A Fast Multipole Boundary Element Code Written in Julia Language
Emerson Bastos1; Éder Lima de Albuquerque2; Lucas Silveira Campos3
1 Universidade Federal dos Vales do Jequitinhonha e Mucuri; 2 Universidade de Brasília; 3 Universidade Federal do Espírito Santo
doi:10.20906/CPS/CILAMCE2017-1262
Resumo
This paper presents a comparison of two fast multipole boundary element method implementations, in Julia and Fortran language, with application to a heat conduction problem. Fortran is a well known compiled language while Julia is a newborn pre-compiled language that offers many resources for the programmer. In this work, firstly, the fast multipole boundary element method using complex variables and Taylor series in the expansion of fundamental solutions is presented. Since influence matrices are not explicitly obtained, it is necessary the use of an iterative method to solve the linear system. The generalized minimum residue method (GMRES) was chosen based on previous works. The hierarchical data structure and the implemented algorithm are described. The two implementations of the fast multipole boundary element method are applied to a heat conduction problem and their performances are compared.
Palavras-chave: Boundary Element Method; Julia Language; Fast MultiPole