- Tytuł:
- Linear computational cost implicit solver for parabolic problems
- Autorzy:
-
Gurgul, Grzegorz
Łoś, Marcin
Paszynski, Maciej
Calo, Victor - Powiązania:
- https://bibliotekanauki.pl/articles/1839258.pdf
- Data publikacji:
- 2020
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
isogeometric analysis
implicit dynamics
linear computational cost
direct solvers - Opis:
- 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.
- Źródło:
-
Computer Science; 2020, 21 (3); 335-352
1508-2806
2300-7036 - Pojawia się w:
- Computer Science
- Dostawca treści:
- Biblioteka Nauki
Artykuł