinear causal mappings (operators) and linear integro-differential parts. Such equations include differential, difference, differential-delay, integro-differential and other traditional equations.

Sensitivity kernels for seismic Fresnel volume tomography

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. U35-U46 ◽  
Author(s):  
Yuzhu Liu ◽  
Liangguo Dong ◽  
Yuwei Wang ◽  
Jinping Zhu ◽  
Zaitian Ma
Keyword(s):  
Green's Functions ◽  
Heterogeneous Media ◽  
Green’S Functions ◽  
Dominant Frequency ◽  
Sensitivity Kernel ◽  
Distribution Ranges ◽  
Band Limited ◽  
Homogeneous Media ◽  
Limited Sensitivity ◽  
Fresnel Volume Tomography

Fresnel volume tomography (FVT) offers higher resolution and better accuracy than conventional seismic raypath tomography. A key problem in FVT is the sensitivity kernel. We propose amplitude and traveltime sensitivity kernels expressed directly with Green’s functions for transmitted waves for 2D/3D homogeneous/heterogeneous media. The Green’s functions are calculated with a finite-difference operator of the full wave equation in the frequency-space domain. In the special case of homogeneous media, we analyze the properties of the sensitivity kernels extensively and gain new insight into these properties. According to the constructive interference of waves, the spatial distribution ranges of the monochromatic sensitivity kernels in FVT differ from each other greatly and are [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] periods of seismic waves, respectively, for 2D amplitude, 3D amplitude, 2D traveltime, and 3D traveltime conditions. We also have a new understanding of the relationship between raypath tomography and FVT. Within the first Fresnel volume of the dominant frequency, the band-limited sensitivity kernels of FVT in homogeneous media or smoothly heterogeneous media are very close to those of the dominant frequency. Thus, it is practical to replace the band-limited sensitivity kernel with a few selected frequencies or even the single dominant frequency to save computation when performing band-limited FVT. The numerical experiment proves that FVT using our sensitivity kernels can achieve more accurate results than traditional raypath tomography.

The Singularity at the Apex of a Bonded Wedge-Shaped Stamp

1979 ◽  
Vol 46 (3) ◽  
pp. 577-580 ◽  
Author(s):  
K. S. Parihar ◽  
L. M. Keer
Keyword(s):  
Eigenvalue Problem ◽  
Numerical Solution ◽  
Integral Equations ◽  
Half Space ◽  
Singular Integral ◽  
Green's Functions ◽  
Green’S Functions ◽  
Singular Integral Equations ◽  
Elastic Half Space

The problem of determining the singularity at the apex of a rigid wedge bonded to an elastic half space is formulated by considerations of Green’s functions for the loaded half space. The eigenvalue problem is reduced to finding the solution of a coupled pair of singular integral equations. A numerical solution for small wedge angles is given.

scholarly journals Integral Equations and the Determination of Green's Functions in the Theory of Potential

1912 ◽  
Vol 31 ◽  
pp. 71-89 ◽  
Author(s):  
H. S. Carslaw
Keyword(s):  
Green’S Function ◽  
Integral Equations ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Closed Surface ◽  
Second Derivatives

In the Theory of Potential the term Green's Function, used in a slightly different sense by Maxwell, now denotes a function associated with a closed surface S, with the following properties:—(i) In the interior of S, it satisfies ∇2V = 0.(ii) At the boundary of S, it vanishes.(iii) In the interior of S, it is finite and continuous, as also its first and second derivatives, except at the point (x1, y1,z1).

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