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<div dir="ltr" data-setdir="false">Hi François,</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">thanks for clarifying!</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">Marco </div><div><br></div>
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Il domenica 15 marzo 2020, 11:12:10 CET, François Henrotte <francois.henrotte@uclouvain.be> ha scritto:
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<div>Hello Marco,</div>
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<div>Yes.</div>
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<div>The first three terms in the formulation below</div>
<div>describe equations associated with the test functions</div>
<div>of the edge unknowns (or node unknowns in 2D) </div>
<div>of the magnetic vector potential field ‘a’</div>
<div>in the whole domain of computation ‘Domain’.</div>
<div>They express the weak form fo the Euler-Lagrange equation:</div>
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<div>curl (nu curl a) + sigma( dadt + grad u) = 0 (curl h = j)</div>
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<div>The next 2 terms are associated with the test functions</div>
<div>of the node unknowns of the scalar electric potential ‘v’,</div>
<div>only for nodes in the conducting domain ‘DomainC’. </div>
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<div>They express the weak form fo the Euler-Lagrange equation:</div>
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<div>div ( sigma( dadt + grad u) ) = 0 (div j=0)</div>
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<div>By analyzing the ‘Quantity’ section of the ‘Formulation’ field,</div>
<div>which I reproduce below</div>
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<pre class="ydp6b9545d1yiv9906703319code ydp6b9545d1yiv9906703319highlight" lang="cpp"><span class="ydp6b9545d1yiv9906703319line" id="ydp6b9545d1yiv9906703319LC179" lang="cpp"> <span class="ydp6b9545d1yiv9906703319n">Quantity</span> <span class="ydp6b9545d1yiv9906703319p">{</span></span>
<span class="ydp6b9545d1yiv9906703319line" id="ydp6b9545d1yiv9906703319LC180" lang="cpp"> <span class="ydp6b9545d1yiv9906703319p">{</span> <span class="ydp6b9545d1yiv9906703319n">Name</span> <span class="ydp6b9545d1yiv9906703319n">a</span> <span class="ydp6b9545d1yiv9906703319p">;</span> <span class="ydp6b9545d1yiv9906703319n">Type</span> <span class="ydp6b9545d1yiv9906703319n">Local</span> <span class="ydp6b9545d1yiv9906703319p">;</span> <span class="ydp6b9545d1yiv9906703319n">NameOfSpace</span> <span class="ydp6b9545d1yiv9906703319n">Hcurl_a_3D</span> <span class="ydp6b9545d1yiv9906703319p">;</span> <span class="ydp6b9545d1yiv9906703319p">}</span></span>
<span class="ydp6b9545d1yiv9906703319line" id="ydp6b9545d1yiv9906703319LC181" lang="cpp"></span>
<span class="ydp6b9545d1yiv9906703319line" id="ydp6b9545d1yiv9906703319LC182" lang="cpp"> <span class="ydp6b9545d1yiv9906703319p">{</span> <span class="ydp6b9545d1yiv9906703319n">Name</span> <span class="ydp6b9545d1yiv9906703319n">v</span> <span class="ydp6b9545d1yiv9906703319p">;</span> <span class="ydp6b9545d1yiv9906703319n">Type</span> <span class="ydp6b9545d1yiv9906703319n">Local</span> <span class="ydp6b9545d1yiv9906703319p">;</span> <span class="ydp6b9545d1yiv9906703319n">NameOfSpace</span> <span class="ydp6b9545d1yiv9906703319n">Hregion_u_3D</span> <span class="ydp6b9545d1yiv9906703319p">;</span> <span class="ydp6b9545d1yiv9906703319p">}</span></span>
<span class="ydp6b9545d1yiv9906703319line" id="ydp6b9545d1yiv9906703319LC183" lang="cpp"> <span class="ydp6b9545d1yiv9906703319p">{</span> <span class="ydp6b9545d1yiv9906703319n">Name</span> <span class="ydp6b9545d1yiv9906703319n">U</span> <span class="ydp6b9545d1yiv9906703319p">;</span> <span class="ydp6b9545d1yiv9906703319n">Type</span> <span class="ydp6b9545d1yiv9906703319n">Global</span> <span class="ydp6b9545d1yiv9906703319p">;</span> <span class="ydp6b9545d1yiv9906703319n">NameOfSpace</span> <span class="ydp6b9545d1yiv9906703319n">Hregion_u_3D</span> <span class="ydp6b9545d1yiv9906703319p">[</span><span class="ydp6b9545d1yiv9906703319n">U</span><span class="ydp6b9545d1yiv9906703319p">]</span> <span class="ydp6b9545d1yiv9906703319p">;</span> <span class="ydp6b9545d1yiv9906703319p">}</span></span>
