Parallel numerical computation of an analytical method for solving an inverse problem
Advanced Mathematical Models and Applications, vol.6, no.2, pp.162-173, 2021 (Scopus)
- Publication Type: Article / Article
- Volume: 6 Issue: 2
- Publication Date: 2021
- Journal Name: Advanced Mathematical Models and Applications
- Journal Indexes: Scopus
- Page Numbers: pp.162-173
- Keywords: Analytical regularization solution, Inverse Cauchy problem, Message Passing Inter-face, Parallelization
- Open Archive Collection: Article
- Azerbaijan State University of Economics (UNEC) Affiliated: Yes
Abstract
We solve the inverse Cauchy problems for the Laplace and Poisson equations using a closed-form regularization analytical solution. The formula is written in the form of series whose terms are integrals. The discretization is done using a Gaussian quadrature and the finite sum thus obtained is implemented on distributed memory using the Message Passing Interface (MPI). A detailed study of the parallelization procedure is presented.