### Numéro : 2148 - Year : 1991

# MELINA, a finite element code for the external problem, application to naval hydrodynamics

**O. DE BAYSER, GROUPE G.H.N., E.N.S. T.A.,UNITE ASSOCIEE AU C.N.R.S. ET A L \'UNIVERSITE P. ET M. CURIE (PARIS VI)**

Melina is a Fortran routine kernel for the solution of partial differential equations by the finite element method in 2 or 3 dimensions. Routines for solving exterior problems are included, interesting examples of which can be found in naval hydrodynamics, such as the sea-keeping problem or the wave resistance problem. Such problems are numerically dealt with as applications of Melina. The making of an application of Melina mainly sums up to writing a main program and a few specific procedures for the computation of quantities relevant to the physics of the problem. One of the main features of the code is to build the whole application with subprograms\' calls from the main program only, while all object.. handled by the subprograms are designed by names (these objects are for example geometrical domains, matrices and vectors which are discrete forms of integrals of the variational formulation, data, ...).

We present in this paper the detailed derivation of an application of the code, the numerical solution of the linearized sea-keeping problem in 3 dimensions, starting from its variational formulation using the method of coupling between finite element and integral representation. We next show two other examples, related to the wave resistance problem : a non-linear approach in 20 and the linear 3D problem.

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