Rapid solution of integral equations of scattering theory in two dimensions
Journal of Computational Physics
A domain decomposition method for the Helmholtz equation and related optimal control problems
Journal of Computational Physics
The fast multipole method: numerical implementation
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Numerical Analysis
The Fast Multipole Method I: Error Analysis and Asymptotic Complexity
SIAM Journal on Numerical Analysis
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Boundary element methods: an overview
Applied Numerical Mathematics - Selected papers from the first Chilean workshop on numerical analysis of partial differential equations (WONAPDE 2004)
Journal of Computational and Applied Mathematics
Some numerical aspects of the PUFEM for efficient solution of 2D Helmholtz problems
Computers and Structures
Combining the Ultra-Weak Variational Formulation and the multilevel fast multipole method
Applied Numerical Mathematics
Hi-index | 31.45 |
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 increase as a function of the wavenumber k. Many methods have been developed 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 recently developed methods is presented. This coupling enables one to reduce CPU time very efficiently for large wavenumbers. 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 26λ using a resolution based on a mesh with an average edge length of about 2λ, where λ is the wavelength. Results are also given for an industrial test case from Dassault-Aviation, the Cetaf.