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710 changes: 357 additions & 353 deletions advection__field__rp_8hpp_source.html

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191 changes: 96 additions & 95 deletions annotated.html

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1 change: 1 addition & 0 deletions annotated.js
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85 changes: 44 additions & 41 deletions bsl__advection__rp_8hpp_source.html

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4 changes: 2 additions & 2 deletions bsl__predcorr_8hpp_source.html
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<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>&#160; <span class="keywordflow">return</span> allfdistribu;</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>&#160; }</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>&#160;};</div>
<div class="ttc" id="aclassAdvectionFieldFinder_html"><div class="ttname"><a href="classAdvectionFieldFinder.html">AdvectionFieldFinder</a></div><div class="ttdoc">Solve the Poisson-like equation and return the electric field for the coupled Vlasov equation.</div><div class="ttdef"><b>Definition:</b> advection_field_rp.hpp:90</div></div>
<div class="ttc" id="aclassAdvectionFieldFinder_html"><div class="ttname"><a href="classAdvectionFieldFinder.html">AdvectionFieldFinder</a></div><div class="ttdoc">Solve the Poisson-like equation and return the electric field for the coupled Vlasov equation.</div><div class="ttdef"><b>Definition:</b> advection_field_rp.hpp:91</div></div>
<div class="ttc" id="aclassBslAdvectionRTheta_html"><div class="ttname"><a href="classBslAdvectionRTheta.html">BslAdvectionRTheta</a></div><div class="ttdoc">Define an advection operator on 2D index range.</div><div class="ttdef"><b>Definition:</b> bsl_advection_rp.hpp:60</div></div>
<div class="ttc" id="aclassBslPredCorrRTheta_html"><div class="ttname"><a href="classBslPredCorrRTheta.html">BslPredCorrRTheta</a></div><div class="ttdoc">Predictor-corrector for the Vlasov-Poisson equations.</div><div class="ttdef"><b>Definition:</b> bsl_predcorr.hpp:58</div></div>
<div class="ttc" id="aclassBslPredCorrRTheta_html_aadad583aa00746824d7ab288466bc564"><div class="ttname"><a href="classBslPredCorrRTheta.html#aadad583aa00746824d7ab288466bc564">BslPredCorrRTheta::BslPredCorrRTheta</a></div><div class="ttdeci">BslPredCorrRTheta(Mapping const &amp;mapping, BslAdvectionRTheta&lt; FootFinder, Mapping &gt; const &amp;advection_solver, SplineRThetaBuilder const &amp;builder, SplineRThetaEvaluatorNullBound const &amp;rhs_evaluator, PolarSplineFEMPoissonLikeSolver const &amp;poisson_solver)</div><div class="ttdoc">Instantiate a BslPredCorrRTheta.</div><div class="ttdef"><b>Definition:</b> bsl_predcorr.hpp:88</div></div>
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<div class="ttc" id="aclassPoissonLikeRHSFunction_html"><div class="ttname"><a href="classPoissonLikeRHSFunction.html">PoissonLikeRHSFunction</a></div><div class="ttdoc">Type of right-hand side (rhs) function of the Poisson equation.</div><div class="ttdef"><b>Definition:</b> poisson_like_rhs_function.hpp:16</div></div>
<div class="ttc" id="aclassPolarBSplines_html_ae187bdd3ed2fd780c51fa644c45386a9"><div class="ttname"><a href="classPolarBSplines.html#ae187bdd3ed2fd780c51fa644c45386a9">PolarBSplines&lt; BSplinesR, BSplinesTheta, 1 &gt;::continuity</a></div><div class="ttdeci">static constexpr int continuity</div><div class="ttdoc">The continuity enforced by the bsplines at the singular point.</div><div class="ttdef"><b>Definition:</b> polar_bsplines.hpp:61</div></div>
<div class="ttc" id="aclassPolarSplineEvaluator_html"><div class="ttname"><a href="classPolarSplineEvaluator.html">PolarSplineEvaluator&lt; PolarBSplinesRTheta, ddc::NullExtrapolationRule &gt;</a></div></div>
<div class="ttc" id="aclassPolarSplineFEMPoissonLikeSolver_html"><div class="ttname"><a href="classPolarSplineFEMPoissonLikeSolver.html">PolarSplineFEMPoissonLikeSolver</a></div><div class="ttdoc">Define a polar PDE solver for a Poisson-like equation.</div><div class="ttdef"><b>Definition:</b> polarpoissonlikesolver.hpp:37</div></div>
