Alternating direction implicit time integrations for finite difference acoustic wave propagation: parallelization and convergence

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 tempor...

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Detalhes bibliográficos
Autores: Otero Calviño, Beatriz|||0000-0002-9194-559X, Rojas, Otilio, Moya, Ferrán, Castillo, José
Formato: artículo
Fecha de publicación:2020
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/190495
Acesso em linha:https://hdl.handle.net/2117/190495
https://dx.doi.org/10.1016/j.compfluid.2020.104584
Access Level:acceso abierto
Palavra-chave:Finite differences
Application program interfaces (Computer software)
Sound-waves
CUDA and OpenMP programming
ADI
Compact finite differences
Mimetic operators
Diferències finites
Interfícies de programació d'aplicacions (Programari)
Ones sonores
Àrees temàtiques de la UPC::Enginyeria de la telecomunicació::Processament del senyal::Processament de la parla i del senyal acústic
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oai_identifier_str oai:upcommons.upc.edu:2117/190495
network_acronym_str ES
network_name_str España
repository_id_str
dc.title.none.fl_str_mv Alternating direction implicit time integrations for finite difference acoustic wave propagation: parallelization and convergence
title Alternating direction implicit time integrations for finite difference acoustic wave propagation: parallelization and convergence
spellingShingle Alternating direction implicit time integrations for finite difference acoustic wave propagation: parallelization and convergence
Otero Calviño, Beatriz|||0000-0002-9194-559X
Finite differences
Application program interfaces (Computer software)
Sound-waves
CUDA and OpenMP programming
ADI
Compact finite differences
Mimetic operators
Diferències finites
Interfícies de programació d'aplicacions (Programari)
Ones sonores
Àrees temàtiques de la UPC::Enginyeria de la telecomunicació::Processament del senyal::Processament de la parla i del senyal acústic
title_short Alternating direction implicit time integrations for finite difference acoustic wave propagation: parallelization and convergence
title_full Alternating direction implicit time integrations for finite difference acoustic wave propagation: parallelization and convergence
title_fullStr Alternating direction implicit time integrations for finite difference acoustic wave propagation: parallelization and convergence
title_full_unstemmed Alternating direction implicit time integrations for finite difference acoustic wave propagation: parallelization and convergence
title_sort Alternating direction implicit time integrations for finite difference acoustic wave propagation: parallelization and convergence
dc.creator.none.fl_str_mv Otero Calviño, Beatriz|||0000-0002-9194-559X
Rojas, Otilio
Moya, Ferrán
Castillo, José
author Otero Calviño, Beatriz|||0000-0002-9194-559X
author_facet Otero Calviño, Beatriz|||0000-0002-9194-559X
Rojas, Otilio
Moya, Ferrán
Castillo, José
author_role author
author2 Rojas, Otilio
Moya, Ferrán
Castillo, José
author2_role author
author
author
dc.subject.none.fl_str_mv Finite differences
Application program interfaces (Computer software)
Sound-waves
CUDA and OpenMP programming
ADI
Compact finite differences
Mimetic operators
Diferències finites
Interfícies de programació d'aplicacions (Programari)
Ones sonores
Àrees temàtiques de la UPC::Enginyeria de la telecomunicació::Processament del senyal::Processament de la parla i del senyal acústic
topic Finite differences
Application program interfaces (Computer software)
Sound-waves
CUDA and OpenMP programming
ADI
Compact finite differences
Mimetic operators
Diferències finites
Interfícies de programació d'aplicacions (Programari)
Ones sonores
Àrees temàtiques de la UPC::Enginyeria de la telecomunicació::Processament del senyal::Processament de la parla i del senyal acústic
description 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.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-06-15
2020
2020-06-11
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/190495
https://dx.doi.org/10.1016/j.compfluid.2020.104584
url https://hdl.handle.net/2117/190495
https://dx.doi.org/10.1016/j.compfluid.2020.104584
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv European Commission http://doi.org/10.13039/100010661 Horizon 2020 Framework Programme 777778 Multiscale Inversion of Porous Rock Physics using High-Performance Simulators: Bridging the Gap between Mathematics and Geophysics
European Commission http://doi.org/10.13039/100010661 Horizon 2020 Framework Programme 823844 Centre of Excellence for Exascale in Solid Earth
European Commission http://doi.org/10.13039/100010661 Horizon 2020 Framework Programme 828947 Supercomputing and Energy for Mexico
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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spelling Alternating direction implicit time integrations for finite difference acoustic wave propagation: parallelization and convergenceOtero Calviño, Beatriz|||0000-0002-9194-559XRojas, OtilioMoya, FerránCastillo, JoséFinite differencesApplication program interfaces (Computer software)Sound-wavesCUDA and OpenMP programmingADICompact finite differencesMimetic operatorsDiferències finitesInterfícies de programació d'aplicacions (Programari)Ones sonoresÀrees temàtiques de la UPC::Enginyeria de la telecomunicació::Processament del senyal::Processament de la parla i del senyal acústicThis 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.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.Peer ReviewedElsevier20202020-06-1520202020-06-11journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/190495https://dx.doi.org/10.1016/j.compfluid.2020.104584reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengEuropean Commission http://doi.org/10.13039/100010661 Horizon 2020 Framework Programme 777778 Multiscale Inversion of Porous Rock Physics using High-Performance Simulators: Bridging the Gap between Mathematics and GeophysicsEuropean Commission http://doi.org/10.13039/100010661 Horizon 2020 Framework Programme 823844 Centre of Excellence for Exascale in Solid EarthEuropean Commission http://doi.org/10.13039/100010661 Horizon 2020 Framework Programme 828947 Supercomputing and Energy for Mexicoopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttps://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1904952026-05-27T15:37:01Z
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