Large-Scale Structures in Acoustics and Electromagnetics Proceedings of a Symposium (1996) / Chapter Skim
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11 DISCUSSION
11 DISCUSSION
Pages 221-240
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From page 221... ...
In the time domain, ~ believe there are similar approaches in both communities dealing strictly with waves. For example, one of the outstanding electromagnetics problems is to get better absorbing boundary conditions.
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From page 222... ...
For that reason and without any calculations, one can probably anticipate that there must be a tradeoff between the number of finite elements put in between the scatter and that artificial boundary (on which are positioned the infinite elements or nonreflecting boundary condition) , and the numbers of terms in the real direction for the infinite element.
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From page 223... ...
PETER PINSKY: Concerning DtN versus infinite elements, the comment made by Leszek Demkow~cz was a very sensible one in that there is an underlying relationship in the formulation between DtN and infinite elements. In fact, we have recently been performing numerical convergence studies at Stanford between these two types of boundary conditions, the local infinite element and the non-local D^.N.
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From page 224... ...
That is an old problem in acoustics, and there is an enormous field of activity in inversions. ADRIANUS DE HOOP: One of the symposium goals that John Tucker put forward is to evaluate frequency domain versus time domain.
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I do not know of anyone who has done it in one region in the time domain and in another region in the frequency domain, but if you can do one, you could probably do the other.
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From page 226... ...
Now, if one continues with an infinite time signal, those single pulses become double pulses. Furthermore, when it comes to the Fourier inverse transform of such a function involving double pulses, it is no surprise that some difficulties arise because one cannot numerically integrate a function even with a single pulse; actually, one can do it by using the Cauchy principal value integral sum, but it is not simple, and it is almost hopeless with a double-order pulse.
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From page 227... ...
In predictions for finite difference methods, what are the effects? " BELYTSCHKO: ~ do not believe we have studied the problem for stretched grids, but the transmissivity and the wave propagation characteristics through grids of both finite element and finite difference types have been studied for plane waves.
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From page 228... ...
There are a number of hybrid approaches, and for the last couple of years using hybrid approaches has seemed to be the big push in electromagnetics modeling. Yet in all the talks from the structural acoustics side, I did not hear about anyone trying hybrid approaches.
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From page 229... ...
He has, further, used asymptotic methods in dynamic wave propagation shell problems and combined some of this technology into what he calls a big-element finite element approach that is based on the asymptotic solution. He can mode!
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From page 230... ...
This is all done in the frequency domain and so is an example of a hybrid combining technique in the fr`~nilPn~.v domain for in`7-roP scattering.
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From page 231... ...
One either can take, in the nofield point-source case, solutions for which the source points are not in the domain of interest, or can take wave function expansions in the frequency domain, such as spherical waves or cylindrical waves or any other type of waves convenient to the problem. Based on what T have seen, this signature-combination approach is the only technique involving a specific strategy for combining properties in the acoustics or electrodynamics problems, and also electromagnetic problems, so that once the signatures of the separate elements have been built up, one can combine them in a systematic mathematical manner.
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From page 232... ...
The time differentiation is a firstorder convolution of the material properties of the wave function, with losses present. An interesting property, which was very surprising to me, is that this differential operator enfolds all the types of wave motions in a common structure.
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From page 233... ...
If one develops a successful adaptive scheme based on parallel computing, multiprocess computing, and domain decomposition techniques, be prepared to include the error estimation package as part of the package that must be parallelized. Hand in hand with error estimation and adaptive methods is the ability to control data at the boundary.
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From page 234... ...
At Stanford, we have attempted to do some of this when looking at the effects of point-loaded cylindrical shells in the context of finite elements, and making an exact representation of the pressure loading on a cylindrical shell. We are analyzing the ability of the finite element discretization to represent propagating waves emanating from the point drive as well as the decaying evanescent waves.
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From page 235... ...
One direction that the electromagnetics community has decided to pursue is that of hybrid approaches. A number of different hybrid approaches need to be addressed further, including coupling the discrete techniques with integral techniques and with asymptotic techniques, and doing so in an effective manner for the particular types of problems of interest as well as for the different computer architectures that are coming on line.
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From page 236... ...
In the frequency domain, this means essentially that the real and imaginary parts of the constitutive coefficient should obey the Kramers-Konig causality relations. In the time domain, they should be of the convolution twe.
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From page 237... ...
The third subject with promise involves looking at the complex frequency domain for positive real values of the complex frequency. One takes the time Laplace transform for any causal function and works with the positive real values of S to solve the problem.
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From page 238... ...
Perhaps when computing, for instance, in the frequency domain, one may want to go back to the time domain. It would be necessary to take a Fourier transform and then the time domain is an infinite domain.
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From page 239... ...
On behalf of the audience and the panelists, I want to give a word of thanks first to Phil Abraham for having conceived the idea of holding this symposium, to Louise Couchman for providing the resources of her office toward making this event happen, and to John Tucker of the National Research Council for his excellent hospitality and organization. TUCKER: And I want to express my thanks to all of you for coming.
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