Parallel numerical computation of an analytical method for solving an inverse problem

Abdeljalil Nachaoui (1) , Mourad Nachaoui (2) , Bayram Gasimov (3)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 Laboratoire de Mathématiques et Applications, FST, Beni-Mellal, Maroc
3 Azerbaijan State University of Economics (UNEC), Baku, Azerbaijan

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.

Mots clés: nverse Cauchy problem; analytical regularization solution; parallelization; Message Passing Inter-face.AMS Subject Classi cation:65N21

Domaines: Mathématiques [math]; Analyse numérique [math.NA]; Calcul parallèle, distribué et partagé [cs.DC]

Abdeljalil Nachaoui, Mourad Nachaoui, Bayram Gasimov. Parallel numerical computation of an analytical method for solving an inverse problem. Advanced Mathematical Models & Applications, 2021, 6 (2), pp.162-173. ⟨hal-03327196⟩