Large-Scale Structures in Acoustics and Electromagnetics Proceedings of a Symposium (1996) / Chapter Skim
Currently Skimming:
3 ACOUSTIC, ELASTODYNAMIC, AND ELECTROMAGNETIC WAVEFIELD COMPUTATION - A STRUCTURED APPROACH BASED ON RECIPROCITY
3 ACOUSTIC, ELASTODYNAMIC, AND ELECTROMAGNETIC WAVEFIELD COMPUTATION - A STRUCTURED APPROACH BASED ON RECIPROCITY
Pages 72-88
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 72... ...
de Hoop Schiumberger Cambridge Research Cambridge, England The reciprocity theorems for acoustic, elastodynamic, and electromagnetic wavefields in linear, time-invariant configurations show a common structure that can serve as a guideline for the development of computational methods for these wavefields. To this end, the wavefield reciprocity theorems are taken as points of departure.
|
From page 73... ...
de Hoop (1987, 198S, 1989, 1990, 1991, 1992) and in a forthcoming book (de Hoop, 1995~.
|
From page 74... ...
of the wave motion be composed of the components of the two wavefield quantities whose inner product represents the area density of power flow (Poynting vector)
|
From page 75... ...
where or = particle velocity and up g = dynamic stress, and QI aft, f2, f3,hll,hl2,hl3,h21,h22,h23,h31,h3 2, h331 ~ where fk = volume source density of force and hi j = volume source density of deformation rate. For electromagnetic waves, ,J Fp = [E1, E2 ~ E3 ,O,-H3, H2, H3,0,-H1 ,-H2, Hi ,0]
|
From page 76... ...
It is therefore conjectured that the indicated structure of the spatial differential matrix operator could prove to be fundamental in order that a system of first-order partial differential equations be representative for a physical wave motion. It is noted that the medium matrix Me p is not subjected to any restriction of this kind.
|
From page 77... ...
THE RECIPROCITY THEOREMS In the wavefield reciprocity theorems certain interaction quantities are considered that are representative for the interaction between two admissible states of the pertaining wavefield in a given (proper or improper) subdomain D of SR3 .
|
From page 78... ...
over the domain }~ and applying Gauss' integral theorem to the first term on the left-handed side over each subdomain of 10 where the field quantities are continuously differentiable. Adding the contributions from these subdomains, the contributions from sourcefree interfaces of discontinuity in medium properties in the interior of }O cancel in view of the boundary conditions given in (3.19)
|
From page 79... ...
For an isotropic medium, the medium matrix is diagonal; an instantaneously reacting isotropic medium is therefore always time-reverse selfadjoint. The terms containing the volume source densities yield the contribution from the volume sources to the interaction of the two states.
|
From page 80... ...
to the global energy balance for the domain Jib, provided that MQP=MPQ. This implies that for the energy considerations pertaining to a physical wavefield to hold, the medium matrix must be symmetric.
|
From page 81... ...
. In these cases, time Laplace and spatial Fourier transform techniques provide the analytical tools to determine the wave motion or, in fact, the relevant Green's tensor.
|
From page 82... ...
;xe}~:D,te9t,n=1,...,\} is an appropriate sequence of known, linearly independent expansion functions with }~ as their supports, and {oc[n] ;n = 1,...,\} is the sequence of expansion coefficients to be computed.
|
From page 83... ...
(3.39) Application of the earlier reciprocity theorems to the State A and the sequence of States Z leads to a system of linear algebraic equations in the expansion coefficients.
|
From page 84... ...
and Mur (1990, 1991, 1993) for the application to electromagnetic fields and Stam and de Hoop (1988, 1989, 1990)
|
From page 85... ...
Using these properties, the space-time wave motion can be recovered after having solved a sequence of space problems with appropriate values of the time Laplace transform parameter. For recent results in this direction, see Lee et al.
|
From page 86... ...
Stam, H.J., and A.T. de Hoop, 1988, "Time-domain reciprocity theorems for elastodynamic wave fields in solids with relaxation and their application to inverse problems," Wave Motion 10,479-489.
|
From page 87... ...
Elastic Waves in Solids form: in which and (3.A1 ~ (3.A2) For elastic waves in so:lids, the spatial differential operator in the system of (3.12)
|
From page 88... ...
mass and Si j p g is the corr~pliance. Electromagnetic Waves For electromagnetic waves the spatial differential operator in the system of (3.12)
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.