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Alternating direction implicit time integrations for finite difference acoustic wave propagation: parallelization and convergence
dc.contributor.author | Otero Calviño, Beatriz |
dc.contributor.author | Rojas, Otilio |
dc.contributor.author | Moya, Ferrán |
dc.contributor.author | Castillo, José |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament d'Arquitectura de Computadors |
dc.contributor.other | Barcelona Supercomputing Center |
dc.date.accessioned | 2020-06-11T09:12:56Z |
dc.date.available | 2022-05-15T00:28:15Z |
dc.date.issued | 2020-06-15 |
dc.identifier.citation | Otero, B. [et al.]. Alternating direction implicit time integrations for finite difference acoustic wave propagation: parallelization and convergence. "Computers and fluids", 15 Juny 2020, vol. 205, article 104584, p. 1-12. |
dc.identifier.issn | 0045-7930 |
dc.identifier.other | http://arxiv.org/abs/2006.07583 |
dc.identifier.uri | http://hdl.handle.net/2117/190495 |
dc.description.abstract | This work studies the parallelization and empirical convergence of two finite difference acoustic wave propagation methods on 2-D rectangular grids, that use the same alternating direction implicit (ADI) time integration. This ADI integration is based on a second-order implicit Crank-Nicolson temporal discretization that is factored out by a Peaceman-Rachford decomposition of the time and space equation terms. In space, these methods highly diverge and apply different fourth-order accurate differentiation techniques. The first method uses compact finite differences (CFD) on nodal meshes that requires solving tridiagonal linear systems along each grid line, while the second one employs staggered-grid mimetic finite differences (MFD). For each method, we implement three parallel versions: (i) a multithreaded code in Octave, (ii) a C++ code that exploits OpenMP loop parallelization, and (iii) a CUDA kernel for a NVIDIA GTX 960 Maxwell card. In these implementations, the main source of parallelism is the simultaneous ADI updating of each wave field matrix, either column-wise or row-wise, according to the differentiation direction. In our numerical applications, the highest performances are displayed by the CFD and MFD CUDA codes that achieve speedups of 7.21x and 15.81x, respectively, relative to their C++ sequential counterparts with optimal compilation flags. Our test cases also allow to assess the numerical convergence and accuracy of both methods. In a problem with exact harmonic solution, both methods exhibit convergence rates close to 4 and the MDF accuracy is practically higher. Alternatively, both convergences decay to second order on smooth problems with severe gradients at boundaries, and the MDF rates degrade in highly-resolved grids leading to larger inaccuracies. This transition of empirical convergences agrees with the nominal truncation errors in space and time. |
dc.description.sponsorship | First author was partially supported by the Generalitat de Catalunya under agreement 2017-SGR-962 and the RIS3CAT DRAC project (001-P-001723). The research leading to these results has received funding from the European Union’s Horizon 2020 Programme, grant agreement No. 828947, and from the Mexican Department of Energy, CONACYT-SENER Hidrocarburos grant agreement No. B-S-69926. This project has also received funding from the European Union’s Horizon 2020research and innovation programme under the Marie Sklodowska-Curie grant agreement No 777778 (MATHROCKS). O. Rojas also thank the European Union’s Horizon 2020 Programme under the ChEESE Project, grant agreement no. 823844. |
dc.format.extent | 12 p. |
dc.language.iso | eng |
dc.publisher | Elsevier |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International |
dc.rights | ©2020 Elsevier |
dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ |
dc.subject | Àrees temàtiques de la UPC::Enginyeria de la telecomunicació::Processament del senyal::Processament de la parla i del senyal acústic |
dc.subject.lcsh | Finite differences |
dc.subject.lcsh | Application program interfaces (Computer software) |
dc.subject.lcsh | Sound-waves |
dc.subject.other | CUDA and OpenMP programming |
dc.subject.other | ADI |
dc.subject.other | Compact finite differences |
dc.subject.other | Mimetic operators |
dc.title | Alternating direction implicit time integrations for finite difference acoustic wave propagation: parallelization and convergence |
dc.type | Article |
dc.subject.lemac | Diferències finites |
dc.subject.lemac | Interfícies de programació d'aplicacions (Programari) |
dc.subject.lemac | Ones sonores |
dc.contributor.group | Universitat Politècnica de Catalunya. VIRTUOS - Virtualisation and Operating Systems |
dc.identifier.doi | 10.1016/j.compfluid.2020.104584 |
dc.description.peerreviewed | Peer Reviewed |
dc.relation.publisherversion | https://www.sciencedirect.com/science/article/pii/S0045793020301560 |
dc.rights.access | Open Access |
local.identifier.drac | 28486179 |
dc.description.version | Postprint (author's final draft) |
dc.relation.projectid | info:eu-repo/grantAgreement/EC/H2020/777778/EU/Multiscale Inversion of Porous Rock Physics using High-Performance Simulators: Bridging the Gap between Mathematics and Geophysics/MATHROCKS |
dc.relation.projectid | info:eu-repo/grantAgreement/EC/H2020/823844/EU/Centre of Excellence for Exascale in Solid Earth/ChEESE |
dc.relation.projectid | info:eu-repo/grantAgreement/EC/H2020/828947/EU/Supercomputing and Energy for Mexico/ENERXICO |
local.citation.author | Otero, B.; Rojas, O.; Moya, F.; Castillo, J. |
local.citation.publicationName | Computers and fluids |
local.citation.volume | 205 |
local.citation.number | article 104584 |
local.citation.startingPage | 1 |
local.citation.endingPage | 12 |
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