- 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