Document Zbl 0636.65133

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H.</a>; <a href="/authors/?q=ai%3Achen.gaoli%7Cchen.guang-long%7Cchen.gui-lian%7Cchen.gangli%7Cchen.guolin%7Cchen.guolan%7Cchen.guolu%7Cchen.guoliang.1%7Cchen.gaolin%7Cchen.gengli%7Cchen.genlong%7Cchen.genliang%7Cchen.guilin%7Cchen.guiling%7Cchen.guolong%7Cchen.gongliang%7Cchen.guo-li%7Cchen.gwo-liang%7Cchen.guo-linag%7Cchen.guanlong%7Cchen.guanlie%7Cchen.guanglei%7Cchen.guanlun%7Cchen.guangliang%7Cchen.guoling%7Cchen.gonglian" title="Author Profile">Chen, G. L.</a>; <a href="/authors/raridon.r-j" title="Author Profile">Raridon, R. J.</a>; <a href="/authors/mcgaffey.r-w" title="Author Profile">McGaffey, R. W.</a>; <a href="/authors/jaeger.e-f" title="Author Profile">Jaeger, E. F.</a>; <a href="/authors/bell.m-a" title="Author Profile">Bell, M. A.</a>; <a href="/authors/hoffman.d-j" title="Author Profile">Hoffman, D. J.</a></div> <h2 class="title"> <strong>A 3D analysis of Maxwell’s equations for cavities of arbitrary shape.</strong> <i>(English)</i> <a class="label nowrap" href="/0636.65133">Zbl 0636.65133</a> </h2> <div class="source"> <a href="/serials/127" title="Journal Profile">J. Comput. Phys.</a> <a href="/?q=in%3A166851" title="Articles in this Issue">75, No. 1, 168-189 (1988)</a>. </div> <div class="abstract">The authors consider the problem of three-dimensional cavity antennas. They approximate the relevant equations by finite difference equations which are solved by successive overrelaxation and indicate how the methods can be used to find the eigenfrequencies of arbitrarily shaped cavities. A number of results are given but there is no detailed analysis, and nearly all the results are given in graphical rather than numerical form.<div class="reviewer"> Reviewer: <a href="/authors/?q=Ll+G%2A+Chambers">Ll.G.Chambers</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A4037136">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65Z05" title="MSC2020">65Z05</a> </td> <td class="space"> Applications to the sciences </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65N06" title="MSC2020">65N06</a> </td> <td class="space"> Finite difference methods for boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65N25" title="MSC2020">65N25</a> </td> <td class="space"> Numerical methods for eigenvalue problems for boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A78A50" title="MSC2020">78A50</a> </td> <td class="space"> Antennas, waveguides in optics and electromagnetic theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35Q99" title="MSC2020">35Q99</a> </td> <td class="space"> Partial differential equations of mathematical physics and other areas of application </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35J05" title="MSC2020">35J05</a> </td> <td class="space"> Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AMaxwell%27s+equation">Maxwell’s equation</a>; <a href="/?q=ut%3Acavities+of+arbitrary+shape">cavities of arbitrary shape</a>; <a href="/?q=ut%3Athree-dimensional+cavity+antennas">three-dimensional cavity antennas</a>; <a href="/?q=ut%3Afinite+difference+equations">finite difference equations</a>; <a href="/?q=ut%3Asuccessive+overrelaxation">successive overrelaxation</a>; <a href="/?q=ut%3Aeigenfrequencies">eigenfrequencies</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 0636.65133" data-ciurl="/ci/04037136" data-biburl="/bibtex/04037136.bib" data-amsurl="/amsrefs/04037136.bib" data-xmlurl="/xml/04037136.