Application of multiprocessor systems for solving three-dimensional Fredholm integral equations of the first kind for vector functions

Authors

Keywords:

three-dimensional Fredholm integral equations of the first-kind, conjugate gradient method, Tikhonov regularization, parallel algorithms

Abstract

Some features of the numerical implementation of solving tree-dimensional Fredholm integral equations of the first kind for vector-functions with application of multiprocessor systems are considered. The Tikhonov regularization is applied to solve this ill-posed problem. The conjugate gradient method is used as a minimization procedure. The choice of the regularization parameter is performed according to the generalized discrepancy principle. A parallelization scheme for this problem is proposed; the efficiency of the approach under consideration is shown by the example of restoring magnetization parameters. This work was supported by the Russian Foundation for Basic Research (projects N 08-01-00160-a and N 10-01-91150-NFSC). The numerical results were obtained using the Computing Cluster of Moscow State University.

Author Biographies

D.V. Lukyanenko

A.G. Yagola

References

  1. Тихонов А.Н., Гончарский А.В., Степанов В.В., Ягола А.Г. Численные методы решения некорректных задач. М.: Наука, 1990.
  2. Воеводин В.В., Воеводин Вл.В. Параллельные вычисления. СПб.: БХВ-Петербург, 2002.
  3. Васильев М.П., Ягола А.Г. Применение многопроцессорных систем для решения двумерных интегральных уравнений Фредгольма 1-го рода // Вычислительные методы и программирование. 2003. 4, № 2. 156-159.
  4. Ягола А.Г., Титаренко В.Н., Васильев М.П., Шимановская Е.В. Особенности решения задач картирования распределения химических элементов по поверхностям звезд как некорректных задач с использованием многопроцессорных систем // Вычислительные методы и программирование. 2002. 3, № 1. 5-17.
  5. Вычислительный кластер НИВЦ МГУ (http://parallel.ru/cluster).

Published

2010-10-26

How to Cite

Лукьяненко Д.В., Ягола А.Г. Application of Multiprocessor Systems for Solving Three-Dimensional Fredholm Integral Equations of the First Kind for Vector Functions // Numerical methods and programming. 2010. 11. 336-343

Issue

Section

Section 1. Numerical methods and applications

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