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

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.