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1
Content available On speeding up nano- and micromechanical calculations for irregular systems with long-range potentials
Rybarska-Rusinek L., Rejwer E., Linkov A.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2020
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Vol. 68, nr 2
337--344
EN
Irregular systems with long-range interactions and multiple clusters are considered. The presence of clusters leads to excessive computational complexity of conventional fast multipole methods (FMM), used for modeling systems with large number of DOFs. To overcome the difficulty, a modification of the classical FMM is suggested. It tackles the very cause of the complication by accounting for higher intensity of fields, generated by clusters in upward and especially in downward translations. Numerical examples demonstrate that, in accordance with theoretical estimations, in typical cases the modified FMM significantly reduces the time expense without loss of the accuracy.
2
Content available On evaluation of influence coefficients for edge and intermediate boundary elements in 3D problems involving strong field concentrations
Rybarska-Rusinek L.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2019
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Vol. 67, nr 1
69--76
EN
The paper presents a tool for accurate evaluation of high field concentrations near singular lines, such as contours of cracks, notches and grains intersections, in 3D problems solved the BEM. Two types of boundary elements, accounting for singularities, are considered: (i) edge elements, which adjoin a singular line, and (ii) intermediate elements, which while not adjoining the line, are still under strong influence of the singularity. An efficient method to evaluate the influence coefficients and the field intensity factors is suggested for the both types of the elements. The method avoids time expensive numerical evaluation of singular and hypersingular integrals over the element surface by reduction to 1D integrals. The method being general, its details are explained by considering a representative examples for elasticity problems for a piecewise homogeneous medium with cracks, inclusions and pores. Numerical examples for plane elements illustrate the exposition. The method can be extended for curvilinear elements.
3
Content available remote On efficient evaluation of integrals entering boundary equations of 3D potential and elasticity theory
Rybarska-Rusinek L., Jaworski D., Linkov A.
Journal of Mathematics and Applications
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2014
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Vol. 37
85--96
EN
The paper presents recurrent formulae for efficient evaluation of all the integrals needed for colving static 3D potential and elasticity problems by the boundary elements method. The power-type asymptoties for the density at edges of the boundary are accounted for explicitly.
4
Content available remote The asymptotic stochastic stabilityin large of finite interconnected systems
Dronka J., Rybarska-Rusinek L.
Demonstratio Mathematica
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2002
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Vol. 35, nr 4
915-925
EN
The sufficient conditions of asymptotic string stability in large of some finite composite stochastic systems are established. Nonlinear systems are considered with random noise which obeys the law of large numbers. The objective is to analyze composite systems in their lower order subsystems and in term of their interconnecting structure.
5
The asymptotic p-stability of finite interconnected systems
Rybarska-Rusinek L.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
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2001
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z. 25 [190]
185-196
EN
The sufficient conditions of asymptotic p-stability of some finite composite stochastic systems are established. Nonlinear systems are considered with gaussian random noise.
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