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Wyszukujesz frazę "linear computational cost" wg kryterium: Temat


Wyświetlanie 1-2 z 2
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
Tytuł:
ADI-based, conditionally stable schemes for seismic P-wave and elastic wave propagation problems
Autorzy:
Łoś, Marcin
Behnoudfar, Pouria
Dobija, Mateusz
Paszyński, Maciej
Powiązania:
https://bibliotekanauki.pl/articles/2173701.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
conditional stability
P-wave propagation problems
elastic wave propagation problems
linear computational cost
time-dependent simulations
stabilność warunkowa
problemy z propagacją fali P
problemy z propagacją fali sprężystej
koszt obliczeniowy liniowy
symulacje zależne od czasu
Opis:
The modeling of P-waves has essential applications in seismology. This is because the detection of the P-waves is the first warning sign of the incoming earthquake. Thus, P-wave detection is an important part of an earthquake monitoring system. In this paper, we introduce a linear computational cost simulator for three-dimensional simulations of P-waves. We also generalize our formulations and derivation for elastic wave propagation problems. We use the alternating direction method with isogeometric finite elements to simulate seismic P-wave and elastic propagation problems. We introduce intermediate time steps and separate our differential operator into a summation of the blocks, acting along the particular coordinate axis in the sub-steps. We show that the resulting problem matrix can be represented as a multiplication of three multi-diagonal matrices, each one with B-spline basis functions along the particular axis of the spatial system of coordinates. The resulting system of linear equations can be factorized in linear O (N) computational cost in every time step of the semi-implicit method. We use our method to simulate P-wave and elastic wave propagation problems. We derive the condition for the stability for seismic waves; namely, we show that the method is stable when τ < C min{ hx,hy,hz}, where C is a constant that depends on the PDE problem and also on the degree of splines used for the spatial approximation. We conclude our presentation with numerical results for seismic P-wave and elastic wave propagation problems.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2022, 70, 5; art. no. e141985
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
    Wyświetlanie 1-2 z 2

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