A comparison of approximate boundary conditions and infinite element methods for exterior Helmholtz problems
We compare the accuracy of a variety of approximate boundary conditions (ABCs) and two versions of an infinite element method (IEM) for approximating solutions of exterior Helmholtz problems. The infinite elements are of variable order in the radial direction and differ only in whether the test func...
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| Published in | Computer methods in applied mechanics and engineering Vol. 164; no. 1; pp. 121 - 139 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
02.10.1998
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| Online Access | Get full text |
| ISSN | 0045-7825 1879-2138 |
| DOI | 10.1016/S0045-7825(98)00050-4 |
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| Abstract | We compare the accuracy of a variety of approximate boundary conditions (ABCs) and two versions of an infinite element method (IEM) for approximating solutions of exterior Helmholtz problems. The infinite elements are of variable order in the radial direction and differ only in whether the test functions in the weak formulation are conjugated or not. We find that the accuracy of the ABCs decreases with increasing frequency, and that at higher frequencies their accuracy is several orders of magnitude lower than that obtained with the IEMs. We show that the convergence rate of the conjugated element is slower than the rate for the unconjugated element and that the latter element fails to converge in the far field. |
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| AbstractList | We compare the accuracy of a variety of approximate boundary conditions (ABCs) and two versions of an infinite element method (IEM) for approximating solutions of exterior Helmholtz problems. The infinite elements are of variable order in the radial direction and differ only in whether the test functions in the weak formulation are conjugated or not. We find that the accuracy of the ABCs decreases with increasing frequency, and that at higher frequencies their accuracy is several orders of magnitude lower than that obtained with the IEMs. We show that the convergence rate of the conjugated element is slower than the rate for the unconjugated element and that the latter element fails to converge in the far field. |
| Author | Shirron, Joseph J. Babuška, Ivo |
| Author_xml | – sequence: 1 givenname: Joseph J. surname: Shirron fullname: Shirron, Joseph J. organization: Naval Research Laboratory, Code 7131, Washington, DC 20375-5320, USA – sequence: 2 givenname: Ivo surname: Babuška fullname: Babuška, Ivo organization: TICAM, The University of Texas at Austin, Austin, TX 78712, USA |
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| Cites_doi | 10.1016/0022-460X(83)90678-8 10.1002/nme.1620110107 10.1142/S0218396X97000046 10.1016/0021-9991(89)90041-7 10.1007/BF01220037 10.1121/1.1911085 10.1137/0142032 10.1002/cpa.3160140318 10.1006/jcph.1995.1210 10.1002/cpa.3160330603 10.1016/0045-7825(92)90108-V 10.1109/8.366346 10.1142/S0218396X97000071 10.1093/qjmam/27.1.129 10.1080/14786444908561291 10.2514/3.8843 10.1108/eb023829 10.1121/1.399743 10.1002/cpa.3160320303 10.1121/1.411994 10.1002/(SICI)1099-0887(199604)12:4<257::AID-CNM977>3.0.CO;2-8 10.1007/BF02165003 10.1006/jsvi.1994.1136 10.1002/nme.1620151105 10.1002/nme.1620170214 10.2514/3.13017 10.1016/0045-7825(94)90089-2 10.1006/jsvi.1994.1048 10.1090/S0025-5718-1977-0436612-4 10.1016/0021-9991(91)90135-8 10.1002/nme.1620110808 10.1002/cnm.1630030113 10.1108/eb023830 10.1121/1.411286 10.1016/0022-460X(81)90273-X 10.1002/fld.1650030506 10.1002/cpa.3160090202 10.1016/S0045-7825(96)01150-4 |
