On Solving an Acoustic Wave Problem Via Frequency-Domain Approach and Tensorial Spline Galerkin Method
In this paper, we introduce a numerical method for solving the dynamical acoustic wave propagation problem with Robin boundary conditions. The method used here is divided into two stages. In the first stage, the equations are transformed, via the Fourier Transform, into an equivalent problem for the...
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| Veröffentlicht in: | Journal of scientific computing 2018-03, Vol.74 (3), p.1193-1220 |
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| creator | Addam, Mohamed Bouhamidi, Abderrahman Heyouni, Mohammed |
| description | In this paper, we introduce a numerical method for solving the dynamical acoustic wave propagation problem with Robin boundary conditions. The method used here is divided into two stages. In the first stage, the equations are transformed, via the Fourier Transform, into an equivalent problem for the frequency variables. This allow us to avoid a discretization of the time variable in the considered system. Existence and uniqueness for the equation in frequency-domain are given. An approximation of the acoustic density in frequency-domain approach is also proposed by using a tensorial spline finite element Galerkin method. In the second stage, a Gauss–Hermite quadrature method is used for the computation of inverse Fourier transform of the frequency acoustic density to obtain the time-dependent solution of the acoustic wave problem. Error estimates in Sobolev spaces and convergence behavior of the presented methods are studied. Several numerical test examples are given to illustrate the performance of the proposed method, effectiveness and good resolution properties for smooth and discontinuous heterogeneous solutions. |
| doi_str_mv | 10.1007/s10915-017-0490-z |
| format | Article |
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The method used here is divided into two stages. In the first stage, the equations are transformed, via the Fourier Transform, into an equivalent problem for the frequency variables. This allow us to avoid a discretization of the time variable in the considered system. Existence and uniqueness for the equation in frequency-domain are given. An approximation of the acoustic density in frequency-domain approach is also proposed by using a tensorial spline finite element Galerkin method. In the second stage, a Gauss–Hermite quadrature method is used for the computation of inverse Fourier transform of the frequency acoustic density to obtain the time-dependent solution of the acoustic wave problem. Error estimates in Sobolev spaces and convergence behavior of the presented methods are studied. Several numerical test examples are given to illustrate the performance of the proposed method, effectiveness and good resolution properties for smooth and discontinuous heterogeneous solutions.</description><identifier>ISSN: 0885-7474</identifier><identifier>EISSN: 1573-7691</identifier><identifier>DOI: 10.1007/s10915-017-0490-z</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Acoustic propagation ; Acoustic waves ; Acoustics ; Algorithms ; Approximation ; Boundary conditions ; Computational Mathematics and Numerical Analysis ; Density ; Finite element method ; Fourier transforms ; Frequency domain analysis ; Galerkin method ; Inequality ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematical functions ; Mathematics ; Mathematics and Statistics ; Numerical analysis ; Numerical methods ; Propagation ; Quadratures ; Review Paper ; Sobolev space ; Theoretical ; Time dependence ; Velocity ; Wave propagation</subject><ispartof>Journal of scientific computing, 2018-03, Vol.74 (3), p.1193-1220</ispartof><rights>Springer Science+Business Media, LLC 2017</rights><rights>Springer Science+Business Media, LLC 2017.</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c350t-8cd22a1077511d6a1afed050b45f18df66fe3374f522b2e7c8ca5d3a462d55d13</citedby><cites>FETCH-LOGICAL-c350t-8cd22a1077511d6a1afed050b45f18df66fe3374f522b2e7c8ca5d3a462d55d13</cites><orcidid>0000-0003-0248-5331 ; 0000-0002-5675-7251</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10915-017-0490-z$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2918314392?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>230,314,780,784,885,21379,27915,27916,33735,41479,42548,43796,51310,64374,64378,72230</link.rule.ids><backlink>$$Uhttps://hal.science/hal-04359554$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Addam, Mohamed</creatorcontrib><creatorcontrib>Bouhamidi, Abderrahman</creatorcontrib><creatorcontrib>Heyouni, Mohammed</creatorcontrib><title>On Solving an Acoustic Wave Problem Via Frequency-Domain Approach and Tensorial Spline Galerkin Method</title><title>Journal of scientific computing</title><addtitle>J Sci Comput</addtitle><description>In this paper, we introduce a numerical method for solving the dynamical acoustic wave propagation problem with Robin boundary conditions. The method used here is divided into two stages. In the first stage, the equations are transformed, via the Fourier Transform, into an equivalent problem for the frequency variables. This allow us to avoid a discretization of the time variable in the considered system. Existence and uniqueness for the equation in frequency-domain are given. An approximation of the acoustic density in frequency-domain approach is also proposed by using a tensorial spline finite element Galerkin method. In the second stage, a Gauss–Hermite quadrature method is used for the computation of inverse Fourier transform of the frequency acoustic density to obtain the time-dependent solution of the acoustic wave problem. Error estimates in Sobolev spaces and convergence behavior of the presented methods are studied. Several numerical test examples are given to illustrate the performance of the proposed method, effectiveness and good resolution properties for smooth and discontinuous heterogeneous solutions.