ÿþ<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> <meta content="text/html; charset=ISO-8859-1" http-equiv="Content-Type"> <title>Snorre Christiansen's publications</title> <script type="text/javascript"> var _gaq = _gaq || []; _gaq.push(['_setAccount', 'UA-23630705-1']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); </script> </head> <body> <h2 style="font-family: sans-serif;"><a href="http://folk.uio.no/snorrec">Snorre H. Christiansen</a> <br> </h2> <span style="font-family: sans-serif;"><span style="font-weight: bold;"><br> </span></span> <h3 style="font-family: sans-serif;">Research topics<br> </h3> <ul style="font-family: sans-serif;"> <li>Boundary integral equations, preconditioning [2,3,4,5,6,7,8,17]<br> </li> <li>Finite element spaces, in particular for differential forms [10,12,13,14,15,21,24,25,26,28]<br> </li> <li>Yang-Mills-Higgs equations, lattice gauge theory [11,16,19,20,22,23,27]<br> </li> <li>General relativity, Regge calculus [9,18]<br> </li> </ul> <h3><br> <span style="font-family: sans-serif;"></span></h3> <h3><span style="font-family: sans-serif;">Papers in chronological order [submitted/published]</span></h3> <ul style="font-family: serif;"> </ul> <ol style="font-family: serif;"> <li style="font-family: sans-serif;"><span style="font-style: italic;"><span style="color: rgb(102, 0, 0);">Stochastic bilevel programming in structural optimization</span>&nbsp;</span><br> Struct.&nbsp; Multidiscip. Optim. <span style="font-style: italic;"></span>[1999/2001] with M. Patriksson and L. Wynter&nbsp; <a href="http://dx.doi.org/10.1007/s001580100115">article</a><br> <span class="title"></span> </li> <li style="font-family: sans-serif;"><span class="title"><span style="font-style: italic; color: rgb(102, 0, 0);">Des pr&eacute;conditionneurs pour la r&eacute;solution num&eacute;rique des &eacute;quations int&eacute;grales de fronti&egrave;re de l'acoustique </span><br> </span><span class="title"></span><span class="title"> C. R. Acad. Sci. Paris Math. [1999/2000] </span><span class="title">with J.-C. N&eacute;d&eacute;lec&nbsp;</span><span class="title"> <a href="http://dx.doi.org/10.1016/S0764-4442%2800%2900225-1">cras</a></span></li> <li style="font-family: sans-serif;"><span class="title"><span style="font-style: italic; color: rgb(102, 0, 0);">Des pr&eacute;conditionneurs pour la r&eacute;solution num&eacute;rique des &eacute;quations int&eacute;grales de fronti&egrave;re de l'&eacute;lectromagn&eacute;tisme </span><br> </span><span class="title"></span><span class="title">C. R. Acad. Sci. Paris Math. [2000/2000] </span> <span class="title">with J.-C. N&eacute;d&eacute;lec&nbsp;</span><span class="title"> <a href="http://dx.doi.org/10.1016/S0764-4442%2800%2901717-1">cras</a><br> </span></li> <li style="font-family: sans-serif;"><a href="http://dx.doi.org/10.1090/S0025-5718-03-01581-3"><span title="Discrete Fredholm properties for the EFIE "></span></a><span style="font-style: italic; color: rgb(102, 0, 0);">Discrete Fredholm properties and convergence estimates for the Electric Field Integral Equation </span><br> Math. Comp. [2000/2004]&nbsp; <a href="http://dx.doi.org/10.1090/S0025-5718-03-01581-3"><span title="Discrete Fredholm properties for the EFIE ">article</span></a> </li> <li style="font-family: sans-serif;"><a href="http://dx.doi.org/10.1137/S0036142901388731"><span title="A preconditioner for the EFIE based on Calderon formulas"></span></a><span style="font-style: italic; color: rgb(102, 0, 0);">A preconditioner for the Electric Field Integral Equation based on Calderon formulas</span><br> <span class="title"></span>SIAM J. Numer. Anal.