Browsing by Author "Avdzhieva A."

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    A Coupled PDE-ODE Model for Nonlinear Transient Heat Transfer with Convection Heating at the Boundary: Numerical Solution by Implicit Time Discretization and Sequential Decoupling
    (2023-04-01) Filipov S.M.; Hristov J.; Avdzhieva A.; Faragó I.
    This article considers heat transfer in a solid body with temperature-dependent thermal conductivity that is in contact with a tank filled with liquid. The liquid in the tank is heated by hot liquid entering the tank through a pipe. Liquid at a lower temperature leaves the tank through another pipe. We propose a one-dimensional mathematical model that consists of a nonlinear PDE for the temperature along the solid body, coupled to a linear ODE for the temperature in the tank, the boundary and the initial conditions. All equations are converted into a dimensionless form reducing the input parameters to three dimensionless numbers and a dimensionless function. A steady-state analysis is performed. To solve the transient problem, a nontrivial numerical approach is proposed whereby the differential equations are first discretized in time. This reduces the problem to a sequence of nonlinear two-point boundary value problems (TPBVP) and a sequence of linear algebraic equations coupled to it. We show that knowing the temperature in the system at time level n − 1 allows us to decouple the TPBVP and the corresponding algebraic equation at time level n. Thus, starting from the initial conditions, the equations are decoupled and solved sequentially. The TPBVPs are solved by FDM with the Newtonian method.
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    COVERING A MAXIMUM NUMBER OF POINTS BY A FIXED NUMBER OF EQUAL DISKS VIA SIMULATED ANNEALING
    (2024-01-01) Tomova F.; Filipov S.; Avdzhieva A.
    The presented paper considers the problem of covering a maximum number of n given points in the plane by m equal disks of radius r. A point is covered if it is inside one or more than one disk. The disks need to be placed in the plane in such a way that a maximum number of points are covered. To solve the problem, an objective function, called energy, is introduced in such a way that the greater the covering is, the lower the energy is. Thus, a configuration of disks with minimum energy is a configuration with maximum covering. To find a configuration of disks that minimizes the energy, a stochastic algorithm based on the Monte Carlo simulated annealing technique is proposed. The algorithm overcomes potential local minima, which, as shown in the paper, are quite likely to occur. The computational complexity of the algorithm is O(mn). The algorithm is tested on several cases demonstrating its efficiency in finding global minima of the energy, i.e. configurations with maximum covering.
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    Shooting-projection method for a small object moving under the influence of a force
    (2021-09-20) Filipov S.M.; Faragó I.; Avdzhieva A.
    We consider a small object in 3D moving under the influence of a force that may depend explicitly on time, on the position of the object, and on its velocity. The equations of motion of classical mechanics are assumed to hold. If the position of the object is specified at some initial and some final time, obtaining the trajectory of the object requires the solution of a two-point boundary value problem. To solve the problem various numerical technics can be applied. This paper extends the recently proposed shooting-projection method to 3D. We introduce a Lagrangian from which, applying the principle of least action, the projection trajectory is derived. Analysis of the action reveals the meaning of the projection trajectory. Using the shooting-projection method, the considered two-point boundary value problem is solved for the case of a projectile motion in the presence of air resistance and wind.