Multiple scattering in thermal diffusion: iteration and preconditioning

Ricardo Celorrio ^[1] ; Francisco Javier Sayas ^[1]
1. [1] Universidad de Zaragoza
  
  Universidad de Zaragoza
  
  Zaragoza, España
Localización: XVII Congreso de Ecuaciones Diferenciales y Aplicaciones ; VII Congreso de Matemática Aplicada: Salamanca, 14-28 septiembre 2001 / coord. por Luis Ferragut Canals , Anastasio Pedro Santos Yanguas , 2001, ISBN 8469961446, págs. 389-390
Idioma: inglés
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Resumen
- Integral–equation methods are often used to deal with exterior problems of wave propagation. This approach is used here for an exterior problem where plane time–harmonic thermal diffusion waves propagating through a semi–infinite material are scattered by aligned cylindrical holes. By an indirect method for the two–dimensional Helmholtz equation the problem is reduced to a system of inte- gral equations of the second with continuous non–smooth kernels. The numerical approximation by a boundary element method leads to a large complex and full system. For an efficient solution of the system, we propose use the physical idea of the multiple scattering to precondition the GMRES method.