Կիրակոսյան Գագիկ, Փոթիկյան Մարինա, Ավետիսյան Հրայր, Ավետիսյան Քաջիկ 028
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METHODS AND PROBLEMS OF NUMERICAL MODELING FOR REDUCING COMPUTATIONAL MEMORY
KIRAKOSYAN GAGIK
Associate Professor at the Chair of Computer Systems and Network,
National Polytechnic University of Armenia
POTIKYAN MARINA
Associate Professor at the Chair of Natural Sciences,
Rescue Service and Crisis Management Educational Unit,
Educational Complex of the Ministry of Internal Affairs of the Republic of Armenia
AVETISYAN HRAYR
Associate Professor at the Chair of Algorithmic Languages and Programming,
National Polytechnic University of Armenia
AVETISYAN KAJIK
Associate Professor at the Chair of Mechatronics
of Yerevan State College of Informatics
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Abstract․ In this scientific article modified numerical integration methods and modeling approaches have been analyzed for their application in simulations of electromagnetic transient phenomena in transmission lines. Two primary objectives are considered: minimizing numerical errors caused by Gibbs oscillations and reducing the computational memory required for such simulations. In this respect, transmission lines have been represented as cascades of π circuits. For the minimization of numerical errors, two approaches have been examined. The first approach is related to the manner in which the numerical integration method is applied. Specifically, numerical integration is performed using second-order matrices associated with each π circuit used to model the transmission line. The second approach involves the application of damping resistance. This is achieved by introducing damping resistances into the longitudinal structure of the π circuits.
To reduce computational memory requirements, sparse matrices have been employed. These matrices contain a large number of zero elements when the cascade of π circuits is represented by a single high-order matrix, making them efficient for such simulations.
Key words: π circuit, transmission line, Kirchhoff's laws, numerical integration, cascades, sparse matrices, damping resistance, memory, computational time, transient processes, circuit modeling.