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

Authors:
Haotao Cai
Affiliations:
School of Statistics and Mathematics, Shandong Finance Institute, Jinan, Shandong, 250014, PR China
Venue:
Journal of Complexity
Year:
2009

Citing 5
Cited 3

A fast algorithm for solving the generalized airfoil equation

Journal of Computational and Applied Mathematics - Orthogonal polynomials and numerical methods
Rates of convergence for collocation with Jacobi polynomials for the airfoil equation

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Numerical Solution of the Generalized Airfoil Equation for an Airfoil with a Flap

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A Collocation Method for the Generalized Airfoil Equation for an Airfoil with a Flap

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A Fast Fourier-Galerkin Method for Solving Singular Boundary Integral Equations

SIAM Journal on Numerical Analysis

Iterated fast multiscale Galerkin methods for Fredholm integral equations of second kind with weakly singular kernels

Applied Numerical Mathematics
A fast multiscale Kantorovich method for weakly singular integral equations

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

Calcolo: a quarterly on numerical analysis and theory of computation

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Abstract

In this paper we develop a fast Petrov-Galerkin method for solving the generalized airfoil equation using the Chebyshev polynomials. The conventional method for solving this equation leads to a linear system with a dense coefficient matrix. When the order of the linear system is large, the computational complexity for solving the corresponding linear system is huge. For this we propose the matrix truncation strategy, which compresses the dense coefficient matrix into a sparse matrix. We prove that the truncated method preserves the optimal order of the approximate solution for the conventional method. Moreover, we solve the truncated equation using the multilevel augmentation method. The computational complexity for solving this truncated linear system is estimated to be linear up to a logarithmic factor.