<span class="title"></span> [2001/2002] with J.-C. <span style="text-decoration: underline;"></span><span class="title">N&eacute;d&eacute;lec&nbsp;</span> <span style="text-decoration: underline;"></span><a href="http://dx.doi.org/10.1137/S0036142901388731"><span title="A preconditioner for the EFIE based on Calderon formulas">article</span></a></li> <li style="font-family: sans-serif;"><a href="http://dx.doi.org/10.1007/s00211-002-0422-0"><span title="The EFIE on Lipschitz screens"></span></a> <span style="font-style: italic; color: rgb(102, 0, 0);">The Electric Field Integral Equation on Lipschitz screens: definitions and numerical approximation </span><br> Numer. Math.&nbsp; [2001/2002] with A. Buffa&nbsp; <a href="http://dx.doi.org/10.1007/s00211-002-0422-0"><span title="The EFIE on Lipschitz screens">article</span></a> </li> <li style="font-family: sans-serif;"><a href="http://dx.doi.org/10.1016/S1631-073X%2803%2900156-0"><span title="Stable BEM for low frequency electromagnetic scattering"></span></a><span style="font-style: italic; color: rgb(102, 0, 0);">Uniformly stable preconditioned mixed boundary element method for low-frequency electromagnetic scattering</span><br> C. R. Math. Acad. Sci. Paris [2002/2003]&nbsp; <a href="http://www.sam.math.ethz.ch/reports/2002/17">preprint</a> <a href="http://dx.doi.org/10.1016/S1631-073X%2803%2900156-0"><span title="Stable BEM for low frequency electromagnetic scattering">cras</span></a> <a href="Chr03StableSlides.ps">slides</a><br> <a href="http://dx.doi.org/10.1016/S1631-073X%2803%2900156-0"> </a> </li> <li style="font-family: sans-serif;"><span title="Stable BEM for low frequency electromagnetic scattering"><span style="font-style: italic; color: rgb(102, 0, 0);">Mixed boundary element method for eddy current problems </span><br> [2002] <a href="http://www.sam.math.ethz.ch/reports/2002/16">preprint</a><br> </span></li> <li style="font-family: sans-serif;"><a href="http://dx.doi.org/10.1142/S0218202504003854"><span title="A Finite Element interpretation of Regge Calculus"></span></a><span style="font-style: italic; color: rgb(102, 0, 0);">A characterization of second order differential operators on finite element spaces </span><br> M3AS Math. Models Methods Appl. Sci. [2003/2004]&nbsp; <a href="http://dx.doi.org/10.1142/S0218202504003854"><span title="A Finite Element interpretation of Regge Calculus">article</span></a></li> <li style="font-family: sans-serif;"><a href="http://dx.doi.org/10.1137/S0036142903433807"><span title="Div-Curl lemma for edge elements"></span></a> <span style="font-style: italic; color: rgb(102, 0, 0);">A div-curl lemma for edge elements </span><br> SIAM J. Numer. Anal. [2003/2005]&nbsp; <a href="http://dx.doi.org/10.1137/S0036142903433807"><span title="Div-Curl lemma for edge elements">article</span></a></li> <li style="font-family: sans-serif;"><span style="font-style: italic; color: rgb(102, 0, 0);">On constraint preservation in numerical simulations of Yang-Mills equations </span><br> SIAM J. Sci. Comp. [2004/2006] with R. Winther&nbsp; <a href="http://dx.doi.org/10.1137/040616887">article</a></li> <li style="font-family: sans-serif;"><span style="font-style: italic; color: rgb(102, 0, 0);">A dual finite element complex on the barycentric refinement </span><br> Math. Comp. [2005/2007] with A. Buffa&nbsp; <a href="http://dx.doi.org/10.1016/j.crma.2004.12.022">cras</a> <a href="http://dx.doi.org/10.1090/S0025-5718-07-01965-5">article</a></li> <li style="font-family: sans-serif;"><span style="font-style: italic; color: rgb(102, 0, 0);">Stability of Hodge decompositions