ОБОСНОВАНИЕ ПОДХОДА К ПОСТАНОВКЕ ЗАДАЧИ НА РАЗРАБОТКУ МАТЕМАТИЧЕСКОГО МЕТОДА МОДЕЛИРОВАНИЯ ПАРАМЕТРОВ ЭКРАНИРУЮЩЕЙ КОНСТРУКЦИИ, ОБЕСПЕЧИВАЮЩЕЙ ФУНКЦИОНАЛЬНУЮ УСТОЙЧИВОСТЬ КОМПОНЕНТОВ ОБЪЕКТОВ КРИТИЧЕСКОЙ ИНФОРМАЦИОННОЙ ИНФРАСТРУКТУРЫ ПРИ ВОЗДЕЙСТВИИ ЭЛЕКТРОМАГНИТНЫХ ИМПУЛЬСОВ

Mathematical model construction of complicate physical phenomenon often leads to the setting and solving problems of parameters optimal control in differential equations in partial derivatives. Chosen equation with boundary and initial conditions is usually mathematical model basis of the object, which is under analysis. Optimal control of right-hand side function in non-linear problem for inhomogeneous biharmonic has been investigated. With the help of various gradient methods the problems of parameters control in such equations are solved successfully. Herewith linear problem is solved with the potential method on every step. In this work biharmonic potentials with logarithmic singularity are under consideration. That is why parameters optimization in these problems are conducted together with elimination of their incorrectness. It should be noted that system optimal control problems, described with biharmonic equations in irregular shape region, are studied poorly. Therefore the object of investigation is one of boundary conditions for inhomogeneous biharmonic equation. The circumstance which complicated the problem was irregularity of function domain. Clearly that this problem can be solved with computational mathematics methods. Without precise solution of linear problem, it is impossible to use gradient method, build converging iterative process, and obtain precise solution of optimization problem. Algorithm for linear boundary value problem solution with boundary integral equations overcomes this problem successfully. Physical examples of numerical implementation have been presented, analysis of obtained solutions have been conducted. Their accuracy, algorithm simplicity and time spent evidence about this approach promising for practical results obtaining in plate theory and mathematical physics problems successful numerical solving

Group method analysis of steady free-convective laminar boundary-layer flow on a nonisothermal vertical circular cylinder

This work presents a parallel implementation of the Parareal method using Portable Extensible Toolkit for Scientific Computation (PETSc). An optimal control problem of a parabolic partial differential equation with known boundary conditions and initial state is solved, where the minimized cost function relates the controller v usage and the approximation of the solution y to an optimal known function y*, measured by ∥y∥ and ∥y*∥, respectively. The equations that model the process are discretized in space using Finite Elements and in time using Finite Differences. After the discretizations, the problem is transformed to a large linear system of algebraic equations, that is solved by the Conjugate Gradient method. A Parareal preconditioner is implemented to speed up the convergence of the Conjugate Gradient. The main advantage in using the Parareal approach is to speed up the resolution time, when comparing to implementations that use only the Conjugate Gradient or GMRES methods. The implementation developed in this work offers a parallelization relative efficiency for the strong scaling of approximately 70% each time the process count doubles. For weak scaling, 75% each time the process count doubles for a constant solution size per process and 96% each time the process count doubles for a constant data size per process.

This paper presents an analysis of the inverse problem of parameter (or parameters) identification in unsteady ground-water flow. The response of the system is governed by a typical nonlinear second-order partial differential equation for which there exists no closed-form solution. Identification is an inverse process whereby the parameters embedded in a differential equation are determined from observations of the system's input and output along with appropriate initial and boundary conditions. These parameters are usually not physically measurable. In this paper, a simple but illustrative inverse problem is analyzed by quasilinearization, maximum principle, gradient method, the influence coefficient method, and linear programming. A comparison is made between these methods. The problem of convergence and stability is examined and demonstrated by numerical experimentation.

Evaluating three measurement methods of soil ground heat flux based on actively heated distributed temperature sensing technology

