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dolfinx/main/cpp/demos/demo_biharmonic.html

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@@ -268,8 +268,8 @@ <h3>Weak formulation<a class="headerlink" href="#weak-formulation" title="Link t
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\forall \ K \in \mathcal{T} \right\}
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\]</div>
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<p>and considering the boundary conditions</p>
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<div class="amsmath math notranslate nohighlight" id="equation-74e0000f-3225-49a0-a560-3e818c342c59">
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<span class="eqno">(1)<a class="headerlink" href="#equation-74e0000f-3225-49a0-a560-3e818c342c59" title="Permalink to this equation">#</a></span>\[\begin{align}
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<div class="amsmath math notranslate nohighlight" id="equation-634225d8-673d-422e-8ab4-8f4e0a0c6014">
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<span class="eqno">(1)<a class="headerlink" href="#equation-634225d8-673d-422e-8ab4-8f4e0a0c6014" title="Permalink to this equation">#</a></span>\[\begin{align}
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u &amp;= 0 \quad {\rm on} \ \partial\Omega, \\
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\nabla^{2} u &amp;= 0 \quad {\rm on} \ \partial\Omega,
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\end{align}\]</div>

dolfinx/main/cpp/doxygen/d0/d75/fem_2petsc_8h_source.html

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<div class="ttc" id="anamespacedolfinx_1_1fem_1_1petsc_html_abe7acc7e8e24dd0937a0c0beddde1a10"><div class="ttname"><a href="../../d4/d44/namespacedolfinx_1_1fem_1_1petsc.html#abe7acc7e8e24dd0937a0c0beddde1a10">dolfinx::fem::petsc::apply_lifting</a></div><div class="ttdeci">void apply_lifting(Vec b, std::vector&lt; std::optional&lt; std::reference_wrapper&lt; const Form&lt; PetscScalar, T &gt; &gt; &gt; &gt; a, const std::vector&lt; std::span&lt; const PetscScalar &gt; &gt; &amp;constants, const std::vector&lt; std::map&lt; std::pair&lt; IntegralType, int &gt;, std::pair&lt; std::span&lt; const PetscScalar &gt;, int &gt; &gt; &gt; &amp;coeffs, const std::vector&lt; std::vector&lt; std::reference_wrapper&lt; const DirichletBC&lt; PetscScalar, T &gt; &gt; &gt; &gt; &amp;bcs1, const std::vector&lt; Vec &gt; &amp;x0, PetscScalar alpha)</div><div class="ttdoc">Modify RHS vector to account for Dirichlet boundary conditions.</div><div class="ttdef"><b>Definition</b> petsc.h:333</div></div>
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<div class="ttc" id="anamespacedolfinx_1_1fem_1_1petsc_html_ad698bc5002fb92a75274994209bb7531"><div class="ttname"><a href="../../d4/d44/namespacedolfinx_1_1fem_1_1petsc.html#ad698bc5002fb92a75274994209bb7531">dolfinx::fem::petsc::create_vector_nest</a></div><div class="ttdeci">Vec create_vector_nest(const std::vector&lt; std::pair&lt; std::reference_wrapper&lt; const common::IndexMap &gt;, int &gt; &gt; &amp;maps)</div><div class="ttdoc">Create nested (VecNest) vector. Vector is not zeroed.</div><div class="ttdef"><b>Definition</b> petsc.cpp:62</div></div>
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<div class="ttc" id="anamespacedolfinx_1_1fem_html"><div class="ttname"><a href="../../d8/dbf/namespacedolfinx_1_1fem.html">dolfinx::fem</a></div><div class="ttdoc">Finite element method functionality.</div><div class="ttdef"><b>Definition</b> assemble_expression_impl.h:23</div></div>
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<div class="ttc" id="anamespacedolfinx_1_1fem_html_a5c0589b9e21481958b76c8862dd29903"><div class="ttname"><a href="../../d8/dbf/namespacedolfinx_1_1fem.html#a5c0589b9e21481958b76c8862dd29903">dolfinx::fem::extract_function_spaces</a></div><div class="ttdeci">std::vector&lt; std::vector&lt; std::array&lt; std::shared_ptr&lt; const FunctionSpace&lt; U &gt; &gt;, 2 &gt; &gt; &gt; extract_function_spaces(const std::vector&lt; std::vector&lt; const Form&lt; T, U &gt; * &gt; &gt; &amp;a)</div><div class="ttdoc">Extract test (0) and trial (1) function spaces pairs for each bilinear form for a rectangular array o...</div><div class="ttdef"><b>Definition</b> utils.h:172</div></div>
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<div class="ttc" id="anamespacedolfinx_1_1fem_html_a5c0589b9e21481958b76c8862dd29903"><div class="ttname"><a href="../../d8/dbf/namespacedolfinx_1_1fem.html#a5c0589b9e21481958b76c8862dd29903">dolfinx::fem::extract_function_spaces</a></div><div class="ttdeci">std::vector&lt; std::vector&lt; std::array&lt; std::shared_ptr&lt; const FunctionSpace&lt; U &gt; &gt;, 2 &gt; &gt; &gt; extract_function_spaces(const std::vector&lt; std::vector&lt; const Form&lt; T, U &gt; * &gt; &gt; &amp;a)</div><div class="ttdoc">Extract test (0) and trial (1) function spaces pairs for each bilinear form for a rectangular array o...</div><div class="ttdef"><b>Definition</b> utils.h:173</div></div>
