On the numerical resolution of the generalized airfoil equation with Possio kernel

Monegato, Giovanni; Lepora, P.

doi:10.1007/bf01405288

Cited by 5 publications

(2 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Petrov-Galerkin method using the Chebyshev polynomial basis for solving the generalized airfoil equation is a standard numerical method (see [1][2][3][4][5][6][7][8][9]). This method preserves the optimal order of the approximate solution.…”

Section: Introductionmentioning

confidence: 99%

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

Cai¹

2009

Journal of Complexity

View full text Add to dashboard Cite

The generalized airfoil equation The Petrov-Galerkin method The truncation strategy The multilevel augmentation methods a b s t r a c t 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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

Cai¹

2009

Journal of Complexity

View full text Add to dashboard Cite

show abstract

“…where λ is real and the integrals are defined in the Cauchy principal value sense, is of key importance in many applications. Among the several authors who have examined this problem, Söhngen, [13,14], and Tricomi, [7,16,17], appear to be the first to have obtained fundamental results on this topic. Here we recall some of them.…”

Section: Introduction the Representation Of All Solutions Of The Sing...mentioning

confidence: 99%

On the Analytical Solutions of Two Singular Integral Equations with Hilbert Kernels

Monegato¹,

Strozzi²

2005

J. Integral Equations Applications

Self Cite

View full text Add to dashboard Cite

show abstract

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

Cai

2012

Calcolo

View full text Add to dashboard Cite

On the numerical resolution of the generalized airfoil equation with Possio kernel

Abstract: Summary. In this paper we consider the so-called generalized airfoil singular integral equation, with a smooth input function, and present "ad hoc" quadrature rules to compute efficiently the elements of collocation and Galerkin matrices.

Cited by 5 publications

References 19 publications

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

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

On the Analytical Solutions of Two Singular Integral Equations with Hilbert Kernels

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

Contact Info

Product

Resources

About