Recently new methods of numerical simulation hâve appeared. Thèse methods based on a cloud of nodes do not use any mesh as for the finite élément method. In spite of their number, their theoretical basis is similar. Moreover, to their récent character, their developments are still to the begining. This work deals with the broad outline of the essential procédures for a resolution using a meshless method called HP-Clouds method. The mathematical basis by the création of new meshless shape fonctions, supported by balls, are presented in afirst chapter. Then, a procédure of resolution of the Maxwell's équations in electromagnetism using the HP-Clouds method is presented by precisely describing the method of Ritz-Galerkin in a simple case. We stressed upon the data structure based on the balls, supports of the shape functions, thus rending the insertion of the HP-Clouds easy in a software of numerical simulation. In ail thèse stages we tend to avoid any kind of mesh even fictious. Lastly, we validated our résulta on three concrète problems which lets predict a great future for the meshless methods.
