Numerical solution of boundary integral equations of the plane theory of elasticity in curvilinear polygons

被引：0

作者：

Arushanyan I.O. ^{[1
]}

机构：

[1] Moscow State University, Leninskie Gory, Moscow

来源：

Moscow University Mathematics Bulletin | 2015年 / 70卷 / 4期

基金：

俄罗斯基础研究基金会;

关键词：

Integral Equation; Finite Number; Quadrature Formula; Boundary Integral Equation; Corner Point;

D O I：

10.3103/S0027132215040099

中图分类号：

学科分类号：

摘要：

A numerical method for solving boundary integral equations of the plane theory of elasticity in domains with piecewise analytic boundaries and a finite number of corner points is proposed. This method is based on the application of a family of composite quadrature formulas on condensing grids. It is proved that the proposed method is exponentially convergent with respect to the number of quadrature nodes in use. © 2015, Allerton Press, Inc.

引用

页码：193 / 196

页数：3

共 11 条

[1]

Babushka I., Guo B.Q., Stephan E.P., On the Exponential Convergence of the h-p Version for Boundary Element Galerkin Methods on Polygons, Math. Meth. Appl. Sci., 12, 5, (1990)

[2]

Bremer J., Rokhlin V., Efficient Discretization of Laplace Boundary Integral Equations on Polygonal Domains, J. Comput. Phys., 229, 7, (2010)

[3]

Chandler G.A., Superconvergent Approximations to the Solution of a Boundary Integral Equation on Polygonal Domains, SIAM J. Numer. Anal., 23, 6, (1986)

[4]

Kress R., A Nystrom Method for Boundary Integral Equations in Domains with Corners, Numer. Math., 58, 1, (1990)

[5]

Kress R., Linear Integral Equations, (1999)

[6]

Arushanyan I.O., On the Numerical Solution of Boundary Integral Equations of the Second Kind in Domains with Corner Points, Zh. Vychisl. Matem. Matem. Fiz., 36, 6, (1996)

[7]

Arushanyan I.O., Application of the Quadrature Method for Solving Boundary Integral Equations of Plane Elasticity Theory on Polygons, Vychisl. Metody Programm, 4, (2003)

[8]

Arushanyan I.O., A Family of Quadrature Formulas for Solving Boundary Integral Equations, Vychisl. Metody Programm, 14, (2013)

[9]

Arushanyan I.O., Numerical Solution of Boundary Integral Equations on Curvilinear Polygons, Vestn. Mosk. Univ., Matem. Mekhan., 4, (2014)

[10]

Arushanyan I.O., An Exponentially Convergent Method for Solving Boundary Integral Equations on Polygons, Vychisl. Metody Programm, 15, (2014)

← 1 2 →