in finite element spaces of differential forms in arbitrary dimension </span><br> Numer. Math. [2005/2007]&nbsp; <a href="http://dx.doi.org/10.1007/s00211-007-0081-2"> article</a>&nbsp; (the <a href="http://arxiv.org/abs/1007.1120">preprint</a> is richer)</li> <li style="font-family: sans-serif;"><span style="font-style: italic; color: rgb(102, 0, 0);">A construction of spaces of compatible differential forms on cellular complexes </span><br> M3AS Math. Models Methods Appl. Sci. [2005/2008]&nbsp; <a href="http://dx.doi.org/10.1142/S021820250800284X">article</a></li> <li style="font-family: sans-serif;"><span style="font-style: italic; color: rgb(102, 0, 0);">Smoothed projections in finite element exterior calculus </span><br> Math. Comp. [2006/2008] with R. Winther&nbsp; <a href="http://dx.doi.org/10.1090/S0025-5718-07-02081-9">article</a><br> </li> <li style="font-family: sans-serif;"><span style="font-style: italic; color: rgb(102, 0, 0);">Constraint preserving schemes for some gauge invariant wave equations </span><br> SIAM J. Sci. Comp. [2007/2009]&nbsp; <a href="http://dx.doi.org/10.1137/070690900">article</a></li> <li style="font-family: sans-serif;"><span style="font-style: italic; color: rgb(102, 0, 0);">A multiplicative Calderon preconditioner for the electric field integral equation </span><br> IEEE Trans. Ant. Prop. [2007/2008] with A. Buffa, E. Michielssen and coworkers&nbsp; <span class="title"><a href="http://dx.doi.org/10.1109/TAP.2008.926788">article</a></span></li> <li style="font-family: sans-serif;"><span style="font-style: italic; color: rgb(102, 0, 0);">On the linearization of Regge calculus </span><br> Numer. Math. [2008/2011] <a href="http://dx.doi.org/10.1007/s00211-011-0394-z">article</a><a href="http://arxiv.org/abs/1106.4266"><br> </a></li> <li style="font-family: sans-serif;"><span style="font-style: italic; color: rgb(102, 0, 0);">Discretizing the Maxwell-Klein-Gordon equation by the Lattice Gauge Theory formalism </span><br> IMA J. Numer. Anal.&nbsp; [2008/2011] with T. G. Halvorsen <a href="http://dx.doi.org/10.1093/imanum/drp019">article</a><span style="text-decoration: underline;"></span><a href="http://www.math.uio.no/eprint/pure_math/2008/17-08.html"><br> </a></li> <li style="font-family: sans-serif;"><span style="font-style: italic; color: rgb(102, 0, 0);">Convergence of Lattice Gauge Theory for Maxwell's equation </span><br> BIT Numerical Mathematics&nbsp; [2008/2009] with T. G. Halvorsen&nbsp; <a href="http://dx.doi.org/10.1007/s10543-009-0242-z">article<br> </a></li> <li style="font-family: sans-serif;"><span style="font-style: italic; color: rgb(102, 0, 0);">Foundations of finite element methods for wave equations of Maxwell type </span><br> Springer, Applied Wave Mathematics [2008/2009]&nbsp; <a href="http://dx.doi.org/10.1007/978-3-642-00585-5_17">chapter</a><br> </li> <li style="font-family: sans-serif;"><span style="font-style: italic; color: rgb(102, 0, 0);">Convergence of a constrained finite element discretization of the Maxwell Klein Gordon equation </span><br> M2AN Math. Model. Numer. Anal. [2009/2011] with C. Scheid <a href="http://dx.doi.org/10.1051/m2an/2010100">article</a> <br> </li> <li style="font-family: sans-serif;"><span style="font-style: italic; color: rgb(102, 0, 0);">A gauge invariant discretization on simplicial grids of the Schr&ouml;dinger eigenvalue problem in an electromagnetic field </span><br> <span style="font-family: sans-serif;"></span>SIAM J. Numer. Anal. [2009/2011] <span style="font-family: sans-serif;">with T. G. Halvorsen</span>&nbsp;<a href="http://dx.doi.org/10.1137/090757502">article</a></li> <li