Linear computational cost implicit solver for parabolic problems

• Autorzy: Gurgul Grzegorz , Łoś Marcin , Paszynski Maciej , Calo Victor

Identyfikatory

DOI

10.7494/csci.2020.21.3.3824

• Języki publikacji: EN

Abstrakty

EN

In this paper, we use the alternating direction method for isogeometric finite elements to simulate transient problems. Namely, we focus on a parabolic problem and use B-spline basis functions in space and an implicit time-marching method to fully discretize the problem. We introduce intermediate time-steps and separate our differential operator into a summation of the blocks that act along a particular coordinate axis in the intermediate time-steps. We show that the resulting stiffness matrix can be represented as a multiplication of two (in 2D) or three (in 3D) multi-diagonal matrices, each one with B-spline basis functions along the particular axis of the spatial system of coordinates. As a result of these algebraic transformations, we get a system of linear equations that can be factorized in a linear O(N) computational cost at every time-step of the implicit method. We use our method to simulate the heat transfer problem. We demonstrate theoretically and verify numerically that our implicit method is unconditionally stable for heat transfer problems (i.e., parabolic). We conclude our presentation with a discussion on the limitations of the method.

Słowa kluczowe

EN

isogeometric analysis; implicit dynamics; linear computational cost; direct solvers

• Wydawca: Wydawnictwa AGH
• Czasopismo: Computer Science
• Rocznik: 2020
• Tom: T. 21 (3)
• Strony: 335–352
• Opis fizyczny: Bibliogr. 34 poz., rys., tab.

Twórcy

autor

Gurgul Grzegorz

• AGH University of Science and Technology, Department of Computer Sciences, Krakow, Poland

autor

Łoś Marcin

• AGH University of Science and Technology, Department of Computer Sciences, Krakow, Poland

autor

Paszynski Maciej

• AGH University of Science and Technology, Department of Computer Sciences, Krakow, Poland

autor

Calo Victor

• Curtin University, Perth, Western Australia

Bibliografia

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