Two-dimensional hp-adaptive algorithm for continuous approximations of material data using space projection

• Autorzy: Gurgul P. , Sieniek M. , Paszyński M. , Madej Ł. , Collier N.
• Języki publikacji: EN

Abstrakty

EN

In this paper we utilize the concept of the L 2 and H 1 projections used to adaptively generate a continuous approximation of an input material data in the finie element (FE) base.This approximation, along with a corresponding FE mesh, can be used as material data for FE solvers. We begin with abrief theoretical background, followed by description of the hp -adaptive algorithm adopted here to improve gradually quality of the projections. We investigate also a few distinct sample problems, apply the aforementioned algorithms and conclude with numerical results evaluation.

Słowa kluczowe

EN

adaptive finite element method; projection operator; digital material representation

• Wydawca: Wydawnictwa AGH
• Czasopismo: Computer Science
• Rocznik: 2013
• Tom: Vol. 14 (1)
• Strony: 97--112
• Opis fizyczny: Bibliogr. 9 poz., rys.

Twórcy

autor

Gurgul P.

• AGH University of Science and Technology, Krakow, Poland

autor

Sieniek M.

• AGH University of Science and Technology, Krakow, Poland

autor

Paszyński M.

• AGH University of Science and Technology, Krakow, Poland

autor

Madej Ł.

• AGH University of Science and Technology, Krakow, Poland

autor

Collier N.

• King Abdullah University of Science and Technology, Thuwal, Saudi Arabia

Bibliografia

• [1] Demkowicz L.: Computing with Hp-adaptive Finite Elements. Vol. 1: One and Two Dimensional Elliptic and Maxwell Problems. Chapman&HallCRC,Texas, 2006.
• [2] DemkowiczL. F.: Computing with hp -ADAPTIVE FINITE ELEMENTS: Volume 1 One and Two Dimensional Elliptic and Maxwell problems. CRC Press, United States of America, 2007.
• [3] Gurgul P., Sieniek M., Magiera K., Skotniczny M.: Application of multi-agent paradig to hp-adaptiveprojection-based interpolation operator. Journal of Computational Science, 2011.
• [4] Madej L., Cybulka P., Perzyński K., Rauch L.: Numerical analysis of strain inhomogeneities during deformation on the basis of the three dimensional digital material representation. Computer Methods in Materials Science, 10:375–380, 2011.
• [5] Madej L., Rauch L., Perzyński K., Cybulka P.: Digital material representation as an efficient tool for strain inhomogeneities analysis at the micro-scale level. Archives of Civil and Mechanical Engineering,11:661–679, 2011.
• [6] Paszyński M.: Graph Grammar-Driven Parallel Adaptive PDE Solvers. Uczelniane Wydawnictwa Naukowo-Dydaktyczne AGH, Krakow, 2009.
• [7] Paszyński M., Pardo D., Torres-Verdin C., Demkowicz L., Calo V.: A parallel direct solver for self-adaptive hp finie element method. Journal of Parallel and Distributed Computing, 70(3) : 270–281, 2010.
• [8] Paszyński M., Romkes A., Collister E., Mering J., Semkowicz L.: On the modeling of step-and-flash imprint lithography Rusing molecular statics models. CG Willson ICES Report, pp.05–38,2005.
• [9] Sieniek M., Gurgul P., Skotniczny M., Magiera K., Paszyński M.: Agent-oriented mage processing with the hp-adaptive projection-based interpolation method. Procedia Computer Science, 4(1):1844–1853, 2011.