On Mathematical modeling of Fractional-Differential Dynamics of Flushing Process for Saline Soils with Parallel Algorithms Usage

2016 ◽  
Vol 48 (10) ◽  
pp. 1-12 ◽  
Author(s):  
Vsevolod A. Bogaenko ◽  
Vladimir M. Bulavatskiy ◽  
Iuriy G. Kryvonos
Keyword(s):  
Mathematical Modeling ◽  
Parallel Algorithms ◽  
Saline Soils ◽  
Fractional Differential

scholarly journals Mathematical modeling of the smoking dynamics using fractional differential equations with local and nonlocal kernel

2018 ◽  
Vol 11 (08) ◽  
pp. 994-1014 ◽  
Author(s):  
V. F. Morales-Delgado ◽  
J. F. Gómez-Aguilar ◽  
M. A. Taneco-Hernández ◽  
R. F. Escobar-Jiménez ◽  
V. H. Olivares-Peregrino
Keyword(s):  
Mathematical Modeling ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Differential

scholarly journals Mathematical Modeling and Functional Order Pursuits with Separated Dynamics

2021 ◽  
Vol 2068 (1) ◽  
pp. 012002
Author(s):  
Mashrabjon Mamatov ◽  
Xakimjon Alimov
Keyword(s):  
Mathematical Modeling ◽  
Dynamic Systems ◽  
Sufficient Conditions ◽  
Order Equation ◽  
Matrix Functions ◽  
Pursuit Problem ◽  
Controlled Systems ◽  
Generalized Matrix ◽  
Fractional Differential ◽  
Qualitative Dynamics

Abstract This work is devoted to the study of the pursuit problem in controlled systems described by a fractional-order equation with divided dynamics. For fixed player controls, representations of solutions are established in the form of analogs of the Cauchy formula using generalized matrix functions. Sufficient conditions are obtained for the possibility of completing the pursuit. Specific types of fractional differential equations and models of fractional dynamical systems are considered. The qualitative dynamics, issues of stability and controllability of such systems are discussed. Considered, try which, the motion of the equation is described with irrational orders. Problems of the type under study are encountered in modeling the processes of economic growth and in problems of stabilizing dynamic systems.

On improving the efficiency of mathematical modeling of the problem of stability of construction

2020 ◽  
Vol 25 (3) ◽  
pp. 27-36
Author(s):  
Chistyakov A.V. ◽  
Keyword(s):  
Mathematical Modeling ◽  
Parallel Computing ◽  
Parallel Algorithms ◽  
High Performance ◽  
Sparse Matrices ◽  
Multicore Processors ◽  
Automatic Parallelization ◽  
Hybrid Architecture ◽  
Graphics Processors ◽  
Algorithmic Software

Algorithmic software for mathematical modeling of structural stability is considered, which is reduced to solving a partial generalized eigenvalues problem of sparse matrices, with automatic parallelization of calculations on modern parallel computers with graphics processors. Peculiarities of realization of parallel algorithms for different structures of sparse matrices are presented. The times of solving the problem of stability of composite materialsusing a three-dimensional model of "finite size fibers" on computers of different architectures are given. In mathematical modeling of physical and technical processes in many cases there is a need to solve problems of algebraic problem of eigenvalues (APVZ) with sparse matrices of large volumes. In particular, such problems arise in the analysis of the strength of structures in civil and industrial construction, aircraft construction, electric welding, etc. The solving to these problems is to determine the eigenvalues and eigenvectors of sparse matrices of different structure. The efficiency of solving these problems largely depends on the effectiveness of mathematical modeling of the problem as a whole. Continuous growth of task parameters, calculation of more complete models of objects and processes on computers require an increase in computer productivity. High-performance computing requirements are far ahead of traditional parallel computing, even with multicore processors. High-performance computing requirements are far ahead of traditional parallel computing, even with multicore processors. Today, this problem is solved by using powerful supercomputers of hybrid architecture, such as computers with multicore processors (CPUs) and graphics processors (GPUs), which combine MIMD and SIMD architectures. But the potential of high-performance computers can be used to the fullest only with algorithmic software that takes into account both the properties of the task and the features of the hybrid architecture. Complicating the architecture of modern high-performance supercomputers of hybrid architecture, which are actively used for mathematical modeling (increasing the number of computer processors and cores, different types of computer memory, different programming technologies, etc.) means a significant complication of efficient use of these resources in creating parallel algorithms and programs. here are problems with the creation of algorithmic software with automatic execution of stages of work, which are associated with the efficient use of computing resources, ways to store and process sparse matrices, analysis of the reliability of computer results. This makes it possible to significantly increase the efficiency of mathematical modeling of practical problems on modern high-performance computers, as well as free users from the problems of parallelization of complex problems. he developed algorithmic software automatically implements all stages of parallel computing and processing of sparse matrices on a hybrid computer. It was used at the Institute of Mechanics named after S.P. Tymoshenko NAS of Ukraine in modeling the strength problems of composite material. A significant improvement in the time characteristics of mathematical modeling was obtained. Problems of mathematical modeling of the properties of composite materials has an important role in designing the processes of deformation and destruction of products in various subject areas. Algorithmic software for mathematical modeling of structural stability is considered, which is reduced to solving a partial generalized problem of eigen values of sparse matrices of different structure of large orders, with automatic parallelization of calculations on modern parallel computers with graphics processors. The main methodological principles and features of implementation of parallel algorithms for different structures of sparse matrices are presented, which ensure effective implementation of multilevel parallelism of a hybrid system and reduce data exchange time during the computational process. As an example of these approaches, a hybrid algorithm of the iteration method in subspace for tape and block-diagonal matrices with a frame for computers of hybrid architecture is given. Peculiarities of data decomposition for matrices of profile structure at realization of parallel algorithms are considered. The proposed approach provides automatic determination of the required topology of the hybrid computer and the optimal amount of resources for the organization of an efficient computational process. The results of testing the developed algorithmic software for problems from the collection of the University of Florida, as well as the times of solving the problem of stability of composite materials using a three-dimensional model of "finite size fibers" on computers of different architectures. The results show a significant improvement in the time characteristics of solving problems.

Cerebral Blood Circulation in Premature Infants by Means of Mathematical Modeling

2015 ◽  
Vol 46 (S 01) ◽  
Author(s):  
R. Lampe ◽  
N. Botkin ◽  
V. Turova ◽  
T. Blumenstein ◽  
A. Alves-Pinto
Keyword(s):  
Mathematical Modeling ◽  
Premature Infants ◽  
Blood Circulation ◽  
Cerebral Blood Circulation
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