Two-dimensional HP-adaptive Algorithm for Continuous Approximations of Material Data Using Space Projection

Piotr Gurgul, Marcin Sieniek, Maciej Paszynski, Lukasz Madej, Nathan Collier


In this paper we utilize the concept of the L2 and H1 projections used toadaptively generate a continuous approximation of an input material data inthe finite element (FE) base. This approximation, along with a correspondingFE mesh, can be used as material data for FE solvers. We begin with a brieftheoretical background, followed by description of the hp-adaptive algorithmadopted here to improve gradually quality of the projections. We investigatealso a few distinct sample problems, apply the aforementioned algorithms andconclude with numerical results evaluation.


adaptive finite element method, projection operator, digital material representation

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Demkowicz L.: Computing With Hp-adaptive Finite Elements. Vol. 1: One and Two Dimensional Elliptic and Maxwell Problems. Chapman & Hall CRC, Texas, 2006.

Demkowicz L. F.: Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume 1 One and Two Dimensional Elliptic and Maxwell problems. CRC Press, United States of America, 2007.

Gurgul P., Sieniek M., Magiera K., Skotniczny M.: Application of multi-agent paradigm to hp-adaptive projection-based interpolation operator. Journal of Computational Science, 2011.

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.

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.

Paszyński M.: Graph Grammar-Driven Parallel Adaptive PDE Solvers. Uczelniane Wydawnictwa Naukowo-Dydaktyczne AGH, Krakow, 2009.

Paszyński M., Pardo D., Torres-Verdin C., Demkowicz L., Calo V.: A parallel direct solver for self-adaptive hp finite element method. Journal of Parallel and Distributed Computing, 70(3):270–281, 2010.

Paszyński M., Romkes A., Collister E., Meiring J., Demkowicz L.: On the modeling of step-and-flash imprint lithography using molecular statics models. CG Willson ICES Report, pp. 05–38, 2005.

Sieniek M., Gurgul P., Skotniczny M., Magiera K., Paszyński M.: Agent-oriented image processing with the hp-adaptive projection-based interpolation method. Procedia Computer Science, 4(1):1844–1853, 2011.



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