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<title>PHPC - nBody project: N-Body project</title>
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<div class="title">N-Body project </div> </div>
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<div class="textblock"><p>Project in the case of the course of Parallel and High Performance Computing at EPFL - Ecole Polytechnique Fédérale de Lausanne.</p>
<h1><a class="anchor" id="Description"></a>
Description</h1>
<p>The n-body problem aims at simulating a dynamical system of particles under the influence of physical forces. We’ll restrain on the gravity field applied on celestial bodies : </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ F_{ij} = \frac{G m_i m_j (q_j - q_i)}{|| q_j - q_i ||} \]" src="form_0.png"/>
</p>
<p>where <img class="formulaInl" alt="$ G $" src="form_1.png"/> is the gravitational constant, <img class="formulaInl" alt="$ m_i $" src="form_2.png"/> and <img class="formulaInl" alt="$ m_j $" src="form_3.png"/> the masses of the <img class="formulaInl" alt="$ i $" src="form_4.png"/>-th and <img class="formulaInl" alt="$j$" src="form_5.png"/>-th bodies and <img class="formulaInl" alt="$ q_i $" src="form_6.png"/> and <img class="formulaInl" alt="$ q_j $" src="form_7.png"/> their positions.</p>
<h1><a class="anchor" id="Implementation"></a>
Implementation</h1>
<p>The solution is implemented using Barnes-Hut algorithm and quadtree/octree data-structure. The particularity is that the user can choose differents parameters as define :</p><ul>
<li>NB_DIM : set at DIM_2 or DIM_3 to choose between 2D and 3D problem solution</li>
<li>NB_PARTICLES : number of particles</li>
<li>PRINT : save solution in csv file, at each time-step, to display solution animation in programs (e.g. paraview)</li>
<li>DELTA_T : time-step of each iteration </li>
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