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Вычислительные методы и приложения

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

D. V. Luk'yanenko, A. G. Yagola

Lomonosov Moscow State University, Faculty of Physics

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 08-01-00160-a and 10-01-91150-NFSC). The numerical results were obtained using the Computing Cluster of Moscow State University.

Keywords: three-dimensional Fredholm integral equations of the first kind; conjugate gradient method; Tikhonov regularization; parallel algorithms.

UDC: 519.6