Document Zbl 1348.65127

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Sci. Comput.</a> <a href="/?q=in%3A356839" title="Articles in this Issue">38, No. 4, A2535-A2557 (2016)</a>. </div> <div class="abstract">Summary: The paper investigates a variant of semi-implicit spectral deferred corrections (SISDC) in which the stiff, fast dynamics correspond to fast propagating waves (“fast-wave slow-wave problem”). We show that for a scalar test problem with two imaginary eigenvalues $i \lambda_{\mathrm{f}}$, $i \lambda_{\mathrm{s}}$, having $\Delta t (|\lambda_{\mathrm{f}} | + | \lambda_{\mathrm{s}}|) < 1$ is sufficient for the fast-wave slow-wave SDC (<span class="zbmathjax-textsc">fwsw</span>-SDC) iteration to converge and that in the limit of infinitely fast waves the convergence rate of the nonsplit version is retained. Stability function and discrete dispersion relation are derived and show that the method is stable for essentially arbitrary fast-wave Courant-Friedrichs-Lewy numbers as long as the slow dynamics are resolved. The method causes little numerical diffusion and its semidiscrete phase speed is accurate also for large wave number modes. Performance is studied for an acoustic-advection problem and for the linearised Boussinesq equations, describing compressible, stratified flow. <span class="zbmathjax-textsc">fwsw</span>-SDC is compared to diagonally implicit Runge-Kutta (DIRK) and implicit-explicit (IMEX) Runge-Kutta methods and found to be competitive in terms of both accuracy and cost.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6624661">Cited in <strong>18</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M20" title="MSC2020">65M20</a> </td> <td class="space"> Method of lines for initial value and initial-boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M70" title="MSC2020">65M70</a> </td> <td class="space"> Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35L65" title="MSC2020">35L65</a> </td> <td class="space"> Hyperbolic conservation laws </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65L06" title="MSC2020">65L06</a> </td> <td class="space"> Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76N99" title="MSC2020">76N99</a> </td> <td class="space"> Compressible fluids and gas dynamics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aspectral+deferred+corrections">spectral deferred corrections</a>; <a href="/?q=ut%3Afast-wave+slow-wave+splitting">fast-wave slow-wave splitting</a>; <a href="/?q=ut%3AEuler+equations">Euler equations</a>; <a href="/?q=ut%3Aacoustic+advection">acoustic advection</a>; <a href="/?q=ut%3Asemidiscretization">semidiscretization</a>; <a href="/?q=ut%3Aconvergence">convergence</a>; <a href="/?q=ut%3Astability">stability</a>; <a href="/?q=ut%3ACourant-Friedrichs-Lewy+numbers">Courant-Friedrichs-Lewy numbers</a>; <a href="/?q=ut%3Aacoustic-advection+problem">acoustic-advection problem</a>; <a href="/?q=ut%3Alinearised+Boussinesq+equation">linearised Boussinesq equation</a>; <a href="/?q=ut%3ARunge-Kutta+methods">Runge-Kutta methods</a></div> <div class="software"> <h3>Software:</h3><a href="/software/6590">Matplotlib</a>; <a href="/software/940">SymPy</a>; <a href="/software/16754">pySDC</a>; <a href="/software/6293">SciPy</a>; <a href="/software/452">IRKC</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 1348.65127" data-ciurl="/ci/06624661" data-biburl="/bibtex/06624661.bib" data-amsurl="/amsrefs/06624661.bib" data-xmlurl="/xml/06624661.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06624661.pdf" title="Zbl 1348.65127 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/10.1137/16M1060078" aria-label="DOI for “Spectral deferred corrections with fast-wave slow-wave splitting”" title="10.1137/16M1060078">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1602.01626"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">R. 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