The numerical integration scheme for a fast Petrov---Galerkin method for solving the generalized airfoil equation

Authors:
Haotao Cai
Affiliations:
School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, China 250014
Venue:
Calcolo: a quarterly on numerical analysis and theory of computation
Year:
2013

Citing 5
Cited 0

A fast algorithm for solving the generalized airfoil equation

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A fast Petrov-Galerkin method for solving the generalized airfoil equation

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Abstract

The main purpose of this paper is to give the numerical integration scheme for a fast Petrov---Galerkin method for solving the generalized airfoil equation, considered in a recent paper (Cai, J. Complex. 25:420---436, 2009). This scheme leads to a fully discrete sparse linear system. We show that it requires a nearly linear computational cost to get this system, and the approximate solution of the resulting linear system preserves the optimal convergent order. Numerical experiments are presented to confirm the theoretical estimates.