<div class="ttc" id="aclassPolarSplineFEMPoissonLikeSolver_html"><div class="ttname"><a href="classPolarSplineFEMPoissonLikeSolver.html">PolarSplineFEMPoissonLikeSolver</a></div><div class="ttdoc">Define a polar PDE solver for a Poisson-like equation.</div><div class="ttdef"><b>Definition:</b> polarpoissonlikesolver.hpp:39</div></div>
<div class="ttc" id="aclassRK2_html"><div class="ttname"><a href="classRK2.html">RK2</a></div><div class="ttdoc">A class which provides an implementation of a second-order Runge-Kutta method.</div><div class="ttdef"><b>Definition:</b> rk2.hpp:34</div></div>
<div class="ttc" id="aclassRK2_html_afedd4b2ac6d505e801544ed4c65f7492"><div class="ttname"><a href="classRK2.html#afedd4b2ac6d505e801544ed4c65f7492">RK2::update</a></div><div class="ttdeci">void update(ValField y, double dt, std::function&lt; void(DerivFieldMem, ValConstField)&gt; dy) const</div><div class="ttdoc">Carry out one step of the Runge-Kutta scheme.</div><div class="ttdef"><b>Definition:</b> rk2.hpp:79</div></div>
<div class="ttc" id="aclassVectorField_html"><div class="ttname"><a href="classVectorField.html">VectorField</a></div><div class="ttdoc">A class which holds multiple (scalar) fields in order to represent a vector field.</div><div class="ttdef"><b>Definition:</b> vector_field.hpp:54</div></div>
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4 changes: 2 additions & 2 deletions bsl__predcorr__second__order__explicit_8hpp_source.html
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<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>&#160; <span class="keywordflow">return</span> allfdistribu;</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>&#160; }</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>&#160;};</div>
<div class="ttc" id="aclassAdvectionFieldFinder_html"><div class="ttname"><a href="classAdvectionFieldFinder.html">AdvectionFieldFinder</a></div><div class="ttdoc">Solve the Poisson-like equation and return the electric field for the coupled Vlasov equation.</div><div class="ttdef"><b>Definition:</b> advection_field_rp.hpp:90</div></div>
<div class="ttc" id="aclassAdvectionFieldFinder_html"><div class="ttname"><a href="classAdvectionFieldFinder.html">AdvectionFieldFinder</a></div><div class="ttdoc">Solve the Poisson-like equation and return the electric field for the coupled Vlasov equation.</div><div class="ttdef"><b>Definition:</b> advection_field_rp.hpp:91</div></div>
<div class="ttc" id="aclassBslAdvectionRTheta_html"><div class="ttname"><a href="classBslAdvectionRTheta.html">BslAdvectionRTheta</a></div><div class="ttdoc">Define an advection operator on 2D index range.</div><div class="ttdef"><b>Definition:</b> bsl_advection_rp.hpp:60</div></div>
<div class="ttc" id="aclassBslExplicitPredCorrRTheta_html"><div class="ttname"><a href="classBslExplicitPredCorrRTheta.html">BslExplicitPredCorrRTheta</a></div><div class="ttdoc">A second order explicit predictor-corrector for the Vlasov-Poisson equations.</div><div class="ttdef"><b>Definition:</b> bsl_predcorr_second_order_explicit.hpp:66</div></div>
<div class="ttc" id="aclassBslExplicitPredCorrRTheta_html_ae36c44a957553444d4bfa2c806671a1b"><div class="ttname"><a href="classBslExplicitPredCorrRTheta.html#ae36c44a957553444d4bfa2c806671a1b">BslExplicitPredCorrRTheta::BslExplicitPredCorrRTheta</a></div><div class="ttdeci">BslExplicitPredCorrRTheta(IdxRangeAdvection const &amp;advection_idx_range, Mapping const &amp;mapping, BslAdvectionRTheta&lt; SplineFootFinder&lt; EulerMethod, IdxRangeAdvection &gt;, Mapping &gt; &amp;advection_solver, IdxRangeRTheta const &amp;grid, SplineRThetaBuilder const &amp;builder, SplineRThetaEvaluatorNullBound const &amp;rhs_evaluator, PolarSplineFEMPoissonLikeSolver const &amp;poisson_solver, SplineRThetaEvaluatorConstBound const &amp;advection_evaluator)</div><div class="ttdoc">Instantiate a BslExplicitPredCorrRTheta.</div><div class="ttdef"><b>Definition:</b> bsl_predcorr_second_order_explicit.hpp:111</div></div>
