Comparison of two methods for numerical upscaling

• Autorzy: Klimczak M. , Cecot W.
• Języki publikacji: EN

Abstrakty

EN

The main objective of this paper is to compare two discretization-based homogenization methods. A local numerical homogenization and a multiscale finite element method (MsFEM) are first briefly presented and next numerically tested. In the case of MsFEM, a new shape function construction is also presented. Extensive comparison of both techniques constitutes the main part of this study. Novelty of this research is to combine aforementioned methods with mesh adaptivity at the coarse mesh level and the application of the higher-order approximation.

Słowa kluczowe

EN

local numerical homogenization; multiscale FEM; multigrid homogenization

PL

lokalna homogenizacja numeryczna; homogenizacja numeryczna; metoda elementów skończonych; MES

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Engineering Transactions
• Rocznik: 2016
• Tom: Vol. 64, iss. 4
• Strony: 385--392
• Opis fizyczny: Bibliogr. 7 poz., rys., wykr.

Twórcy

autor

Klimczak M.

• Cracow University of Technology Warszawska 24, 31-155 Kraków, Poland

autor

Cecot W.

• Cracow University of Technology Warszawska 24, 31-155 Kraków, Poland

Bibliografia

• 1. Jhurani C., Demkowicz L., Multiscale modeling using goal-oriented adaptivity and numerical homogenization. Part I: Mathematical formulation and numerical results, Computer Methods in Applied Mechanics and Engineering, 213–21: 399–417, 2012.
• 2. Klimczak M., Cecot W., Application of local numerical homogenization and hp-adaptive FEM for modeling of heterogeneous viscoelastic materials, Engineering Transactions, 63(3): 317–327, 2015.
• 3. Ben-Israel A., Greville T.N.E., Generalized Inverses, Springer-Verlag, 2003.
• 4. Neuss N., Jaeger W., Wittum G., Homogenization and multigrid, Computing, 66(1): 1–26, 2001.
• 5. Efendiev Y., Hou T., Multiscale finite element methods for porous media flows and their applications, Applied Numerical Mathematics, 57: 577–596, 2007.
• 6. Cecot W., Oleksy M., High order FEM for multigrid homogenization, Computers and Mathematics with Applications, 70(7): 1391–1400, 2015.
• 7. Demkowicz L., Kurtz J., Pardo D., Paszynski M., Rachowicz W., Zdunek A., Computing with hp-adaptive finite elements. Vol 2. Frontiers: Three-dimensional elliptic and Maxwell problems with applications, Chapman & Hall/CRC, 2008.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).