APPLICATION OF PARALLEL CALCULATIONS IN THE INVERSE DIFFRACTION PROBLEM ON DIELECTRIC OBJECTS WITH INHOMOGENEITIES
- Authors: Kondyrev O.V.1, Lapich A.O.1, Medvedik M.Y.1
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Affiliations:
- Penza State University
- Issue: No 2 (2025)
- Pages: 95-106
- Section: MODELS, SYSTEMS, MECHANISMS IN THE TECHNIQUE
- URL: https://journal-vniispk.ru/2227-8486/article/view/307582
- DOI: https://doi.org/10.21685/2227-8486-2025-2-8
- ID: 307582
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Abstract
Background. The main objective of the study is to effectively solve the computationally complex inverse diffraction problem applicable to objects of arbitrary geometry. Parallel algorithms are used to achieve this goal. Special attention is paid to minimizing the calculation time. Materials and methods. To solve this problem, it is necessary to numerically solve the integral equation. A two-step method is used to effectively solve the inverse problem. Results. Graphical images illustrating the original and reconstructed values for inhomogeneous objects are presented. Estimates of the acceleration and effectiveness of the program are presented. Conclusions. A numerical method has been developed and implemented to solve the problem of determining inhomogeneities in objects. The MPI programming interface is used to speed up the computing process. A comparison of the results demonstrates the possibility of identifying different types of inhomogeneities.
About the authors
Oleg V. Kondyrev
Penza State University
Author for correspondence.
Email: kow20002204@mail.ru
Head of the laboratory of software development
(40 Krasnaya street, Penza, Russia)Andrey O. Lapich
Penza State University
Email: lapich.a@yandex.ru
Assistant of the sub-department of mathematics and supercomputer modeling
(40 Krasnaya street, Penza, Russia)Mikhail Yu. Medvedik
Penza State University
Email: _medv@mail.ru
Candidate of physical and mathematical sciences, associate professor of the sub-department of mathematics and supercomputer modeling
(40 Krasnaya street, Penza, Russia)References
- Dmitriev V.I. Obratnye zadachi geofiziki = Inverse problems of geophysics. Moscow: MAKS Press, 2012:340. (In Russ.)
- Brown B.M., Marlett M., Reyes J.M. Uniqueness for an inverse problem in electromagnetism with partial data. J. Differential Equations. 2016;260:525–654.
- Bakushinsky A.B., Kokurin M.Yu. Iterative Methods for Approximate Solution of Inverse Problems. New York: Springer, 2004:291.
- Beilina L., Klibanov M. Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems. New York: Springer, 2012:407.
- Kabanikhin S.I., Satybaev A.D., Shishlenin M.A. Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems Utrecht. VSP, 2004:179.
- Romanov V.G. Inverse Problems of Mathematical Physics. Utrecht, The Netherlands: VNU, 1986:236.
- Olenev N.N. Osnovy parallel'nogo programmirovaniya v sisteme MPI = Fundamentals of parallel programming in the MPI system. Moscow: VTs RAN, 2005:77. (In Russ.)
- Antonov A.S. Parallel'noe programmirovanie s ispol'zovaniem tekhnologii MPI = Parallel programming using MPI technology. Moscow: Izd-vo MGU, 2004:71. (In Russ.)
- Korneev V.D. Parallel'noe programmirovanie v MPI = Parallel programming in MPI. Novosibirsk: Izd-vo SO RAN, 2000:215. (In Russ.)
- Nemnyugin S.A., Stesik O.L. Parallel'noe programmirovanie dlya mnogoprotsessornykh vychislitel'nykh system = Parallel programming for multi-processor computing systems. Saint Petersburg: BKhV-Peterburg, 2002:397. (In Russ.)
- Khutorova O.G. Osnovy raboty s bibliotekoy MPI.: ucheb.-metod. posobie = Basics of working with the MPI library.: studies.- the method. stipend. Kazan: Kazan. un-t. 2022:32. (In Russ.)
- Malyavko A.A. Parallel'noe programmirovanie na osnove tekhnologiy OpenMP, MPI, CUDA: ucheb. posobie = Parallel programming based on OpenMP, MPI, and CUDA technologies : a tutorial. Novosibirsk: NGTU., 2015:116. (In Russ.)
- Zemlyanaya E.V., Bashashin M.V. Vvedenie v parallel'noe programmirovanie na osnove tekhnologiy MPI i OpenMP: ucheb. posobie = Introduction to parallel programming based on MPI and OpenMP technologies: a tutorial. Dubna: Gosudarstvennyy universitet «Dubna», 2023:101. (In Russ.)
- Smirnov Yu.G., Tsupak A.A. Matematicheskaya teoriya difraktsii akusticheskikh i elektromagnitnykh voln na sisteme ekranov i neodnorodnykh tel = Mathematical theory of diffraction of acoustic and electromagnetic waves on a system of screens and inhomogeneous bodies. Moscow: Rusayns, 2016:223. (In Russ.)
- Sommerfeld A. Die Greensche Funktion der Schwingungsgleichung. Jahresber. Dtsch. Math.-Ver. 1912;21:309–353.
- Lapich A.O., Medvedik M.Yu. Solving a scalar two-dimensional nonlinear diffraction problem on objects of arbitrary shape. Uchenye zapiski Kazanskogo universiteta. Ser. fiz.-matem. Nauki = Scientific notes of Kazan University. Ser. phys.-checkmate. sciences. 2023;165(bk.2):166–176. (In Russ.)
- Lapich A.O., Medvedik M.Yu. The method of generalized and combined computational grids for restoring the parameters of body inhomogeneities based on the results of electromagnetic field measurements. Matematicheskoe modelirovanie = Mathematical modeling. 2024;36(4):24–36. (In Russ.)
- Smirnov Yu.G., Tsupak A.A. Direct and inverse scalar scattering problems for the Helm-holtz equation in ℝ m. J. Inverse Ill-Posed Probl. 2022;30(1):101–116.
- Lapich A.O., Medvedik M.Yu. Algorithm for finding inhomogeneities in inverse nonlinear diffraction problems. Uchenye zapiski Kazanskogo universiteta. Ser. Fiz.-matem. nauki = Scientific notes of Kazan University. Ser. phys.- checkmate. sciences. 2024;166(bk.3):395–406. (In Russ.)
- Lapich A.O., Medvedik M.Yu. Method for reconstruction the parameters of body inhomogeneities from the results of electromagnetic field measurements. Lobachevskii Journal of Mathematics. 2024;45(10):4628–4635.
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