New development in freefem++

Abstract

International audienceThis is a short presentation to the capability of the freefem++ software, in section 1, we recall most of the characteristics of the software, In section 2, we recall how to to build a weak form form of an partial differential equation (PDE) from the strong form of the PDE. In three last sections, we present different problem, tools to illustrated the software. First we do mesh adaptation problem in two and three dimension, secondly, we solve numerically a Phase change with Natural Convection, and the finally to show the HPC possibility we show a Schwarz Domain Decomposition problem on parallel computer

A posteriori error analysis of the time-dependent Stokes equations with mixed boundary conditions

“…To validate the theoretical results, we performed several numerical simulations using the FreeFem ++ software (see [14]). We consider the two-dimensional square ψ(x, y, t)) = t e −α(y−y0−β t) 2 −α(x−x0−β t) 2 , and p(x, y, t) = e −t cos(2/3 π x) sin(2/3 π y), where α = 50, β = 1 and (x 0 , y 0 ) = (1, 1).…”

2D simulation and performance evaluation of bifacial rear local contact c-Si solar cells under variable illumination conditions

“…Most of the incoming light is absorbed within few nanometers from the surface, which mathematically translates to the presence of a Dirac-like function supported in a small neighbourhood of the boundary. To resolve this issue numerically we rely on mesh adaptivity, in particular the initial mesh is locally adapted according to the variation of g n , [29], see Figure 1(right). Mesh adaptation is performed also inside the iterative scheme to adjust mainly to the variation of (u, η) and capture their behaviour around the contact.…”

“…The computational domain was covered by a triangulation which initially was adapted according to the variation of g n and subsequently according to the iterates (η , u ), see Figure 1(right). Part of the code was developed using the FreeFem++ finite element library, [29]. All the simulations were performed on a Intel Xeon E5-2680 v3 workstation with 128Gb of ram running Linux.…”

The motion of a 2D pendulum in a channel subjected to an incoming flow

“…The meshes as well as the discrete matrices resulting from Galerkin finite-element method are generated with the software FreeFem++ (see Hecht 2012).…”