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International Journal for Multiscale Computational Engineering

Published 6 issues per year

ISSN Print: 1543-1649

ISSN Online: 1940-4352

The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.4 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.3 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 2.2 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.00034 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.46 SJR: 0.333 SNIP: 0.606 CiteScore™:: 3.1 H-Index: 31

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A COUPLING OF MULTISCALE FINITE ELEMENT METHOD AND ISOGEOMETRIC ANALYSIS

Volume 18, Issue 4, 2020, pp. 439-454
DOI: 10.1615/IntJMultCompEng.2020034287
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ABSTRACT

In this paper, we propose to use modified B-splines spanned on several macroelements as a basis for building the multiscale finite element method (MsFEM) trail functions. The main benefit of our approach is that the calculations of a multiscale function are done in one step on the whole support, in contrast to standard MsFEM shape functions that are evaluated coarse element by element and require a cumbersome gluing. Selected numerical experiments for flow in porous media with periodic and random material properties distributions were performed to test our modified MsFEM with the new basis functions. We found that the method indeed improves standard MsFEM for fast oscillating material properties. We observed that the resonance effect, when the ratio of inclusion size and coarse mesh size approaches 1 (ε/H → 1) can be reduced by increasing the order of B-splines.

REFERENCES
  1. Agrawal, V. and Gautam, S.S., IGA: A Simplified Introduction and Implementation Details for Finite Element Users, J. Inst. Eng. (India): Ser. C, vol. 100, no. 3, pp. 561-585,2019.

  2. Casadei, F., Rimoli, J., and Ruzzene, M., A Geometric Multiscale Finite Element Method for the Dynamic Analysis of Heterogeneous Solids, Comput. Methods Appl. Mechan. Eng., vol. 263, pp. 56-70,2013.

  3. Cecot, W. and Oleksy, M., High Order FEM for Multigrid Homogenization, Comput. Mathemat. Appl., vol. 70, no. 7, pp. 1391-1400,2015.

  4. Degond, P., Lozinski, A., Muljadi, B., and Narski, J., Crouzeix-Raviart MsFEM with Bubble Functions for Diffusion and Advection-Diffusion in Perforated Media, Commun. Comput. Phys, vol. 17, pp. 887-907,2015.

  5. E, W. and Engquist, B., The Heterogeneous Multiscale Methods, Comput. Mater. Sci., vol. 1, pp. 87-133,2003.

  6. Efendiev, Y., Ginting, V., Hou, T., and Ewing, R., Accurate Multiscale Finite Element Methods for Two-Phase Flow Simulations, J. Comput. Phys, vol. 220, no. 1,pp. 155-174,2006.

  7. Feyel, F. and Chaboche, J.L., FE2 Multiscale Approach for Modelling the Elastoviscoplastic Behaviour of Long Fiber SiC/Ti Composite Materials, Comput. Methods Appl. Mechan. Eng., vol. 183, pp. 309-330,2000.

  8. Fish, J., PracticalMultiscaling, New York: Wiley, 2013.

  9. Fish, J. and Yuan, Z., Multiscale Enrichment based on Partition of Unity, Int. J. Numer. Methods Eng., vol. 62, no. 10, pp. 1341-1359,2005.

  10. Fu, P., Liu, H., and Chu, X., An Efficient Multiscale Computational Formulation for Geometric Nonlinear Analysis of Heterogeneous Piezoelectric Composite, Compos. Struct., vol. 167, pp. 191-206,2017.

  11. Gao, K., Fu, S., and Chung, E.T., A High-Order Multiscale Finite-Element Method for Time-Domain Acoustic-Wave Modeling, J. Comput. Phys, vol. 360, pp. 120-136,2018.

  12. Geers, M.G.D., Kouznetsova, V.G., and Brekelmans, W.A.M., Multi-Scale Computational Homogenization, Int. J. Numer. Methods Eng., vol. 54, pp. 1235-1260,2002.

  13. Hollaus, K. and Schoberl, J., Multi-Scale FEM and Magnetic Vector Potential a for 3D Eddy Currents in Laminated Media, COMPEL: Int. J. Comput. Mathemat. Electr. Electron. Eng., vol. 34, no. 5, pp. 1598-1608,2015.

  14. Hou, T. and Wu, X., A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media, J. Comput. Phys, vol. 134, no. 1, pp. 169-189,1997.