<span class="ydp6b9545d1yiv9906703319line" id="ydp6b9545d1yiv9906703319LC184" lang="cpp"> <span class="ydp6b9545d1yiv9906703319p">{</span> <span class="ydp6b9545d1yiv9906703319n">Name</span> <span class="ydp6b9545d1yiv9906703319n">I</span> <span class="ydp6b9545d1yiv9906703319p">;</span> <span class="ydp6b9545d1yiv9906703319n">Type</span> <span class="ydp6b9545d1yiv9906703319n">Global</span> <span class="ydp6b9545d1yiv9906703319p">;</span> <span class="ydp6b9545d1yiv9906703319n">NameOfSpace</span> <span class="ydp6b9545d1yiv9906703319n">Hregion_u_3D</span> <span class="ydp6b9545d1yiv9906703319p">[</span><span class="ydp6b9545d1yiv9906703319n">I</span><span class="ydp6b9545d1yiv9906703319p">]</span> <span class="ydp6b9545d1yiv9906703319p">;</span> <span class="ydp6b9545d1yiv9906703319p">}</span></span>
<span class="ydp6b9545d1yiv9906703319line" id="ydp6b9545d1yiv9906703319LC185" lang="cpp"> <span class="ydp6b9545d1yiv9906703319p">}</span></span>
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<div>together with the informations contained </div>
<div>in the « FunctionSpace » section and the declared « Constraints » acting on it,</div>
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<div>GetDP is able to decide which Dofs are fixed</div>
<div>and which are unknowns (and then associated with a test function).</div>
<div>This is all automatic.</div>
<div>That is the reason why it is enough in the Formulation description</div>
<div>to give the weak form of the equations you want to solve. </div>
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<div>Regards, </div>
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<div>Fr. </div>
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<div>Equation {</div>
<div> Galerkin { [ nu[] * Dof{d a} , {d a} ] ;<br clear="none">
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<div> In Domain ; Jacobian Vol ; Integration I1 ; }<br clear="none">
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<div> Galerkin { DtDof[ sigma[] * Dof{a} , {a} ] ;<br clear="none">
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<div> In DomainC ; Jacobian Vol ; Integration I1 ; }<br clear="none">
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<div> Galerkin { [ sigma[] * Dof{d v} , {a} ] ;<br clear="none">
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<div> In DomainC ; Jacobian Vol ; Integration I1 ; }<br clear="none">
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<div> Galerkin { DtDof[ sigma[] * Dof{a} , {d v} ] ; // <====== A1</div>
<div> In DomainC ; Jacobian Vol ; Integration I1 ; }<br clear="none">
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<div> Galerkin { [ sigma[] * Dof{d v} , {d v} ] ; // <====== A2</div>
<div> In DomainC ; Jacobian Vol ; Integration I1 ; }</div>
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<div> GlobalTerm { [ Dof{I} , {U} ] ; In SurfaceElecWithI ; }</div>
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<div> Galerkin { [ - js0[] , {a} ] ; In DomainS ;</div>
<div> Jacobian Vol ; Integration I1 ; }</div>
<div> }</div>
<div> </div>
<div>I don't understand how A1 and A2 can be part of the same integral. I mean, based on the micro strip tutorial,</div>
<div> every Galerkin{....} term belonging to Equation{...} is added up and this sum is then made equal to zero. And this equation should hold for a single test function.</div>
<div>But here A1 and A2 have a test function different from the other terms. Does this mean that GetDP generates automatically two equations? One for test functions a' and one for test functions v’?<br clear="none">
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<div dir="ltr">I'm lost, help please :D</div>
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<div dir="ltr">Marco</div></div>
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<div>--</div>
<div>François Henrotte Dr Ir - <span><a shape="rect" href="mailto:francois.henrotte@uclouvain.be" rel="nofollow" target="_blank">francois.henrotte@uclouvain.be</a></span><span> - </span><span><a shape="rect" href="mailto:francois.henrotte@uliege.be" rel="nofollow" target="_blank">francois.henrotte@uliege.be</a> </span></div>
<div>UCLouvain - Bât. Euler a.217 - Av. G. Lemaître 4-6 , <span>B-1348 Louvain-la-Neuve - </span><span>+32(0)10 47 23 64 </span></div>
<div><span>ULiège - Institut Montefiore I154 - Allée de la Découverte 10, B-4000 Liège - +32(0)4 366 37 36 </span></div><div class="ydp6b9545d1yiv9906703319yqt7010646160" id="ydp6b9545d1yiv9906703319yqtfd52625">
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