A family of quadrature formulas for solving boundary integral equations

Authors

  • I.O. Arushanyan Lomonosov Moscow State University

Keywords:

double-layer potential, integral equations, corner points, condensing grids, quadrature method

Abstract

A family of exponentially convergent quadrature formulas is proposed for a class of functions with weak singularity. The results obtained are used to solve the boundary integral equations of harmonic potential theory in domains with corner points.

Author Biography

I.O. Arushanyan

References

  1. Арушанян И.О. О численном решении граничных интегральных уравнений второго рода в областях с угловыми точками // Ж. вычисл. матем. и матем. физ. 1996. 36, № 5. 537-548.
  2. Бахвалов Н.С. Об оптимальной скорости интегрирования аналитических функций // Ж. вычисл. матем. и матем. физ. 1967. 7, № 5. 1011-1020.
  3. Заргарян С.С. Об асимптотике решений системы сингулярных интегральных уравнений, порожденной уравнениями Ламе в окрестности угловых точек контура // Докл. АН Арм. ССР. 1983. 77, № 4. 437-439.
  4. Мазья В.Г. Граничные интегральные уравнения // Итоги науки и техники. 27. М.: ВИНИТИ, 1988. 131-228.
  5. Bremer J., Rokhlin V. Efficient discretization of Laplace boundary integral equations on polygonal domains // J. Comput. Phys. 2010. 229, N 7. 2507-2525.
  6. Graham I.G., Chandler G.A. High-order methods for linear functionals of solutions of second kind integral equations // SIAM J. Numer. Anal. 1988. 25, N 5. 1118-1137.
  7. Helsing J., Ojala R. Corner singularities for elliptic problems: integral equations, graded meshes, quadrature, and compressed inverse preconditioning // J. Comput. Phys. 2008. 227, N 20. 8820-8840.
  8. Kress R. A Nyström method for boundary integral equations in domains with corners // Numer. Math. 1990. 58, N 2. 145-161.
  9. Kress R. Linear integral equations. Berlin: Springer, 2012.
  10. Arushanyan I.O., Drutsa A.V., Kobel’kov G.M. The finite difference method for solving a system of equations of tide dynamics // Differential Eqiations. 2009. 45, N 7. 983-990.
  11. Arushanian I.O., Kobelkov G.M. Implementation of a least-squares finite element method for solving the Stokes problem with a parameter // Numerical Linear Algebra with Applications. 1999. 6, N 7. 587-597.
  12. Arushanyan I.O. On the numerical solution of boundary integral equations of the second kind in domains with corner points // Computational Mathematics and Mathematical Physics. 1996. 36, N 6. 773-782.

Published

05-11-2013

How to Cite

Арушанян И.О. A Family of Quadrature Formulas for Solving Boundary Integral Equations // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2013. 14. 461-467

Issue

Section

Section 1. Numerical methods and applications