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8Multiscale and high.performance computing for multiphysical problems
Mini.symposiumMULTISCALEANDHIGH.PERFORMANCECOMPUTINGFORMULTIPHYSICALPROBLEMS
DG.GMsFEMforproblemsinperforateddomainswithnon.homogeneousboundaryconditiononperforations
V. N. Alekseev, M. V. Vasilyeva, U. S. Kalachikova, E. T. Chung
M. K. Ammosov North.Eastern FederalUniversity, Yakutsk Email: alekseev.valen@mail.ru
DOI 10.24412/cl.35065.2021.1.02.76
In this work, we present the Discontinuous Galerkin Generalized Multiscale Finite Element Method (DG.GMsFEM)for problems in perforated domains with non.homogeneous boundary conditions on perforations.
In this method, we divide the perforateddomain into local domains and construct local multiscale basis functions.
We present the construction of the two types of multiscale basis functions related to the outer and perfo�ration boundary of the local domain. Construction of the basis functions contains two steps: snapshot space construction and solution of the local spectral problem in order to reduce the size of the snapshot space. The snapshot space for outer boundary contains a local solution of the problem with various boundary conditions on the interfaces between local domains and homogeneous boundary conditions on perforations. For genera�tion of the snapshot space for perforation boundary, we set various boundary conditions on perforation boundary of the local domain and homogeneous boundary conditions for outer local domain boundary. We present construction of the method for different model problems: elastic and thermoelastic equations with non�.homogeneous boundary conditions on perforations. The different concepts for coarse grid construction and definition of the local domains are presented and investigated numerically.
Numericalinvestigation of the presented method is performed for two test cases with homogeneous and non.homogeneous boundary conditions. For the case with homogeneous boundary conditions on perfora�tions, we present results using only outer boundary basis functions. For non.homogeneous boundary condi�tions, we show that both outer and perforation boundary basis functions are needed in order to obtain good results with smallerrors.
V.A.'s, U.K.'s and V.M.'s works are supported by the mega.grant of the Russian Federation Government N14.Y26.31.0013. V.A.'s work is supported by the Ministry of Science and Higher Education of the Russian Federation, supplementary agreement No. 075.02.2020.1543/1, April 29, 2020.
Multiscalemodelreductionforapiezoelectricprobleminheterogeneousmediausinggeneralizedmultiscalefiniteelementmethod
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D. Ammosov1, M. Vasilyeva1,2, A. Nasedkin3, Ya. Efendiev
1M. K. Ammosov North.Eastern FederalUniversity, Yakutsk 2Institute for Scientific Computation, Texas A&M University 3Southern FederalUniversity, Rostov.on.Don 4Department of Mathematics, Texas A&M University Email: dmitryammosov@gmail.com
DOI 10.24412/cl.35065.2021.1.02.77
We consider a static piezoelectric problem in heterogeneous media. The mathematical modelconsists of a system of equations for the mechanical displacements and the electric potential. We use a finite element
