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ADI-based, conditionally stable schemes for seismic P-wave and elastic wave propagation problems
conditional stability
P-wave propagation problems
elastic wave propagation problems
linear computational cost
time-dependent simulations
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
cris.lastimport.wos | 2024-04-09T20:15:22Z | |
dc.abstract.en | 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 $\mathcal{O}$ (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{ h$_{x}$,h$_{y}$,h$_{z}$}, 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. | pl |
dc.affiliation | Szkoła Doktorska Nauk Ścisłych i Przyrodniczych | pl |
dc.affiliation | Wydział Fizyki, Astronomii i Informatyki Stosowanej | pl |
dc.contributor.author | Łoś, Marcin | pl |
dc.contributor.author | Behnoudfar, Pouria | pl |
dc.contributor.author | Dobija, Mateusz - 257263 | pl |
dc.contributor.author | Paszyński, Maciej | pl |
dc.date.accessioned | 2023-02-21T16:56:40Z | |
dc.date.available | 2023-02-21T16:56:40Z | |
dc.date.issued | 2022 | pl |
dc.date.openaccess | 0 | |
dc.description.accesstime | w momencie opublikowania | |
dc.description.number | 5 | pl |
dc.description.version | ostateczna wersja wydawcy | |
dc.description.volume | 70 | pl |
dc.identifier.articleid | e141985 | pl |
dc.identifier.doi | 10.24425/bpasts.2022.141985 | pl |
dc.identifier.eissn | 2300-1917 | pl |
dc.identifier.issn | 0239-7528 | pl |
dc.identifier.uri | https://ruj.uj.edu.pl/xmlui/handle/item/308106 | |
dc.language | eng | pl |
dc.language.container | eng | pl |
dc.rights | Udzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa | * |
dc.rights.licence | CC-BY | |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/legalcode.pl | * |
dc.share.type | otwarte czasopismo | |
dc.subject.en | conditional stability | pl |
dc.subject.en | P-wave propagation problems | pl |
dc.subject.en | elastic wave propagation problems | pl |
dc.subject.en | linear computational cost | pl |
dc.subject.en | time-dependent simulations | pl |
dc.subtype | Article | pl |
dc.title | ADI-based, conditionally stable schemes for seismic P-wave and elastic wave propagation problems | pl |
dc.title.journal | Bulletin of the Polish Academy of Sciences. Technical Sciences | pl |
dc.type | JournalArticle | pl |
dspace.entity.type | Publication |