Numerous papers deal with asymptotic methods for boundary value problems in domains depending on a small parameter in a complicated way (perforated domains, partially perforated domains, framework structures, thin domains); e.g., see [1–9]. Boundary value problems in thick singularly degenerating junctions (the number of components of such junctions grows infinitely as the perturbation parameter tends to zero) have specific difficulties and require a separate consideration. It was shown in [10] that boundary value problems in thick junctions lose their coercivity under the passage to the limit, which substantially complicates asymptotic studies. The papers [11, 12] were the first in this direction. In [13–19], a classification of thick junctions was given and rigorous mathematical methods were developed for analyzing the main boundary value problems of mathematical physics in thick singularly degenerating junctions of various types. The study of boundary value problems in thick junctions is focused on the asymptotic behavior of their solutions as e → 0, i.e., as the number of thin attached domains grows infinitely and their thickness tends to zero. In the present paper, we consider a thick junction whose thin attached cylinders are divided into two levels depending on the boundary conditions posed on the lateral surface of these cylinders (inhomogeneous Neumann boundary conditions and homogeneous Dirichlet conditions). In addition, thin cylinders of each level e-periodically alternate along the junction zone. Such thick junctions will be called thick two-level junctions. A problem on a thick plane two-level junction was considered for the first time in [20], where the asymptotic behavior of eigenvalues and eigenfunctions of a spectral boundary value problem was analyzed. Other boundary value problems in plane two-level junctions were considered in [21–23]. Asymptotic analysis of boundary value problems with a periodic change of boundary conditions (Neumann and Dirichlet conditions) on the boundary of smooth unperturbed domains was carried out in [24–26], where it was shown that the first term of the asymptotics is mainly the solution of the corresponding boundary value problem with the Dirichlet conditions. The qualitatively new result of the present paper implies that the first term of the asymptotics is a vector function whose components are solutions of two independent boundary value problems (one in the junction body and another in a domain filled with thin cylinders in the limit) with homogeneous Dirichlet conditions in the junction zone. Note also that the second problem is a problem for a second-order ordinary differential equation with a new right-hand side that “remembers” the inhomogeneity in the Neumann boundary conditions of the original problem and the specific “packing density” of thin cylinders.

In the article we obtained sufficient conditions of the existence of the nonlinear Noetherian boundary value problem solution for the system of differential-algebraic equations which are widely used in mechanics, economics, electrical engineering, and control theory. We studied the case of the nondegenerate system of differential algebraic equations, namely: the differential algebraic system that is solvable relatively to the derivative. In this case, the nonlinear system of differential algebraic equations is reduced to the system of ordinary differential equations with an arbitrary continuous function. The studied nonlinear differential-algebraic boundary-value problem in the article generalizes the numerous statements of the non-linear non-Gath boundary value problems considered in the monographs of А.М. Samoilenko, E.A. Grebenikov, Yu.A. Ryabov, A.A. Boichuk and S.M. Chuiko, and the obtained results can be carried over matrix boundary value problems for differential-algebraic systems. The obtained results in the article of the study of differential-algebraic boundary value problems, in contrast to the works of S. Kempbell, V.F. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko and A.A. Boychuk, do not involve the use of the central canonical form, as well as perfect pairs and triples of matrices. To construct solutions of the considered boundary value problem, we proposed the iterative scheme using the method of simple iterations. The proposed solvability conditions and the scheme for finding solutions of the nonlinear Noetherian differential-algebraic boundary value problem, were illustrated with an example. To assess the accuracy of the found approximations to the solution of the nonlinear differential-algebraic boundary value problem, we found the residuals of the obtained approximations in the original equation. We also note that obtained approximations to the solution of the nonlinear differential-algebraic boundary value problem exactly satisfy the boundary condition.

Cuckoo search algorithm with membrane communication mechanism for modeling overhead crane systems using RBF neural networks

The objective of this study was to develop and validate a subject-specific framework for modelling the human foot. This was achieved by integrating medical image-based finite element modelling, individualised multi-body musculoskeletal modelling and 3D gait measurements. A 3D ankle–foot finite element model comprising all major foot structures was constructed based on MRI of one individual. A multi-body musculoskeletal model and 3D gait measurements for the same subject were used to define loading and boundary conditions. Sensitivity analyses were used to investigate the effects of key modelling parameters on model predictions. Prediction errors of average and peak plantar pressures were below 10% in all ten plantar regions at five key gait events with only one exception (lateral heel, in early stance, error of 14.44%). The sensitivity analyses results suggest that predictions of peak plantar pressures are moderately sensitive to material properties, ground reaction forces and muscle forces, and significantly sensitive to foot orientation. The maximum region-specific percentage change ratios (peak stress percentage change over parameter percentage change) were 1.935–2.258 for ground reaction forces, 1.528–2.727 for plantar flexor muscles and 4.84–11.37 for foot orientations. This strongly suggests that loading and boundary conditions need to be very carefully defined based on personalised measurement data.

The problem of identification of coefficients and initial conditions for a boundary value problem for parabolic equations that reduces to a minimization problem of a misfit function is investigated. Firstly, the tensor train decomposition approach is presented as a global convergence algorithm. The idea of the proposed method is to extract the tensor structure of the optimized functional and use it for multidimensional optimization problems. Secondly, for the refinement of the unknown parameters, three local optimization approaches are implemented and compared: Nelder–Mead simplex method, gradient method of minimum errors, adaptive gradient method. For gradient methods, the evident formula for the continuous gradient of the misfit function is obtained. The identification problem for the diffusive logistic mathematical model which can be applied to social sciences (online social networks), economy (spatial Solow model) and epidemiology (coronavirus COVID-19, HIV, etc.) is considered. The numerical results for information propagation in online social network are presented and discussed.

