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On speeding up nano- and micromechanical calculations for irregular systems with long-range potentials

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
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.
Rocznik
Strony
337--344
Opis fizyczny
Bibliogr. 26 poz., rys.
Twórcy
  • Rzeszów University of Technology, ul. Powstańców Warszawy 12, 35-959 Rzeszów, Poland
autor
  • Rzeszów University of Technology, ul. Powstańców Warszawy 12, 35-959 Rzeszów, Poland
autor
  • Rzeszów University of Technology, ul. Powstańców Warszawy 12, 35-959 Rzeszów, Poland
Bibliografia
  • [1] M.S. Bapat and Y.J. Liu, “A new adaptive algorithm for the fast multipole boundary element method”, CMES: Comput. Model. Eng. Sci. 58, 161‒184 (2010).
  • [2] Y. Cao, L. Wen, and J. Rong, “A SVD accelerated kernelinde-pendent fast multipole method and its application to BEM”, WIT Transactions on Modelling and Simulation 56, 431‒443 (2013).
  • [3] A. Dobroskok and A. Linkov, “CV BEM for 2D transient thermo-(poro-)elastic problems concerning with blocky systems with singular points and lines of discontinuities”, Int. J. Eng. Sci. 48, 658‒669 (2010).
  • [4] S. Engblom, “On well-separated sets and fast multipole methods”, Appl. Num. Math. 61, 1096‒1102 (2011).
  • [5] L. Greengard and V.J. Rokhlin, “A fast algorithm for particle simulations”, J. Comput. Phys. 73, 325‒348 (1987).
  • [6] L. Greengard and V.J. Rokhlin, “A new version of Fast Multipole Method for the Laplace equation in three dimensions”, Acta Numer. 6, 229‒269 (1997).
  • [7] N.A. Gumerov and R. Duraiswami, “Fast multipole methods on graphics processors”, J. Comput. Phys. 227, 8290‒8313 (2008).
  • [8] D. Jaworski, A.M. Linkov, and L. Rybarska-Rusinek, “On solving 3D elasticity problems for inhomogeneous region with cracks, pores and inclusions”, Comput. Geotech. 71, 295‒309 (2016).
  • [9] M. Kmiotek and A. Kucaba-Piętal, “Influence of slim obstacle geometry on the flow and heat transfer in microchannels”, Bull. Pol. Ac.: Tech. 66(2), 111‒118 (2018).
  • [10] A. Kordos, and A. Kucaba-Piętal, “Nanovortex evolution in entrance part of the 2D open type long nanocavity”, Bull. Pol. Ac.: Tech. 66(2), 119‒125 (2018).
  • [11] A.M. Linkov, “Real and complex hypersingular integrals and integral equations in computational mechanics”, Demonstr. Math. XXVIII (4), 759‒769 (1995).
  • [12] A.M. Linkov, E. Rejwer, and L. Rybarska-Rusinek, “On solving continuum-mechanics problems by fast multipole methods”, Dokl. Phys. 62(8), 400‒402 (2017).
  • [13] A.M. Linkov, E. Rejwer, and L. Rybarska-Rusinek, “Torsional rigidity of a bar with multiple fibers”, Mech. Solids 52(4), 452‒456 (2017).
  • [14] Y. Liu, Fast Multipole Boundary Method. Theory and Applications in Engineering, Cambridge University Press, Cambridge, 2009.
  • [15] H. Margenau and N.R. Kestner, Theory of Intermolecular Forces. (ed. D. Ter Haar). Pergamon, 1969.
  • [16] A.P. Peirce and E. Siebrits, “A dual mesh multigrid preconditioner for the efficient solution of hydraulically driven fracture problems”, Int. J. Numer. Methods Eng. 63, 1797–1823 (2005).
  • [17] J. Ptaszny, “Parallel fast multipole boundary element method applied to computational homogenization”, AIP Conference Proceedings 1922, 140003 (2018).
  • [18] J. Ptaszny and M. Hatłas, “Evaluation of the FMBEM efficiency in the analysis of porous structures”, Eng. Comput. 35(2), 843‒866 (2018).
  • [19] E. Rejwer, L. Rybarska-Rusinek, and A. Linkov, “The complex variable fast multipole boundary element method for the analysis of strongly inhomogeneous media”, Eng. Anal. Boundary Elem. 43, 105‒116 (2014).
  • [20] L. Rybarska-Rusinek, E. Rejwer, and A. Linkov, “Speeded simulation of seismicity accompanying mining and hydrofracture”, Eng. Comput. 35(5), 1932‒1949 (2018).
  • [21] E.B. Tadmor and R.E. Miller, Modeling Materials: Continuum, Atomistic and Multiscale Techniques, Cambridge University Press, Cambridge, 2011.
  • [22] Y. Wang, Q. Wang, et al. “Graphics processing unit (GPU) accelerated fast multipole BEM with level-skip M2L for 3D elasticity problems”, Adv. Eng. Software 82, 105‒118 (2015).
  • [23] W.K. Winnett and C.P. Nash, “Ewald’s method for calculating lattice sums in ionic crystals”, Comput. Chem. 10(3), 229‒237 (1986).
  • [24] L. Ying, G. Biros, and D. Zorin, “A kernel-independent adaptive fast multipole method in two and three dimensions”, J. Comput. Phys. 196(2), 591‒626 (2004).
  • [25] L. Ying, “Fast algorithms for boundary integral equations”, Multiscale Modeling and Simulation in Science (eds. B. Engquist, P. Lötstedt, O. Runborg), Springer-Verlag Berlin Heidelberg, 139‒193, 2009.
  • [26] O.C. Zienkiewicz, R.L. Taylor, and J.Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, 6-th ed. Elsevier Butterworth – Heinemann, 2005.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-8f50e892-b02f-4252-9501-d2c447fb812a
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