Using the Hypergraph Grammar for generation of quasi optimal element partition trees in two dimensions

• Autorzy: Ryzner Jakub , Paszyński Maciej , Paszyńska Anna
• Języki publikacji: EN

Abstrakty

EN

The paper presents the graph grammar model of Finite Element Method allowing for speeding up performed numerical simulations. In the presented approach, the finite element mesh operations are performed together with operations generating so-called element partition tree. The element partition tree sets the ordering of matrix operations performed by solver in order to solve the computational problem. The quality of element partition tree influences the computational time of the solver. Our method allows for generation good quality element partition trees for h-adaptive Finite Element Method. The paper is concluded with numerical results confirming the quality of generated element partition trees.

Słowa kluczowe

EN

finite element method; multi-frontal solver; hypergraph grammar

• Wydawca: Wydawnictwa AGH
• Czasopismo: Computer Methods in Materials Science
• Rocznik: 2018
• Tom: Vol. 18, No. 1
• Strony: 29--40
• Opis fizyczny: Bibliogr. 21 poz., rys.

Twórcy

autor

Ryzner Jakub

• Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Krakow, Poland

autor

Paszyński Maciej

• Department of Computer Science, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Krakow, Poland

autor

Paszyńska Anna

• Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. St. Łojasiewicza 11, 30-348 Krakow, Poland

Bibliografia

• Babuška, I., Rheinboldt, W., 1978, Error Estimates for Adaptive Finite Element Computations, SIAM Journal of Numerical Analysis, 15(4), 736-754.
• Babuška, I., Szabo, B. A., Katz, I. N., 1981, The p-Version of the Finite Element Method, SIAM Journal on Numerical Analysis, 18, 515-545.
• Babuška, I., 1986, Accuracy estimates and adaptive refinements in finite element computations, John Wiley and Sons.
• Banaś, K., Chłoń, K., Cybułka, P., Michalik, K., Płaszewski, P., Siwek, A, 2014, Adaptive finite element model ling of welding processes, Lecture Notes in Computer Science, 8500, 391-406.
• Demkowicz, L., Pardo, D. , Rachowicz, W., 2002, 3D hpAdaptive Finite Element Package (3Dhp90) Version 2.0. The Ultimate (?) Data Structure for Three-Dimensional Anisotropic hp-Renements, TICAM Report, 2-4.
• Demkowicz, L., 2006, Computing with hp-Adaptive Finite Elements, Vol. I. One and Two Dimensional Elliptic and Maxwell Problems, Chapman and Hall/Crc Applied Mathematics and Nonlinear Science.
• Demkowicz, L., Kurtz, J., Paszyński, M, Rachowicz, W.,Zdunek, A., 2006, Computing with hp-Adaptive FiniteElements, Vol. II. Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications, Chapman and Hall/Crc Applied Mathematics and NonlinearScience.
• Duff, I. S., Reid, J. K., 1983, The multifrontal solution of indefinite sparse symmetric linear, ACM Trans. Math. Softw, 9(3), 302-325.
• Duff, I. S., Reid, J. K., 1984, The multifrontal solution ofunsymmetric sets of linear equations, Journal on Scientific and Statistical Computing, 5, 633-641.
• Hughues, T., 2000, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Dover Civil and Mechanical Engineering.
• Liu, J., 1990, The role of element partition trees in sparse factorization, SIAM Journal of Matrix Analysis Applications, 11(1), 134-172.
• METIS (n.d.). Metis - graph partitioning and fill-reducing matrix ordering, available online at:http://gl ros.dtc.umn.edu/gkhome/views/metis, accessed: 1.02.2018
• MUMPS (n.d.). Multi-frontal massively parallel sparse direct solver, available online at: http://mumps.enseeiht.fr/, accessed: 1.02.2018
• Niemi, A., Babuška, I. , Pitkaranta, J., Demkowicz, L/, 2012,Finite element analysis of Girkmann problem using the modern hp-version and the classical h-version, Engineering with computers, 28(2), 123-134.
• Pardo, D., Demkowicz, L., Torres-Verdin, C., Paszyński,M., 2006, Simulation of Resistivity Logging-WhileDrilling (LWD) Measurements Using a Self-Adaptive Goal-Oriented hp-Finite Element Method, SIAM Journal on Applied Mathematics, 66, 2085-2106.
• Pardo, D., Calo, V. M., Torres-Verdin, C., Nam, M. J.,2008a, Fourier Series Expansion in a Non-Orthogonal System of Coordinates for Simulation of 3D DC Borehole Resistivity Measurements, Computer Methods in Applied Mechanics and Engineering, 197(1-3), 1906-1925.
• Pardo, D., Torres-Verdin, C., Nam, M. J., Paszyński, M.,Calo, V., 2008b, Fourier Series Expansion in a NonOrthogonal System of Coordinates for the Simulation of 3D Alternating Current Borehole Resistivity Measurements, Computer Methods in Applied Mechanics and Engineering, 197(45-48), 3836-3849.
• Paszyńska, A., Paszyński, M., Jopek, K., Woźniak, M., Goik, D., Gurgul, P., AbouEisha, P., Moshkov, M.,Calo, V. M., Lenharth, A., Nguyen, D., Pingali, K., 2015, Quasi-optimal elemination trees for 2d grids with singularities, Scientific Programming, 1-18.
• Paszyński, M., 2016, Fast Solvers for Mesh Based Computations, Taylor & Francis, CRC Press.
• Pingali, K., Nguyen, D., Kulkarni, K., Burtscher, M., Hassaan, M., Kaleem, R., Lee, T.-H., Lenharth, A., Manevich, R., Mendez-Lojo, M., Prountzos, D., Sui, X.,2011, The tao of parallelism in algorithms, Proceedings of the 32nd ACM SIGPLAN conference on Programming language design and implementation, 12-25.
• Ślusarczyk, G., Paszyńska, A., 2012, Hypergraph gram mars in hp-adaptive finite element method, Procedia Computer Science, 18, 1545-1554.
• Yannakakis, M., 1981, Computing the minimum fill-in is np-complete, SIAM Journal on Algebraic Discrete Methods, 2, 77-79.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019)