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<div class="ttc" id="aclassPoissonLikeRHSFunction_html"><div class="ttname"><a href="classPoissonLikeRHSFunction.html">PoissonLikeRHSFunction</a></div><div class="ttdoc">Type of right-hand side (rhs) function of the Poisson equation.</div><div class="ttdef"><b>Definition:</b> poisson_like_rhs_function.hpp:16</div></div>
<div class="ttc" id="aclassPolarBSplines_html_ae187bdd3ed2fd780c51fa644c45386a9"><div class="ttname"><a href="classPolarBSplines.html#ae187bdd3ed2fd780c51fa644c45386a9">PolarBSplines&lt; BSplinesR, BSplinesTheta, 1 &gt;::continuity</a></div><div class="ttdeci">static constexpr int continuity</div><div class="ttdoc">The continuity enforced by the bsplines at the singular point.</div><div class="ttdef"><b>Definition:</b> polar_bsplines.hpp:61</div></div>
<div class="ttc" id="aclassPolarSplineEvaluator_html"><div class="ttname"><a href="classPolarSplineEvaluator.html">PolarSplineEvaluator&lt; PolarBSplinesRTheta, ddc::NullExtrapolationRule &gt;</a></div></div>
<div class="ttc" id="aclassPolarSplineFEMPoissonLikeSolver_html"><div class="ttname"><a href="classPolarSplineFEMPoissonLikeSolver.html">PolarSplineFEMPoissonLikeSolver</a></div><div class="ttdoc">Define a polar PDE solver for a Poisson-like equation.</div><div class="ttdef"><b>Definition:</b> polarpoissonlikesolver.hpp:37</div></div>
<div class="ttc" id="aclassPolarSplineFEMPoissonLikeSolver_html"><div class="ttname"><a href="classPolarSplineFEMPoissonLikeSolver.html">PolarSplineFEMPoissonLikeSolver</a></div><div class="ttdoc">Define a polar PDE solver for a Poisson-like equation.</div><div class="ttdef"><b>Definition:</b> polarpoissonlikesolver.hpp:39</div></div>
<div class="ttc" id="aclassSplineFootFinder_html"><div class="ttname"><a href="classSplineFootFinder.html">SplineFootFinder</a></div><div class="ttdoc">Define a base class for all the time integration methods used for the advection.</div><div class="ttdef"><b>Definition:</b> spline_foot_finder.hpp:21</div></div>
<div class="ttc" id="aclassVectorFieldMem_html"><div class="ttname"><a href="classVectorFieldMem.html">VectorFieldMem</a></div><div class="ttdoc">Pre-declaration of VectorFieldMem.</div><div class="ttdef"><b>Definition:</b> vector_field_mem.hpp:45</div></div>
<div class="ttc" id="astructPolarSpline_html"><div class="ttname"><a href="structPolarSpline.html">PolarSpline</a></div><div class="ttdoc">A structure containing the two Chunks necessary to define a spline on a set of polar basis splines.</div><div class="ttdef"><b>Definition:</b> polar_spline.hpp:20</div></div>
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4 changes: 2 additions & 2 deletions bsl__predcorr__second__order__implicit_8hpp_source.html
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<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>&#160; } <span class="keywordflow">while</span> ((square_difference_feet &gt; tau * tau) and (count &lt; max_count));</div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span>&#160; }</div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>&#160;};</div>
<div class="ttc" id="aclassAdvectionFieldFinder_html"><div class="ttname"><a href="classAdvectionFieldFinder.html">AdvectionFieldFinder</a></div><div class="ttdoc">Solve the Poisson-like equation and return the electric field for the coupled Vlasov equation.</div><div class="ttdef"><b>Definition:</b> advection_field_rp.hpp:90</div></div>
<div class="ttc" id="aclassAdvectionFieldFinder_html"><div class="ttname"><a href="classAdvectionFieldFinder.html">AdvectionFieldFinder</a></div><div class="ttdoc">Solve the Poisson-like equation and return the electric field for the coupled Vlasov equation.</div><div class="ttdef"><b>Definition:</b> advection_field_rp.hpp:91</div></div>
<div class="ttc" id="aclassBslAdvectionRTheta_html"><div class="ttname"><a href="classBslAdvectionRTheta.html">BslAdvectionRTheta</a></div><div class="ttdoc">Define an advection operator on 2D index range.</div><div class="ttdef"><b>Definition:</b> bsl_advection_rp.hpp:60</div></div>
<div class="ttc" id="aclassBslImplicitPredCorrRTheta_html"><div class="ttname"><a href="classBslImplicitPredCorrRTheta.html">BslImplicitPredCorrRTheta</a></div><div class="ttdoc">A second order implicit predictor-corrector for the Vlasov-Poisson equations.</div><div class="ttdef"><b>Definition:</b> bsl_predcorr_second_order_implicit.hpp:66</div></div>