</description><subject>Acoustic propagation</subject><subject>Acoustic waves</subject><subject>Acoustics</subject><subject>Algorithms</subject><subject>Approximation</subject><subject>Boundary conditions</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Density</subject><subject>Finite element method</subject><subject>Fourier transforms</subject><subject>Frequency domain analysis</subject><subject>Galerkin method</subject><subject>Inequality</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical functions</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Numerical analysis</subject><subject>Numerical methods</subject><subject>Propagation</subject><subject>Quadratures</subject><subject>Review Paper</subject><subject>Sobolev space</subject><subject>Theoretical</subject><subject>Time dependence</subject><subject>Velocity</subject><subject>Wave propagation</subject><issn>0885-7474</issn><issn>1573-7691</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp1kE1rGzEQhkVoIW7SH5CboKcelMzoY7V7NGnzAQ4J2G2OQpa08abrlSvZhuTXR2ZLesppYHiel5mXkDOEcwTQFxmhQcUANQPZAHs9IhNUWjBdNfiJTKCuFdNSy2PyJednAGjqhk9Iez_Qeez33fBE7UCnLu7ytnP00e4DfUhx2Yc1_d1ZepXC310Y3Av7Ede2K-hmk6J1q6J5ughDjqmzPZ1v-m4I9Nr2If0p2F3YrqI_JZ9b2-fw9d88Ib-ufi4ub9js_vr2cjpjTijYstp5zi2C1grRVxZtGzwoWErVYu3bqmqDEFq2ivMlD9rVziovrKy4V8qjOCHfx9yV7c0mdWubXky0nbmZzsxhB1KoRim5P7DfRrb8UV7LW_Mcd2ko5xneYC1QioYXCkfKpZhzCu17LII5VG_G6k2p3hyqN6_F4aOTCzs8hfQ_-WPpDUfQhhk</recordid><startdate>20180301</startdate><enddate>20180301</enddate><creator>Addam, Mohamed</creator><creator>Bouhamidi, Abderrahman</creator><creator>Heyouni, Mohammed</creator><general>Springer US</general><general>Springer Nature B.V</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0003-0248-5331</orcidid><orcidid>https://orcid.org/0000-0002-5675-7251</orcidid></search><sort><creationdate>20180301</creationdate><title>On Solving an Acoustic Wave Problem Via Frequency-Domain Approach and Tensorial Spline Galerkin Method</title><author>Addam, Mohamed ; Bouhamidi, Abderrahman ; Heyouni, Mohammed</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c350t-8cd22a1077511d6a1afed050b45f18df66fe3374f522b2e7c8ca5d3a462d55d13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Acoustic propagation</topic><topic>Acoustic waves</topic><topic>Acoustics</topic><topic>Algorithms</topic><topic>Approximation</topic><topic>Boundary conditions</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Density</topic><topic>Finite element method</topic><topic>Fourier transforms</topic><topic>Frequency domain analysis</topic><topic>Galerkin method</topic><topic>Inequality</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical functions</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Numerical analysis</topic><topic>Numerical methods</topic><topic>Propagation</topic><topic>Quadratures</topic><topic>Review Paper</topic><topic>Sobolev space</topic><topic>Theoretical</topic><topic>Time dependence</topic><topic>Velocity</topic><topic>Wave propagation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Addam, Mohamed</creatorcontrib><creatorcontrib>Bouhamidi, Abderrahman</creatorcontrib><creatorcontrib>Heyouni, Mohammed</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central</collection><collection>Advanced Technologies & Aerospace Database (1962 - current)</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Journal of scientific computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Addam, Mohamed</au><au>Bouhamidi, Abderrahman</au><au>Heyouni, Mohammed</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Solving an Acoustic Wave Problem Via Frequency-Domain Approach and Tensorial Spline Galerkin Method</atitle><jtitle>Journal of scientific computing</jtitle><stitle>J Sci Comput</stitle><date>2018-03-01</date><risdate>2018</risdate><volume>74</volume><issue>3</issue><spage>1193</spage><epage>1220</epage><pages>1193-1220</pages><issn>0885-7474</issn><eissn>1573-7691</eissn><abstract>In this paper, we introduce a numerical method for solving the dynamical acoustic wave propagation problem with Robin boundary conditions. The method used here is divided into two stages. In the first stage, the equations are transformed, via the Fourier Transform, into an equivalent problem for the frequency variables. This allow us to avoid a discretization of the time variable in the considered system. Existence and uniqueness for the equation in frequency-domain are given. An approximation of the acoustic density in frequency-domain approach is also proposed by using a tensorial spline finite element Galerkin method. In the second stage, a Gauss–Hermite quadrature method is used for the computation of inverse Fourier transform of the frequency acoustic density to obtain the time-dependent solution of the acoustic wave problem. Error estimates in Sobolev spaces and convergence behavior of the presented methods are studied. 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| subjects | Acoustic propagation Acoustic waves Acoustics Algorithms Approximation Boundary conditions Computational Mathematics and Numerical Analysis Density Finite element method Fourier transforms Frequency domain analysis Galerkin method Inequality Mathematical and Computational Engineering Mathematical and Computational Physics Mathematical functions Mathematics Mathematics and Statistics Numerical analysis Numerical methods Propagation Quadratures Review Paper Sobolev space Theoretical Time dependence Velocity Wave propagation |
| title | On Solving an Acoustic Wave Problem Via Frequency-Domain Approach and Tensorial Spline Galerkin Method |
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