style="font-family: sans-serif;"><span style="font-style: italic; color: rgb(102, 0, 0);">On the div-curl lemma in a Galerkin setting </span><br> Calcolo [2009/2009]&nbsp; <span style="text-decoration: underline;"><a href="http://dx.doi.org/10.1007/s10092-009-0008-7">article</a></span></li> <li style="font-family: sans-serif;"><font style="font-family: sans-serif;"><span style="font-style: italic; color: rgb(102, 0, 0);">&Eacute;l&eacute;ments finis mixtes minimaux sur les poly&egrave;dres </span><br> </font><span style="font-family: sans-serif;">C. R. Math. Acad. Sci. Paris </span><span style="font-family: sans-serif;">[2009/2010]&nbsp; </span><a href="http://dx.doi.org/10.1016/j.crma.2010.01.017"><span style="font-family: sans-serif;">cras</span></a></li> <li style="font-family: sans-serif;"><span style="font-style: italic; color: rgb(102, 0, 0);">On variational eigenvalue approximation of semidefinite operators </span><br> <span style="color: rgb(0, 0, 0);"> IMA J. Numer. Anal. [2010/2012]</span> with R. Winther <a href="http://dx.doi.org/10.1093/imanum/drs002"> article <br> </a></li> <li style="font-family: sans-serif;"> <span style="font-style: italic; color: rgb(102, 0, 0);"> A simplicial gauge theory</span> <br> J. Math. Phys. [2010/2012] with T. G. Halvorsen&nbsp; <a href="http://link.aip.org/link/doi/10.1063/1.3692167">article</a></li> <li style="font-family: sans-serif;"><span style="color: rgb(102, 0, 0); font-style: italic;">Topics in structure preserving discretization </span><br> Acta Numerica [2011] with H. Z. Munthe-Kaas and B. Owren <a href="http://dx.doi.org/10.1017/S096249291100002X">article</a></li> <li style="font-family: sans-serif;"><span style="color: rgb(102, 0, 0); font-style: italic;">Upwinding in finite element systems of differential forms </span><br> FoCM [2011] <a href="http://www.cambridge.org/aus/catalogue/catalogue.asp?isbn=9781107604070" > article </a> </li> </ol> <br> <h3 style="font-family: sans-serif;">Preprints on <a href="http://arxiv.org/a/christiansen_s_1">arXiv</a></h3> <br> <ul style="font-family: sans-serif;"> </ul> <table style="text-align: left; width: 983px; height: 158px;" border="0" cellpadding="2" cellspacing="2"> <tbody> <tr> <td style="vertical-align: top;"> <h3 style="font-family: sans-serif;">Other publications</h3> <ul style="font-family: sans-serif;"> <li><a href="http://tel.ccsd.cnrs.fr/documents/archives0/00/00/45/20/index_fr.html">Th&egrave;se<br> </a></li> <li><a href="http://www.wipo.int/pctdb/en/wo.jsp?wo=2001095159">Patent</a></li> <li><a href="http://www.ams.org/mathscinet/search/publications.html?pg1=RVRI&amp;s1=663397&amp;pg3=authreviews">Reviews</a></li> <li><a href="vaeren.pdf">Dikt</a><br> </li> </ul> </td> <td style="vertical-align: top;"> <h3 style="font-family: sans-serif;">Reviews and citations<br> </h3> <ul style="font-family: sans-serif;"> <li><a href="http://www.zentralblatt-math.org/zmath/en/search/?q=au:christiansen,snorre">Zentralblatt</a></li> <li><a href="http://www.ams.org/mathscinet/search/publications.html?pg1=IID&amp;s1=663397">MathSciNet</a><span style="font-weight: bold;"> <br> </span></li> <li><a href="http://www.researcherid.com/rid/C-8129-2009">Thomson Reuters</a></li> <li><a href="http://www.scopus.com/authid/detail.url?authorId=7103368686">Scopus</a><br> </li> <li><a href="http://scholar.google.com/citations?user=rnKjG6IAAAAJ">Google Scholar</a><br> </li> <li><a href="https://www.researchgate.net/profile/Snorre_Christiansen/">Research Gate </a><br> </li> <span style="font-weight: bold;"></span> </ul> </td> </tr> </tbody> </table> </body> </html>