<div class="ttc" id="aclassBslImplicitPredCorrRTheta_html_a396c933d12a0dd377085da972bdc5208"><div class="ttname"><a href="classBslImplicitPredCorrRTheta.html#a396c933d12a0dd377085da972bdc5208">BslImplicitPredCorrRTheta::operator()</a></div><div class="ttdeci">DFieldRTheta operator()(DFieldRTheta allfdistribu, double const dt, int const steps) const</div><div class="ttdoc">Solves on the equations system.</div><div class="ttdef"><b>Definition:</b> bsl_predcorr_second_order_implicit.hpp:136</div></div>
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<div class="ttc" id="aclassPoissonLikeRHSFunction_html"><div class="ttname"><a href="classPoissonLikeRHSFunction.html">PoissonLikeRHSFunction</a></div><div class="ttdoc">Type of right-hand side (rhs) function of the Poisson equation.</div><div class="ttdef"><b>Definition:</b> poisson_like_rhs_function.hpp:16</div></div>
<div class="ttc" id="aclassPolarBSplines_html_ae187bdd3ed2fd780c51fa644c45386a9"><div class="ttname"><a href="classPolarBSplines.html#ae187bdd3ed2fd780c51fa644c45386a9">PolarBSplines&lt; BSplinesR, BSplinesTheta, 1 &gt;::continuity</a></div><div class="ttdeci">static constexpr int continuity</div><div class="ttdoc">The continuity enforced by the bsplines at the singular point.</div><div class="ttdef"><b>Definition:</b> polar_bsplines.hpp:61</div></div>
<div class="ttc" id="aclassPolarSplineEvaluator_html"><div class="ttname"><a href="classPolarSplineEvaluator.html">PolarSplineEvaluator&lt; PolarBSplinesRTheta, ddc::NullExtrapolationRule &gt;</a></div></div>
<div class="ttc" id="aclassPolarSplineFEMPoissonLikeSolver_html"><div class="ttname"><a href="classPolarSplineFEMPoissonLikeSolver.html">PolarSplineFEMPoissonLikeSolver</a></div><div class="ttdoc">Define a polar PDE solver for a Poisson-like equation.</div><div class="ttdef"><b>Definition:</b> polarpoissonlikesolver.hpp:37</div></div>
<div class="ttc" id="aclassPolarSplineFEMPoissonLikeSolver_html"><div class="ttname"><a href="classPolarSplineFEMPoissonLikeSolver.html">PolarSplineFEMPoissonLikeSolver</a></div><div class="ttdoc">Define a polar PDE solver for a Poisson-like equation.</div><div class="ttdef"><b>Definition:</b> polarpoissonlikesolver.hpp:39</div></div>
<div class="ttc" id="aclassSplineFootFinder_html"><div class="ttname"><a href="classSplineFootFinder.html">SplineFootFinder</a></div><div class="ttdoc">Define a base class for all the time integration methods used for the advection.</div><div class="ttdef"><b>Definition:</b> spline_foot_finder.hpp:21</div></div>
<div class="ttc" id="aclassVectorFieldMem_html"><div class="ttname"><a href="classVectorFieldMem.html">VectorFieldMem</a></div><div class="ttdoc">Pre-declaration of VectorFieldMem.</div><div class="ttdef"><b>Definition:</b> vector_field_mem.hpp:45</div></div>
<div class="ttc" id="aclassVectorField_html"><div class="ttname"><a href="classVectorField.html">VectorField</a></div><div class="ttdoc">A class which holds multiple (scalar) fields in order to represent a vector field.</div><div class="ttdef"><b>Definition:</b> vector_field.hpp:54</div></div>
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4 changes: 2 additions & 2 deletions classAdvectionFieldFinder.html
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<p>Then the advection field along the physical index range axis is given by \(A = E \wedge e_z\).</p>
<p>2- In the second case, the advection field along the logical index range axis is computed with</p><ul>
<li>\( \nabla \phi = \sum_{i,j} \partial_{x_i} f g^{ij} \sqrt{g_{jj}} \hat{e}_j\),</li>
<li>with \(g^{ij}\), the coefficients of the inverse metrix tensor,</li>
<li>\(g_{jj}\), the coefficients of the metrix tensor,</li>
<li>with \(g^{ij}\), the coefficients of the inverse metric tensor,</li>
<li>\(g_{jj}\), the coefficients of the metric tensor,</li>
<li>\(\hat{e}_j\), the normalized covariants vectors.</li>
</ul>
<p>Then, we compute \( E = -\nabla \phi \) and \(A = E \wedge e_z\).</p>
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