Error estimates in the Fast Multipole Method for scattering problems Part 2: Truncation of the Gegenbauer series
Quentin Carayol, Francis Collino (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
Similarity:
We perform a complete study of the truncation error of the Gegenbauer series. This series yields an expansion of the Green kernel of the Helmholtz equation, , which is the core of the Fast Multipole Method for the integral equations. We consider the truncated series where the summation is performed over the indices . We prove that if is large enough, the truncated series gives rise to an error lower than as soon as satisfies where is the Lambert function, depends...