New developments in finite element reactor calculations
1986; Elsevier BV; Volume: 18; Issue: 1-2 Linguagem: Inglês
10.1016/0149-1970(86)90007-7
ISSN1878-4224
Autores Tópico(s)Numerical methods for differential equations
ResumoThe Finite Element Method (FEM) is now widely used for design reactor calculations; a number of reactor engineering programs are based on this method. For PWR calculations, the N E P T U N E system Lz is used in France for design and operation purposes. Other examples of FEM programs are F I N E L M 3 designed at Wurenlingen, D I F G E N 4 at the Stuttgart University and FEM BABEL 5 in Japan. The accuracy benefits of the FEM are known as well as the size of the linear systems of equations to be solved; these systems of equations use sparse matrices and are easily solved on scalar computers using direct methods. This paper is devoted to an improvement of the efficiency of the FEM using a new resolution algorithm 12 which is efficient even on scalar computers and provides large benefits on vector computers. This algorithm is based on a two-step procedure: (1) a new splitting of the diffusion matrix is proposed that leads to solve a finite difference-like matrix, (2) the finite difference matrix is solved using ADI or related algorithms, (3) the coding of the whole procedure has been completely vectorized for the Cray 1 series of computers. This algorithm will be presented in the following parts of this report. First the splitting technique is described in Section 2, the ADI method is reminded and the vectorization coding is presented in Section 3. Numerical results showing the drastic improvement of the efficiency for two-dimensional calculations are given in Section 4 and some three-dimensional results are presented in Section 5.
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