Analisi elastostatica di una ruota dentata: applicazioni con metodo alle differenze finite e multigrid con implementazione parallela su GPU

The implementation of a code number, the GPU-MG, developed by us, solves equations elastostatic Cauchy-Navier (2D case) with the finite difference method and approach the level set. In points inside the domain equations are discretized by a stencil to nine points, in those who have an external point near the internal domain (ghost points), you have to discretize the boundary conditions with a stencil to seven points. The discretized system is solved in parallel on GPU. The study analyzes the stress field, produced by the application of the Lewis’ force, a point on the circumference of parting outside of a toothed drive wheel. The computation was made to compare the method of finite element and to verify the goodness of the application. The optimization of the implementation has produced a remarkable level of precision in the definition of stress fields, validating the search.