Computational Wave Propagation by Thomas Hagstrom (auth.), Bjorn Engquist, Gregory A.

By Thomas Hagstrom (auth.), Bjorn Engquist, Gregory A. Kriegsmann (eds.)

This IMA quantity in arithmetic and its functions COMPUTATIONAL WAVE PROPAGATION relies at the workshop with a similar name and was once a vital part of the 1994-1995 IMA application on "Waves and Scattering." we want to thank Bjorn Engquist and Gregory A. Kriegsmann for his or her exertions in organizing this assembly and in enhancing the lawsuits. We additionally take this chance to thank the nationwide technology beginning, the military study place of work, and the place of work of Naval study, whose monetary aid made this workshop attainable. A vner Friedman Robert Gulliver v PREFACE even though the sector of wave propagation and scattering has its classical roots within the final century, it has loved a wealthy and colourful lifestyles during the last 50 peculiar years. Scientists, engineers, and mathematicians have devel­ oped refined asymptotic and numerical instruments to unravel difficulties of ever expanding complexity. Their paintings has been spurred on via rising and maturing applied sciences, essentially interested by the propagation and reception of knowledge, and the effective transmission of power. The energy of this medical box isn't really waning. elevated calls for to exactly quantify, degree, and regulate the propagation and scattering of waves in more and more advanced settings pose demanding medical and mathematical difficulties. those push the envelope of research and comput­ ing, simply as their forerunners did 50 years in the past. those smooth technological difficulties diversity from utilizing underwater sound to observe and expect international warming, to periodically embedding phase-sensitive amplifiers in optical fibers to insure lengthy variety electronic communication.

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Spherical near-field scanning techniques are formulated for acoustic and electromagnetic fields in the time domain so that a single set of time-domain nearfield measurements yields the far field in the time domain or over a wide range of frequencies. Probe-corrected as well as non-probe-corrected formulations are presented. For bandlimited time-domain fields, sampling theorems and computation schemes are derived that give the field outside the scan sphere in terms of sampled near-field data. 1.

_r 11=4 n::5 / ~,. "". '" ",/ " FIG. 2. The zeros Wns determined by h';;l(aWns/C) == o. 1]' [24] 27fa . n (I) 27fle" h n (w ns l' / e) . Fn(r, t) = --8(t-r/e+a/e)-u(t-r/e+a/e)- L..... 12) 52 THORKILD B. HANSEN where h~l)1 (z) is derivative of the spherical Hankel function with respect to its argument and u(t) is the unit step function given by u(t) = 0 for t :S 0 and u(t) = 1 for t > O. 9) produces the near-field formula for the time-domain acoustic field r>a where we have used the fact that all fields in the region r ~ a are zero for t < to.

Here we obtain higher order conditions that involve Bu, u, U88, and their time derivatives on the artificial boundary. 8). 5) yields: ~Bu=~a (())~(j+~)2-n2r at ~ n=O n ~ )=0 2 rH % ) 26 T. 1. 10) is increased further to O(r-~). 5) by differentiating the equation with respect to time. 14) ~B 8t = _~ ~ 1U 4 ~ an n=O (B) ~ (j ~ J=O + 2)[(j + ~)2 - n2lf~ rH ~ J which is equivalent to We note that _n 2 translates into the second tangential derivative. 15) yields a one asymptotic order higher boundary condition (to O(r-~)).

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