Application of projection-based interpolation algorithm for non-stationary problem

• Autorzy: Woźniak M. , Paszyński M.

Identyfikatory

DOI

10.7494/csci.2016.17.3.297

• Języki publikacji: EN

Abstrakty

EN

In this paper, we present a solver for non-stationary problems using L 2 projec- tion and h -adaptations. The solver utilizes the Euler time integration scheme for time evolution mixed with projection-based interpolation techniques for solving the L 2 projection problem at every time step. The solver is tested on the model problem of a heat transfer in an L-shape domain. We show that our solver delivers linear computational cost at every time step.

Słowa kluczowe

EN

L-shape; h-adaptivity; parallel; L2 projection; non-stationary

• Wydawca: Wydawnictwa AGH
• Czasopismo: Computer Science
• Rocznik: 2016
• Tom: Vol. 17 (3)
• Strony: 297--319
• Opis fizyczny: Bibliogr. 15 poz., rys., wykr., tab.

Twórcy

autor

Woźniak M.

• AGH University of Science and Technology, Krakow, Poland

autor

Paszyński M.

• AGH University of Science and Technology, Krakow, Poland

Bibliografia

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• [3] Demkowicz L.: Polynomial Exact Sequences and Projection-Based Interpolation with Application to Maxwell Equations. Lecture Notes in Mathematics , vol. 1939, pp. 101–158, 2008.
• [4] Duff I.S., Reid J.K.: The multifrontal solution of indefinite sparse symmetric linear systems. ACM Transactions on Mathematical Software , vol. 9, pp. 302– 325, 1983.
• [5] Duff I.S., Reid J.K.: The multifrontal solution of unsymmetric sets of linear systems. SIAM Journal on Scientific and Statistical Computing , vol. 5, pp. 633– 641, 1984.
• [6] Goik D., Jopek K., Paszyński M., Lenharth A., Nguyen D., Pingali K.: Graph Grammar based Multi-thread Multi-frontal Direct Solver with Galois Scheduler. Procedia Computer Science , vol. 29, pp. 960–969, 2014.
• [7] Goik D., Sieniek M., Paszyński M., Madej L.: Employing an Adaptive Projection- based Interpolation to Prepare Discontinuous 3D Material Data for Finite Ele- ment Analysis. Procedia Computer Science , vol. 18, pp. 1535–1544, 2013.
• [8] Goik D., Sieniek M., Woźniak M., Paszyńska A., Paszyński M.: Hypergraph Grammar based Adaptive Linear Computational Cost Projection Solvers for Two and Three Dimensional Modeling of Brain. Procedia Computer Science , International Conference on Computational Science, Cairns, Australia, 10–12.06.2014 , vol. 29, pp. 1002–1013, Elsevier, 2014
• [9] Gurgul P.: A linear complexity direct solver for h-adaptive grids with point singularities. Procedia Computer Science , vol. 29, pp. 1090–1099, 2014.
• [10] Gurgul P., Sieniek M., Magiera K., Skotniczny M.: Application of multi-agent paradigm to hp-adaptive projection-based interpolation operator. Journal of Computational Science , vol. 4(3), pp. 164–169, 2011.
• [11] Gurgul P., Sieniek M., Paszyński M., Madej L.: Three-dimensional adaptive algorithm for continuous approximations of material data using space projection. Computer Methods in Materials Science , vol. 13(2), pp. 245–250, 2013.
• [12] Gurgul P., Sieniek M., Paszyński M., Madej L., Collier N.: Two dimensional hp- adaptive algorithm for continuous approximations of material data using space projections. Computer Science, AGH University of Science and Technology Press , vol. 14(1), pp. 97–112, 2013.
• [13] Larson M.G., Bengzon F.: The Finite Element Method: Theory, Implementation, and Practice. Springer, 2010.
• [14] Paszyńska A., Paszyński M., Jopek K., Woźniak M., Goik D., Gurgul P., AbouEisha H., Moshkov M., Calo V.M., Lenerth A., Nguyen D., Pingali K.: Quasi-Optimal Elimination Trees for 2D Grids with singularities. Scientiffic Pro- gramming , vol. 2015(Article ID 303024), 2015.
• [15] Sieniek M., Paszyński M., Madej L., Goik D.: Adaptive Projection-Based Interpolation as a pre-processing tool in the Finite Element workflow for elasticity simulations of the dual phase microstructures. Steel Research International , vol. 85, pp. 1109–1119, 2014

Uwagi

PL

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