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/04037136.pdf" title="Zbl 0636.65133 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/0021-9991(88)90105-2" aria-label="DOI for “A 3D analysis of Maxwell's equations for cavities of arbitrary shape”" title="10.1016/0021-9991(88)90105-2">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://www.osti.gov/biblio/5918872" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Perkins, F. W.; Kluge, R. F., IEEE Trans. Plasma Sci., PS-12, No. 2, 161 (1984), For example</td> </tr><tr> <td>[2]</td> <td class="space">Cohn, S. B., (Proc. IRE, 35 (1948)), 783</td> </tr><tr> <td>[3]</td> <td class="space">Schwinger, J.; Saxon, D. S., Discontinuities in Waveguides (1968), Gordon & Breach: Gordon & Breach New York, For example</td> </tr><tr> <td>[4]</td> <td class="space">Rao, S. M.; Wilton, D. R.; Glisson, A. W., IEEE Trans. Antennas Propag., AP-30, No. 3, 409 (1982)</td> </tr><tr> <td>[5]</td> <td class="space">Jones, D. S., Methods in Electromagnetic Wave Propagation (1979), Oxford University Press: Oxford University Press Oxford</td> </tr><tr> <td>[6]</td> <td class="space">Davies, H. B.; Muilwyk, C. A., (Proc. IEE (London), 113 (1966)), 277, No. 2</td> </tr><tr> <td>[7]</td> <td class="space">Whealton, J. H.; McGaffey, R. W.; Meszaros, P. S., (presented at the IEEE International Conference on Plasma Science. presented at the IEEE International Conference on Plasma Science, San Diego (1983))</td> </tr><tr> <td>[8]</td> <td class="space">Whealton, J. H.; Jaeger, E. F.; Whitson, J. C., J. Comput. Phys., 27, 32 (1978) · <a href="/0386.76100" class="nowrap">Zbl 0386.76100</a></td> </tr><tr> <td>[9]</td> <td class="space">Whealton, J. H.; Tsai, C. C.; Dagenhart, W. K.; Gardner, W. L.; Haselton, H. H.; Kim, J.; Menon, M. M.; Ryan, P. M.; Schechter, D. E.; Stirling, W. L., Appl. Phys. Lett., 33, 278 (1978)</td> </tr><tr> <td>[10]</td> <td class="space">Whealton, J. H.; Wooten, J. W.; McGaffey, R. W.; McCollough, D. H.; Raridon, R. J.; Bell, M. A.; Meszaros, P. S.; Goswitz, A. M.; Hoffman, D. J., Bull. Amer. Phys. Soc., 28, 1087 (1983)</td> </tr><tr> <td>[11]</td> <td class="space">Hornsby, J. S., A computer Programme for the Solution of Second Order Quasi-Linear Partial Differential Equations of the Elliptic Type Using the Method of Over-Relaxation, (CERN-63-7 (1963), European Organization for Nuclear Research: European Organization for Nuclear Research Geneva) · <a href="/0093.14002" class="nowrap">Zbl 0093.14002</a></td> </tr><tr> <td>[12]</td> <td class="space">Smith, G. D., Numerical Solution of Partial Differential Equations: Finite Difference Methods (1978), Clarendon Press: Clarendon Press Oxford · <a href="/0389.65040" class="nowrap">Zbl 0389.65040</a></td> </tr><tr> <td>[13]</td> <td class="space">McGaffey, R. W.; Whealton, J. H.; Raridon, R. J.; Wooten, J. W.; Bell, M. A., Bull. Amer. Phys. Soc., 29, 146 (1984)</td> </tr><tr> <td>[14]</td> <td class="space">Jones, D. S., Methods in Electromagnetic Wave Propagation, ((1979), Oxford University Press: Oxford University Press Oxford), 135</td> </tr><tr> <td>[15]</td> <td class="space">Hoffman, D. J.; Baity, F. W.; Becraft, W. R.; Caughman, J. B.O.; Owens, T. L., Fusion Technol., 8, No. l, 411 (1985), Pt. 2A</td> </tr><tr> <td>[16]</td> <td class="space">Kapchinskii, I. M.; Lazarev, W. V., IEEE Trans. Nucl. Sci., NS-26, 3462 (1978)</td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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