Coupling of Fast Multipole Method and Microlocal Discretization for the 3-D Helmholtz Equation

Darrigrand, Eric

HAL, hal-00133688 / Harvested from HAL

Résumé

We are concerned with an integral method applied to the solution of the Helmholtz equation where the linear system is solved using an iterative method. We need to perform matrix-vector products whose time and memory requirements are increasing as a function of the wave number $\kappa$. A lot of methods have been developed in order to speed up the matrix-vector product calculation or to reduce the size of the system. Microlocal discretization methods enable one to consider new systems with reduced size. Another method, the fast multipole method, is one of the most efficient and robust methods used to speed up the calculation of matrix-vector products. In this paper, a coupling of these two recent methods is presented. It enables one to reduce the CPU time very efficiently for large wave numbers. Satisfactory numerical tests are also presented to confirm the theoretical study within a new integral formulation. Results are obtained for a sphere with a size of $26 \lambda $ by a resolution based on a mesh with an average edge length about $2 \lambda $ where $\lambda $ is the wavelength.

Détail

Publié le : 2001-07-05
Classification:  Helmholtz,  Integral Equation,  Finite Element,  Fast Multipole Method,  Microlocal Discretization,  [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]