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uodate abstract on P. ventura
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‎2022/pdf/PV.html‎

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<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
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<meta http-equiv="Content-Style-Type" content="text/css">
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<title></title>
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<meta name="Author" content="Pascal Ventura">
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<meta name="Generator" content="Cocoa HTML Writer">
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<meta name="CocoaVersion" content="2113.6">
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<style type="text/css">
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p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica; color: #000000; -webkit-text-stroke: #000000}
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</head>
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<body>
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<p class="p1"><span class="s1">9/11/2022 Friday<span class="Apple-converted-space">  </span>11h30 to 11h55</span></p>
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<p class="p1"><span class="s2">Pascal<span class="Apple-converted-space">  </span>Ventura </span><span class="s1"><br>
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Laboratoire LEM3</span></p>
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<p class="p1"><span class="s1">Université de Lorraine<span class="Apple-converted-space"> </span></span></p>
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<p class="p2"><span class="s1">9/11/2022 Friday<span class="Apple-converted-space">  </span>11h30 to 11h55</span></p>
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<p class="p1"><span class="s1"><b>Pascal VENTURA</b>, Michel Potier-Ferry</span></p>
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<p class="p3"><span class="s1">Laboratoire LEM3</span></p>
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<p class="p2"><span class="s1">Université de Lorraine<span class="Apple-converted-space"> </span></span></p>
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<p class="p4"><span class="s1"><b></b></span><br></p>
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<p class="p4"><span class="s1"><b></b></span><br></p>
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<p class="p4"><span class="s1"><b><span class="Apple-converted-space"> </span></b></span></p>
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<p class="p5"><span class="s1"><b><i>How to accelerate and improve the continuation algorithm called<span class="Apple-converted-space">  </span>Asymptotic Numerical Method using FreeFem++</i></b></span></p>
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<p class="p1"><span class="s1"><br>
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</span></p>
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<p class="p1"><span class="s1">Abstract :</span></p>
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<p class="p6"><span class="s1">The Asymptotic Numerical Method (ANM) [1] is a robust continuation algorithm for solving non-linear problems that depends on a parameter. It has been applied to various fields in solids and fluid mechanics, in physics, in finance, …<span class="Apple-converted-space"> </span></span></p>
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<p class="p6"><span class="s1">We will first explain why FreeFem++ is a very efficient numerical tool to implement the ANM algorithm in order to solve non-linear solid mechanical problems.<span class="Apple-converted-space"> </span></span></p>
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<p class="p6"><span class="s1">Then, new encouraging results obtained regarding convergence acceleration techniques of ANM applied to film/substrate systems will be given.</span></p>
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<p class="p6"><span class="s1">Recently, Henderson et alt. [2] have shown that real solutions of real continuation of non-linear problems frequently have complex solutions bifurcating from then. These complex solutions might connect later to new real solutions which cannot been discovered using the real continuation algorithm. We will show our first attempt to generalize the ANM algorithm for complex continuation, and the first results obtained for a film/substrate thermo-mechanical problem.</span></p>
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<p class="p6"><span class="s1"><br>
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</span></p>
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<p class="p6"><span class="s1">[1] B. Cochelin, N. Damil, M. Potier-Ferry, ″Méthode asymptotique numérique″, Hermes, Lavoisier 2007.</span></p>
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<p class="p6"><span class="s1">[2] M. E. Henderson, H. B. Keller, ″Complex bifurcation from real paths, SIAM Journal on Applied Mathematics″, 50(2), 460-482.</span></p>
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<p class="p6"><span class="s1"><br>
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</span></p>
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</body>
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</html>

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