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<div class="ttc" id="anamespacedolfinx_1_1fem_html_a82077b94a5a2dcf76095afae0f851cfa"><div class="ttname"><a href="../../d8/dbf/namespacedolfinx_1_1fem.html#a82077b94a5a2dcf76095afae0f851cfa">dolfinx::fem::assemble_vector</a></div><div class="ttdeci">void assemble_vector(V &amp;&amp;b, const Form&lt; T, U &gt; &amp;L, std::span&lt; const T &gt; constants, const std::map&lt; std::pair&lt; IntegralType, int &gt;, std::pair&lt; std::span&lt; const T &gt;, int &gt; &gt; &amp;coefficients)</div><div class="ttdoc">Assemble linear form into a vector.</div><div class="ttdef"><b>Definition</b> assembler.h:229</div></div>
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<div class="ttc" id="anamespacedolfinx_1_1fem_html_acc11603e5b1f3155c21556789a7f58c2"><div class="ttname"><a href="../../d8/dbf/namespacedolfinx_1_1fem.html#acc11603e5b1f3155c21556789a7f58c2">dolfinx::fem::apply_lifting</a></div><div class="ttdeci">void apply_lifting(V &amp;&amp;b, std::vector&lt; std::optional&lt; std::reference_wrapper&lt; const Form&lt; T, U &gt; &gt; &gt; &gt; a, const std::vector&lt; std::span&lt; const T &gt; &gt; &amp;constants, const std::vector&lt; std::map&lt; std::pair&lt; IntegralType, int &gt;, std::pair&lt; std::span&lt; const T &gt;, int &gt; &gt; &gt; &amp;coeffs, const std::vector&lt; std::vector&lt; std::reference_wrapper&lt; const DirichletBC&lt; T, U &gt; &gt; &gt; &gt; &amp;bcs1, const std::vector&lt; std::span&lt; const T &gt; &gt; &amp;x0, T alpha)</div><div class="ttdoc">Modify the right-hand side vector to account for constraints (Dirichlet boundary condition constraint...</div><div class="ttdef"><b>Definition</b> assembler.h:337</div></div>
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<div class="ttc" id="anamespacedolfinx_1_1fem_html_adaad0b646d98814dc913c53fd44d7e97"><div class="ttname"><a href="../../d8/dbf/namespacedolfinx_1_1fem.html#adaad0b646d98814dc913c53fd44d7e97">dolfinx::fem::create_sparsity_pattern</a></div><div class="ttdeci">la::SparsityPattern create_sparsity_pattern(const Form&lt; T, U &gt; &amp;a)</div><div class="ttdoc">Create a sparsity pattern for a given form.</div><div class="ttdef"><b>Definition</b> utils.h:197</div></div>
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<div class="ttc" id="anamespacedolfinx_1_1fem_html_adaad0b646d98814dc913c53fd44d7e97"><div class="ttname"><a href="../../d8/dbf/namespacedolfinx_1_1fem.html#adaad0b646d98814dc913c53fd44d7e97">dolfinx::fem::create_sparsity_pattern</a></div><div class="ttdeci">la::SparsityPattern create_sparsity_pattern(const Form&lt; T, U &gt; &amp;a)</div><div class="ttdoc">Create a sparsity pattern for a given form.</div><div class="ttdef"><b>Definition</b> utils.h:198</div></div>
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<div class="ttc" id="anamespacedolfinx_1_1fem_html_ae68fed2204e6da434435b5b526923bd4"><div class="ttname"><a href="../../d8/dbf/namespacedolfinx_1_1fem.html#ae68fed2204e6da434435b5b526923bd4">dolfinx::fem::common_function_spaces</a></div><div class="ttdeci">std::array&lt; std::vector&lt; std::shared_ptr&lt; const FunctionSpace&lt; T &gt; &gt; &gt;, 2 &gt; common_function_spaces(const std::vector&lt; std::vector&lt; std::array&lt; std::shared_ptr&lt; const FunctionSpace&lt; T &gt; &gt;, 2 &gt; &gt; &gt; &amp;V)</div><div class="ttdoc">Extract FunctionSpaces for (0) rows blocks and (1) columns blocks from a rectangular array of (test,...</div><div class="ttdef"><b>Definition</b> FunctionSpace.h:432</div></div>
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<div class="ttc" id="anamespacedolfinx_1_1la_1_1petsc_html_ad59290cd77b5406ab3c50a4e9fdc7acf"><div class="ttname"><a href="../../d6/d2f/namespacedolfinx_1_1la_1_1petsc.html#ad59290cd77b5406ab3c50a4e9fdc7acf">dolfinx::la::petsc::create_matrix</a></div><div class="ttdeci">Mat create_matrix(MPI_Comm comm, const SparsityPattern &amp;sp, std::optional&lt; std::string &gt; type=std::nullopt)</div><div class="ttdef"><b>Definition</b> petsc.cpp:235</div></div>
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<div class="ttc" id="anamespacedolfinx_1_1mesh_html"><div class="ttname"><a href="../../dd/d7d/namespacedolfinx_1_1mesh.html">dolfinx::mesh</a></div><div class="ttdoc">Mesh data structures and algorithms on meshes.</div><div class="ttdef"><b>Definition</b> DofMap.h:32</div></div>

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