This study presents an efficacy comparison of iterative solution methods for solving the compressible-fluid Reynolds equation in modeling air- or gas-lubricated bearings. A direct fixed-point iterative (DFI) method and Newton’s method are employed to transform the Reynolds equation in a form that can be solved iteratively. The iterative solution methods examined are the Gauss–Seidel method, the successive over-relaxation (SOR) method, the preconditioned conjugate gradient (PCG) method, and the multigrid method. The overall solution time is affected by both the transformation method and the iterative method applied. In this study, Newton’s method shows its effectiveness over the straightforward DFI method when the same iterative method is used. It is demonstrated that the use of an optimal relaxation factor is of vital importance for the efficiency of the SOR method. The multigrid method is an order faster than the PCG and optimal SOR methods. Also, the multigrid and PCG methods involve an extended coding work and are less flexible in dealing with gridwork and boundary conditions. Consequently, a compromise has to be made in terms of ease of use as well as programming effort for the solution of the compressible-fluid Reynolds equation.

We solve the variable coefficient Cauchy---Navier equations of elasticity in the unit square, for Dirichlet and Dirichlet-Neumann boundary conditions, using second order finite difference schemes. The resulting linear systems are solved by the preconditioned conjugate gradient (PCG) method with preconditioners corresponding to to the Laplace operator. The multiplication of a vector by the matrices of the resulting systems and the solution of systems with the preconditioners are performed at optimal and nearly optimal costs, respectively. For the case of Dirichlet boundary conditions, we prove the second order accuracy of the scheme in the discrete $$H^1$$ H 1 norm, symmetry of the resulting matrix and its spectral equivalence to the preconditioner. For the case of Dirichlet---Neumann boundary conditions, we prove symmetry of the resulting matrix. Numerical tests demonstrating the convergence properties of the schemes and PCG are presented.

UDC 517.9 At present, there are many articles devoted to the solvability of the boundary value problems describing deformation of static and quasistatic ideally elastoplastic bodies. Namely, solvability of variational inequalities resulting from the original (exact) statements of boundary value problems is proven in the case of quasistatic deformation for the flow-type models and in the case of static deformation for the Hencky-type models [1-7]. A peculiarity of solutions to the variational inequalities is the fact that some boundary conditions are lost. The smoothness assumption on a solution to the variational inequality does not allow us to establish the presence of the lost boundary conditions, since the set of feasible stresses is not a vector space. It was demonstrated in [8-11] that in the case of one-dimensional models of elastoplastic deformation (beam, rod, etc.) a solution to the variational inequality does not loose the boundary conditions that are involved in the original statement of the boundary value problem; i.e., all boundary conditions hold. Until recently, there were no such results for three-dimensional (two-dimensional) models of elastoplasticity. In the present article, we prove an existence theorem for the equilibrium problem for an elastoplastic plate which guarantees validity of all boundary conditions. Moreover, we consider domains with smooth boundaries as well as domains with cuts. The proof is based on a special combination of the regularization method and the penalty method. Namely, we apply elliptic regularization for solving the penalized boundary value problem that approximates the original elastoplastic problem. We obtain an existence theorem for the original problem by passing to the limit over the regularization and penalty parameters. The proposed way of regularization turns out to be rather effective and useful for analysis of other elastoplastic problems. The essence of the method consists in the fact that the regularization of the penalized equations is accompanied by special regularization of the boundary conditions. 1. A domain with smooth boundary. Suppose that fl C R 2 is a bounded domain with smooth boundary F and �9 : R 3 ---* R is a continuous convex function. The equilibrium problem for an elastoplastic plate is stated as follows [12]: Find functions w, m = {mij}, and ~ii, i,j = 1, 2, in satisfying the following equations and inequalities: -rnii,ij = f,

FEMA 356 backbone relations tend to provide conservative estimates of the available strengths and deformation capacities of reinforced concrete components, leading to costly seismic rehabilitation solutions for California hospitals. The conservatism is driven by the lack of test data for older, typically poorly detailed, structural components. Although FEMA 356 does provide for building specific component testing, this approach is not common due to cost concerns and/or schedule constraints. However, a test program on lightly-reinforced, poorly-detailed wall segments was undertaken at UCLA in 2004–2005 to support seismic rehabilitation projects on several southern California hospitals. Presented test results are compared with FEMA 356 backbone relations to highlight the advantages associated with building-specific test programs. In general, the test specimens revealed more strength and deformation capacity than assumed by FEMA 356, and more gradual strength deterioration. The test results, when coupled with the FEMA 356 Nonlinear Static Procedure (NSP) and Nonlinear Dynamic Procedure (NDP), enabled the development of more rational and substantially more economical rehabilitation solutions. The test results were used to help develop new backbone relations that were incorporated into ASCE-41-06 Supplement #1.

Experimental analysis and simulation of a centrifugal jet fan for impulse ventilation systems