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<p class="MsoNormal"><span lang="ES" style="font-size:11.0pt">Hello<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="ES" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">I am interested in implementing the LDG method in “A local discontinuous Galerkin method for directly solving Hamilton–Jacobi equations”
<a href="https://www.sciencedirect.com/science/article/pii/S0021999110005255">https://www.sciencedirect.com/science/article/pii/S0021999110005255</a>. The equation is more or less of the form (for 1D case):<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> </span><span lang="ES" style="font-size:11.0pt">p1 = f(u_x)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="ES" style="font-size:11.0pt"> p2 = g(u_x)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="ES" style="font-size:11.0pt"> u_t = H(p1, p2)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="ES" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">where typically one solves for p1 and p2 using the previous time step solution “u” and then plugs them into the third equation to obtain the next step solution. I am wondering if the TS infrastructure could
be used to implement this solution scheme. Looking at the manual, I think one could set G(t, U) to the right-hand side in the above equations and F(t, u, u’) = 0 to the left-hand side, although the first two equations would not have time derivative. In that
case, how could one take advantage of the operator split scheme I mentioned? Maybe using some block preconditioners?<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">I am trying to solve the Hamilton-Jacobi equation u_t – H(u_x) = 0. I welcome any suggestion for better methods.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Thanks<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Miguel<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="ES" style="font-size:9.0pt;font-family:Consolas;color:black">Miguel A. Salazar de Troya</span><span lang="ES" style="font-size:10.5pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:9.0pt;font-family:Consolas;color:black">Postdoctoral Researcher, Lawrence Livermore National Laboratory</span><span style="font-size:10.5pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:9.0pt;font-family:Consolas;color:black">B141</span><span style="font-size:10.5pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:9.0pt;font-family:Consolas;color:black">Rm: 1085-5</span><span style="font-size:10.5pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:9.0pt;font-family:Consolas;color:black">Ph: 1(925) 422-6411</span><o:p></o:p></p>
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