scholarly journals Efficient calculation of two-dimensional periodic and waveguide acoustic Green’s functions

2002 ◽  
Vol 111 (4) ◽  
pp. 1610-1622 ◽  
Author(s):  
K. V. Horoshenkov ◽  
Simon N. Chandler-Wilde
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Two Dimensional ◽  
Efficient Calculation

Temperature field evaluation of a two-dimensional partial heat flow problem through Green's Functions

2019 ◽  
Author(s):  
Guilherme Ramalho Costa ◽  
José Aguiar santos junior ◽  
José Ricardo Ferreira Oliveira ◽  
Jefferson Gomes do Nascimento ◽  
Gilmar Guimaraes
Keyword(s):  
Temperature Field ◽  
Heat Flow ◽  
Green's Functions ◽  
Flow Problem ◽  
Green’S Functions ◽  
Field Evaluation ◽  
Two Dimensional

THREE‐DIMENSIONAL INDUCED POLARIZATION AND ELECTROMAGNETIC MODELING

Geophysics ◽  
1975 ◽  
Vol 40 (2) ◽  
pp. 309-324 ◽  
Author(s):  
Gerald W. Hohmann
Keyword(s):  
Integral Equation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Induced Polarization ◽  
The Body ◽  
Scale Model ◽  
Two Dimensional ◽  
Electromagnetic Modeling ◽  
The Earth

The induced polarization (IP) and electromagnetic (EM) responses of a three‐dimensional body in the earth can be calculated using an integral equation solution. The problem is formulated by replacing the body by a volume of polarization or scattering current. The integral equation is reduced to a matrix equation, which is solved numerically for the electric field in the body. Then the electric and magnetic fields outside the inhomogeneity can be found by integrating the appropriate dyadic Green’s functions over the scattering current. Because half‐space Green’s functions are used, it is only necessary to solve for scattering currents in the body—not throughout the earth. Numerical results for a number of practical cases show, for example, that for moderate conductivity contrasts the dipole‐dipole IP response of a body five units in strike length approximates that of a two‐dimensional body. Moving an IP line off the center of a body produces an effect similar to that of increasing the depth. IP response varies significantly with conductivity contrast; the peak response occurs at higher contrasts for two‐dimensional bodies than for bodies of limited length. Very conductive bodies can produce negative IP response due to EM induction. An electrically polarizable body produces a small magnetic field, so that it is possible to measure IP with a sensitive magnetometer. Calculations show that horizontal loop EM response is enhanced when the background resistivity in the earth is reduced, thus confirming scale model results.

2.5D AND 3D GREEN'S FUNCTIONS FOR ACOUSTIC WEDGES: IMAGE SOURCE TECHNIQUE VERSUS A NORMAL MODE APPROACH

2013 ◽  
Vol 21 (01) ◽  
pp. 1250025 ◽  
Author(s):  
A. TADEU ◽  
E. G. A. COSTA ◽  
J. ANTÓNIO ◽  
P. AMADO-MENDES
Keyword(s):  
Wave Propagation ◽  
Normal Mode ◽  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Element Formulation ◽  
Two Dimensional ◽  
Image Source ◽  
Point Pressure ◽  
Fluid Channel

2.5D and 3D Green's functions are implemented to simulate wave propagation in the vicinity of two-dimensional wedges. All Green's functions are defined by the image-source technique, which does not account directly for the acoustic penetration of the wedge surfaces. The performance of these Green's functions is compared with solutions based on a normal mode model, which are found not to converge easily for receivers whose distance to the apex is similar to the distance from the source to the apex. The applicability of the image source Green's functions is then demonstrated by means of computational examples for three-dimensional wave propagation. For this purpose, a boundary element formulation in the frequency domain is developed to simulate the wave field produced by a 3D point pressure source inside a two-dimensional fluid channel. The propagating domain may couple different dipping wedges and flat horizontal layers. The full discretization of the boundary surfaces of the channel is avoided since 2.5D Green's functions are used. The BEM is used to couple the different subdomains, discretizing only the vertical interfaces between them.

Green’s Functions for a Point Load and Dislocation in an Annular Region

1991 ◽  
Vol 58 (4) ◽  
pp. 954-959 ◽  
Author(s):  
R. E. Worden ◽  
L. M. Keer
Keyword(s):  
Analytic Continuation ◽  
Rigid Inclusion ◽  
Green's Functions ◽  
Green’S Functions ◽  
Point Load ◽  
Annular Region ◽  
Two Dimensional

This paper contains an analysis of a two-dimensional annular region whose inner boundary is that of either a hole or a perfectly bonded, rigid inclusion. Fast-converging Green’s functions for a point load or a dislocation on the annulus are determined using analytic continuation across the boundaries of the annulus.

A Two-Dimensional Cylindrical Transient Conduction Solution Using Green's Functions

2014 ◽  
Vol 136 (10) ◽  
Author(s):  
Robert L. McMasters ◽  
James V. Beck
Keyword(s):  
Parameter Estimation ◽  
Boundary Conditions ◽  
Green's Functions ◽  
Bessel Functions ◽  
Numerical Solutions ◽  
Green’S Functions ◽  
Two Dimensional ◽  
Trigonometric Functions ◽  
Convective Boundary Conditions ◽  
Convective Boundary

There are many applications for problems involving thermal conduction in two-dimensional (2D) cylindrical objects. Experiments involving thermal parameter estimation are a prime example, including cylindrical objects suddenly placed in hot or cold environments. In a parameter estimation application, the direct solution must be run iteratively in order to obtain convergence with the measured temperature history by changing the thermal parameters. For this reason, commercial conduction codes are often inconvenient to use. It is often practical to generate numerical solutions for such a test, but verification of custom-made numerical solutions is important in order to assure accuracy. The present work involves the generation of an exact solution using Green's functions where the principle of superposition is employed in combining a one-dimensional (1D) cylindrical case with a 1D Cartesian case to provide a temperature solution for a 2D cylindrical. Green's functions are employed in this solution in order to simplify the process, taking advantage of the modular nature of these superimposed components. The exact solutions involve infinite series of Bessel functions and trigonometric functions but these series sometimes converge using only a few terms. Eigenvalues must be determined using Bessel functions and trigonometric functions. The accuracy of the solutions generated using these series is extremely high, being verifiable to eight or ten significant digits. Two examples of the solutions are shown as part of this work for a family of thermal parameters. The first case involves a uniform initial condition and homogeneous convective boundary conditions on all of the surfaces of the cylinder. The second case involves a nonhomogeneous convective boundary condition on a part of one of the planar faces of the cylinder and homogeneous convective boundary conditions elsewhere with zero initial conditions.

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