Library Subscription: Guest
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

Indexed in

MULTISCALE SEAMLESS-DOMAIN METHOD FOR NONPERIODIC FIELDS: NONLINEAR HEAT CONDUCTION ANALYSIS

Volume 17, Issue 1, 2019, pp. 1-28
DOI: 10.1615/IntJMultCompEng.2019024643
Get accessGet access

ABSTRACT

A multiscale numerical solver called the seamless-domain method (SDM) consists of macroscopic global analysis and microscopic local analysis. Previous work presented a nonlinear solver using the SDM technique that does not couple these two analyses interactively. In addition, the practicality of this solver was verified only for use with periodic fields. In this work, we present another nonlinear SDM solver that couples the multiple scales completely interactively. We solve an example problem of a nonlinear heat conduction analysis of a nonperiodic field using the presented SDM, the standard finite difference method, and the conventional domain decomposition method (DDM). The target temperature field has thermal conductivity distribution that is nonuniform, nonperiodic, and has temperature dependency. This problem thus has material nonlinearity. The accuracy of the SDM solution is very high, and the root mean squared error in temperature is less than 0.044% of the maximum temperature in the field. In contrast, the error of the DDM is 0.10%–0.18%, which is larger than twice the error of the SDM. The finite difference method requires 7–36 times the computation time of the SDM to generate a solution as accurate as that of the SDM.

REFERENCES
  1. Balls, G.T. and Colella, P., A Finite Difference Domain Decomposition Method using Local Corrections for the Solution of Poisson's Equation, J. Comput. Phys., vol. 180, pp. 25-53, 2002.

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

  3. Chen, Y., Durlofsky, L.J., Gerritsen, M., and Wen, X.H., A Coupled Local-Global Upscaling Approach for Simulating Flow in Highly Heterogeneous Formations, Adv. Water Resources, vol. 26, no. 10, pp. 1041-1060, 2003.

  4. Chen, Y. and Durlofsky, L.J., Adaptive Local-Global Upscaling for General Flow Scenarios in Heterogeneous Formations, Trans. Porous Media, vol. 62, pp. 157-185, 2006.

  5. Dawson, C.N., Du, Q., and Dupont, T.F., A Finite Difference Domain Decomposition Algorithm for Numerical Solution of the Heat Equation, Math. Comp., vol. 57, pp. 63-71, 1991.

  6. Efendiev, Y., Galvis, J., Li, G., and Presho, M., Generalized Multiscale Finite Element Methods: Oversampling Strategies, Int. J. Multiscale Com., vol. 12, pp. 465-484, 2014.

  7. Fish, J. and Chen, W., Higher-Order Homogenization of Initial/Boundary-Value Problem, J. Eng. Mech., vol. 127, no. 12, pp. 1223-1230, 2001.

  8. Ilic, S. and Hackl, K., Application of the Multiscale FEM to the Modeling of Nonlinear Multiphase Materials, J. Theor. Appl. Mech, vol. 47, no. 3, pp. 537-551, 2009.

  9. Kaczmarczyk, L., Pearce, C.J., and Bicanic, N., Studies of Microstructural Size Effect and Higher-Order Deformation in Second-Order Computational Homogenization, Comput. Struct., vol. 88, nos. 23-24, pp. 1383-1390, 2010.

  10. Larsson, R. and Diebels, S., A Second-Order Homogenization Procedure for Multi-Scale Analysis based on Micropolar Kinematics, Int. J. Numer. Methods Eng., vol. 69, pp. 2485-2512, 2007.

  11. Nakashima, T. and Durlofsky, L.J., Accurate Representation of near-Well Effects in Coarse-Scale Models of Primary Oil Production, Transp. Porous Med., vol. 83, pp. 741-770, 2010.

  12. Suzuki, Y., Three-Scale Modeling of Laminated Structures Employing the Seamless-Domain Method, Compos. Struct., vol. 142, no. 10, pp. 167-186, 2016a.

  13. Suzuki, Y., Multiscale Seamless-Domain Method for Linear Elastic Analysis of Heterogeneous Materials, Int. J. Numer. Methods Eng., vol. 105, no. 8, pp. 563-598, 2016b.

  14. Suzuki, Y., Multiscale Seamless-Domain Method for Solving Nonlinear Problems using Statistical Estimation Methodology, Int. J. Numer. Methods Eng, vol. 113, no. 3, pp. 534-559, 2018.

  15. Suzuki, Y. and Soga, K., Seamless-Domain Method: A Meshfree Multiscale Numerical Analysis, Int. J. Numer. Methods Eng., vol. 106, no. 4, pp. 243-277, 2016.

  16. Suzuki, Y. and Takahashi, M., Multiscale Seamless-Domain Method based on Dependent Variable and Dependent-Variable Gradients, Int. J. Multiscale Comput. Eng., vol. 14, pp. 607-630, 2016.

  17. Suzuki, Y., Takahashi, M., Todoroki, A., and Mizutani, Y., Unsteady Analysis of a Heterogeneous Material using the Multiscale Seamless-Domain Method, Int. J. Multiscale Comput. Eng., vol. 16, no. 3, pp. 245-266, 2018.

  18. Suzuki, Y., Todoroki, A., and Mizutani, Y., Multiscale Seamless-Domain Method for Solving Nonlinear Heat Conduction Problems without Iterative Multiscale Calculations, JSMEMech. Eng. J., vol. 3, no. 4, p. 15-00491, 2016.

  19. Terada, K., Hori, M., Kyoya, T., and Kikuchi, N., Simulation of the Multi-Scale Convergence in Computational Homogenization Approaches, Int. J. Solids Struct., vol. 37, pp. 2285-2311, 2000.

  20. Zhang, Y.X. and Zhang, H.S., Multiscale Finite Element Modeling of Failure Process of Composite Laminates, Compos. Struct., vol. 92, pp. 2159-2165, 2010.

CITED BY
  1. Klimczak Marek, Cecot Witold, Higher Order Multiscale Finite Element Method for Heat Transfer Modeling, Materials, 14, 14, 2021. Crossref

  2. Lihua Lu, Simulation physics-informed deep neural network by adaptive Adam optimization method to perform a comparative study of the system, Engineering with Computers, 38, S2, 2022. Crossref

Begell Digital Portal Begell Digital Library eBooks Journals References & Proceedings Research Collections Prices and Subscription Policies Begell House Contact Us Language English 中文 Русский Português German French Spain