  15. Hou, T.Y., Wu, X.H., and Cai, Z., Convergence of a Multiscale Finite Element Method for Elliptic Problems with Rapidly Oscillating Coefficients, Math. Comput, vol. 68, no. 227, pp. 913-943,1999.

  16. Hughes, T., Cottrell, J., and Bazilevs, Y., Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry and Mesh Refinement, Comput. Methods Appl. Mechan. Eng., vol. 194,no. 39, pp. 4135-4195,2005.

  17. Klimczak, M. and Cecot, W., An Adaptive MsFEM for Nonperiodic Viscoelastic Composites, Int. J. Numer. Methods Eng., vol. 114, no. 8, pp. 861-881,2018.

  18. Krowczynski, M. and Cecot, W., A Fast Three-Level Upscaling for Short Fiber Reinforced Composites, Int. J. Multiscale Comput. Eng., vol. 15, pp. 19-34,2017.

  19. Liu, H., Sun, X., Xu, Y., and Chu, X., A Hierarchical Multilevel Finite Element Method for Mechanical Analyses of Periodical Composite Structures, Compos. Struct., vol. 131, pp. 115-127,2015.

  20. Liu, H., Wang, Y., Zong, H., and Wang, M.Y., Efficient Structure Topology Optimization by Using the Multiscale Finite Element Method, Struct. Multidiscip. Optim., vol. 58, no. 4, pp. 1411-1430,2018.

  21. Liu, H. and Zhang, H., An Equivalent Multiscale Method for 2D Static and Dynamic Analyses of Lattice Truss Materials, Adv. Eng. Software, vol. 75, pp. 14-29,2014.

  22. Madej, L., Hodgson, P.D., and Pietrzyk, M., Multi-Scale Rheological Model for Discontinuous Phenomena in Materials under Deformation Conditions, Comput. Mater. Sci., vol. 38, pp. 685-691,2007a.

  23. Madej, L., Hodgson, P.D., and Pietrzyk, M., The Validation of a Multiscale Rheological Model of Discontinuous Phenomena during Metal Rolling, Comput. Mater. Sci., vol. 41, pp. 236-241,2007b.

  24. Nguyen, L.H. and Schillinger, D., A Residual-Driven Local Iterative Corrector Scheme for the Multiscale Finite Element Method, J. Comput. Phys, vol. 377, pp. 60-88,2019.

  25. Oleksy, M. and Cecot, W., Application of Hp-Adaptive Finite Element Method to Two-Scale Computation, Arch. Comput. Methods Eng., vol. 22, no. 1,pp. 105-134,2015.

  26. Papanicolau, G., Bensoussan, A., and Lions, J., Asymptotic Analysis for Periodic Structures, Studies in Mathematics and Its Applications, Amsterdam, the Netherlands: Elsevier Science, 1978.

  27. Perduta, A. and Putanowicz, R., Tools and Techniques for Building Models for Isogeometric Analysis, Adv. Eng. Software, vol. 127, pp. 70-81,2019.

  28. Piegl, L. and Tiller, W., The NURBS Book, 2nd Ed., New York: Springer-Verlag, 1996.

  29. Soghrati, S. and Stanciulescu, I., Systematic Construction of Higher Order Bases for the Finite Element Analysis of Multiscale Elliptic Problems, Mechan. Res. Commun., vol. 52, pp. 11-18,2013.

  30. Ye, S., Xue, Y., and Xie, C., Application of the Multiscale Finite Element Method to Flow in Heterogeneous Porous Media, Water Resour. Res., vol. 40, no. 9, 2004.

  31. Zhang, H., Wu, J.K., and Fu, Z., Extended Multiscale Finite Element Method for Mechanical Analysis of Periodic Lattice Truss Materials, Int. J. Multiscale Comput. Eng., vol. 8, no. 6, pp. 597-613,2010a.

  32. Zhang, H.W., Wu, J.K., Lu, J., and Fu, Z.D., Extended Multiscale Finite Element Method for Mechanical Analysis of Heterogeneous Materials, Acta Mechan. Sin., vol. 26, no. 6, pp. 899-920,2010b.

  33. Zohdi, T. and Wriggers, P., An Introduction to Computational Micromechanics, Lecture Notes in Applied and Computational Mechanics, Berlin Heidelberg: Springer, 2004.

CITED BY
  1. Dryzek Mateusz, Cecot Witold, The iterative multiscale finite element method for sandwich beams and plates, International Journal for Numerical Methods in Engineering, 122, 22, 2021. Crossref

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