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| References | Demkowicz, Ihlenburg (BIB35) November 1996 Bettess (BIB17) 1981; 17 Panich (BIB54) 1965; 20 Keller, Givoli (BIB50) 1989; 82 Bettess, Bettess (BIB20) 1991; 8 Patlashenko, Givoli, Keller (BIB32) 1997; 143 Demkowicz, Gerdes (BIB34) May 1995 Astley, Eversman (BIB8) 1984; 22 Bettess (BIB18) 1987; 3 Gerdes, Demkowicz (BIB40) 1997; 137 Astley (BIB4) 1996; 12 Bettess (BIB19) 1992 Schenk (BIB56) 1968; 44 Harari, Avraham (BIB44) 1997; 5 Karp (BIB49) 1961; 14 Astley, Eversman (BIB6) 1981; 76 Babuška (BIB10) 1971; 16 Bettess (BIB15) 1977; 11 Szabó, Babuška (BIB59) 1991 Engquist, Majda (BIB37) 1977; 31 Harari, Hughes (BIB45) 1992; 97 Atkinson (BIB9) 1949; 40 R.L. Holford, A multipole expansion for the acoustic field exterior to a prolate or oblate spheroid, AT&T Bell Laboratories, Whippany, NJ., J. Acoust. Soc. Am., to be submitted. Lebedev (BIB51) 1972 Bettess, Bettess (BIB21) 1991; 8 D.S. Burnett and R.L. Holford, An ellipsoidal infinite element for 3D radiation and scattering, Comput. Methods Appl. Mech. Engrg., submitted. Sommerfled (BIB58) 1912; 21 Astley, Coyette, Macaulay (BIB5) 1994; 170 Ursell (BIB60) 1973; 74 Cremers, Fyfe, Coyette (BIB30) 1994; 171 Freund, Malhotra, Pinsky (BIB53) 1997; 146 Amino, Harris, Wilton (BIB2) 1992 Patlashenko, Givoli (BIB55) 1997; 5 Abramowitz, Stegun (BIB1) 1972 Givoli (BIB42) 1991; 94 Burton, Miller (BIB26) 1971; A323 Burnett (BIB24) 1994; 96 Anderson (BIB39) 1992 Peterson, Meade, Slade, Webb (BIB33) 1995; 43 Jones (BIB47) 1974; 27 Engquist, Majda (BIB38) 1979; 32 Grote, Keller (BIB43) 1995; 122 Shirron (BIB57) 1995 D.S. Burnett, 3-D structural acoustic modeling using a new high accuracy acoustic infinite element: A cost comparison with the BEM, Private communication of prepublication results, in preparation. Colton, Kress (BIB28) 1983 Kang (BIB48) 1983 Bayliss, Turkel (BIB12) 1980; 33 Benporat, Givoli (BIB13) 1995; 11 Bayliss, Gunzburger, Turkel (BIB11) 1982; 42 Astley (BIB3) 1983; 3 Bettess, Zienkiewicz (BIB14) 1977; 11 Cremers, Fyfe (BIB31) 1995; 97 Givoli, Keller (BIB41) 1994; 119 A.A. Oberai, M. Malhotra and P.M. Pinsky, On the uyse of infinite elements and the DtN condition for solving large-scale problems in acoustics, to be submitted. Wilcox (BIB61) 1956; 9 Bettess (BIB16) 1980; 15 Chien, Rajiyah, Atluri (BIB27) 1990; 88 Wilcox (BIB62) 1956; 7 Brakhage, Werner (BIB22) 1965; 16 Cremers, Fyfe (BIB29) 1991; 19 Eaton, Regan (BIB36) 1996; 34 Astley, Eversman (BIB7) 1983; 88 Bettess (10.1016/S0045-7825(98)00050-4_BIB15) 1977; 11 Sommerfled (10.1016/S0045-7825(98)00050-4_BIB58) 1912; 21 Wilcox (10.1016/S0045-7825(98)00050-4_BIB61) 1956; 9 Bettess (10.1016/S0045-7825(98)00050-4_BIB17) 1981; 17 Astley (10.1016/S0045-7825(98)00050-4_BIB4) 1996; 12 Abramowitz (10.1016/S0045-7825(98)00050-4_BIB1) 1972 10.1016/S0045-7825(98)00050-4_BIB23 Bettess (10.1016/S0045-7825(98)00050-4_BIB20) 1991; 8 10.1016/S0045-7825(98)00050-4_BIB25 Burton (10.1016/S0045-7825(98)00050-4_BIB26) 1971; A323 Keller (10.1016/S0045-7825(98)00050-4_BIB50) 1989; 82 Anderson (10.1016/S0045-7825(98)00050-4_BIB39) 1992 Atkinson (10.1016/S0045-7825(98)00050-4_BIB9) 1949; 40 Grote (10.1016/S0045-7825(98)00050-4_BIB43) 1995; 122 Cremers (10.1016/S0045-7825(98)00050-4_BIB31) 1995; 97 Demkowicz (10.1016/S0045-7825(98)00050-4_BIB34) 1995 Eaton (10.1016/S0045-7825(98)00050-4_BIB36) 1996; 34 Karp (10.1016/S0045-7825(98)00050-4_BIB49) 1961; 14 Brakhage (10.1016/S0045-7825(98)00050-4_BIB22) 1965; 16 Gerdes (10.1016/S0045-7825(98)00050-4_BIB40) 1997; 137 Engquist (10.1016/S0045-7825(98)00050-4_BIB37) 1977; 31 Givoli (10.1016/S0045-7825(98)00050-4_BIB41) 1994; 119 Bettess (10.1016/S0045-7825(98)00050-4_BIB18) 1987; 3 Patlashenko (10.1016/S0045-7825(98)00050-4_BIB55) 1997; 5 Astley (10.1016/S0045-7825(98)00050-4_BIB5) 1994; 170 Chien (10.1016/S0045-7825(98)00050-4_BIB27) 1990; 88 Bettess (10.1016/S0045-7825(98)00050-4_BIB14) 1977; 11 Astley (10.1016/S0045-7825(98)00050-4_BIB3) 1983; 3 Szabó (10.1016/S0045-7825(98)00050-4_BIB59) 1991 Cremers (10.1016/S0045-7825(98)00050-4_BIB29) 1991; 19 Patlashenko (10.1016/S0045-7825(98)00050-4_BIB32) 1997; 143 Harari (10.1016/S0045-7825(98)00050-4_BIB45) 1992; 97 Amino (10.1016/S0045-7825(98)00050-4_BIB2) 1992 Harari (10.1016/S0045-7825(98)00050-4_BIB44) 1997; 5 Panich (10.1016/S0045-7825(98)00050-4_BIB54) 1965; 20 Kang (10.1016/S0045-7825(98)00050-4_BIB48) 1983 10.1016/S0045-7825(98)00050-4_BIB46 Astley (10.1016/S0045-7825(98)00050-4_BIB8) 1984; 22 Bettess (10.1016/S0045-7825(98)00050-4_BIB21) 1991; 8 Wilcox (10.1016/S0045-7825(98)00050-4_BIB62) 1956; 7 Shirron (10.1016/S0045-7825(98)00050-4_BIB57) 1995 Schenk (10.1016/S0045-7825(98)00050-4_BIB56) 1968; 44 Bayliss (10.1016/S0045-7825(98)00050-4_BIB11) 1982; 42 Astley (10.1016/S0045-7825(98)00050-4_BIB7) 1983; 88 Demkowicz (10.1016/S0045-7825(98)00050-4_BIB35) 1996 Bayliss (10.1016/S0045-7825(98)00050-4_BIB12) 1980; 33 Cremers (10.1016/S0045-7825(98)00050-4_BIB30) 1994; 171 Lebedev (10.1016/S0045-7825(98)00050-4_BIB51) 1972 Givoli (10.1016/S0045-7825(98)00050-4_BIB42) 1991; 94 Colton (10.1016/S0045-7825(98)00050-4_BIB28) 1983 Jones (10.1016/S0045-7825(98)00050-4_BIB47) 1974; 27 Bettess (10.1016/S0045-7825(98)00050-4_BIB16) 1980; 15 10.1016/S0045-7825(98)00050-4_BIB52 Freund (10.1016/S0045-7825(98)00050-4_BIB53) 1997; 146 Peterson (10.1016/S0045-7825(98)00050-4_BIB33) 1995; 43 Astley (10.1016/S0045-7825(98)00050-4_BIB6) 1981; 76 Benporat (10.1016/S0045-7825(98)00050-4_BIB13) 1995; 11 Babuška (10.1016/S0045-7825(98)00050-4_BIB10) 1971; 16 Bettess (10.1016/S0045-7825(98)00050-4_BIB19) 1992 Engquist (10.1016/S0045-7825(98)00050-4_BIB38) 1979; 32 Burnett (10.1016/S0045-7825(98)00050-4_BIB24) 1994; 96 Ursell (10.1016/S0045-7825(98)00050-4_BIB60) 1973; 74 |
| References_xml | – volume: 122 start-page: 231 year: 1995 end-page: 243 ident: BIB43 article-title: On nonreflecting boundary conditions publication-title: J. Comput. Phys. – volume: 96 start-page: 2798 year: 1994 end-page: 2816 ident: BIB24 article-title: A three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion publication-title: J. Acoust. Soc. Am. – volume: 32 start-page: 313 year: 1979 end-page: 357 ident: BIB38 article-title: Radiation boundary conditions for acoustic and elastic wave calculations publication-title: Comm. Pure Appl. Math. – volume: A323 start-page: 201 year: 1971 end-page: 210 ident: BIB26 article-title: The application of integral equation methods to the numerical solution of some exterior boundary value problems publication-title: Proc. Roy. Soc. Lond. – year: 1972 ident: BIB51 article-title: Special Functions and Their Applications – volume: 21 start-page: 309 year: 1912 end-page: 353 ident: BIB58 article-title: Die Greensche funktion der Schwingungsgleichung publication-title: Jber. Deutsch. Math. Verein. – volume: 8 start-page: 99 year: 1991 end-page: 124 ident: BIB20 article-title: Infinite elements for dynamic problems: Part 1 publication-title: Engrg. Comput. – volume: 40 start-page: 645 year: 1949 end-page: 651 ident: BIB9 article-title: On Sommerfled's ‘radiation condition’ publication-title: The Philosophical Mag. – year: 1992 ident: BIB19 article-title: Infinite Elements – year: 1983 ident: BIB28 article-title: Integral equation methods in scattering theory publication-title: Pure and Applied Mathematics – volume: 9 start-page: 115 year: 1956 end-page: 134 ident: BIB61 article-title: An expansion theorem for electromagnetic fields publication-title: Comm. Pure Appl. Math. – volume: 143 start-page: 13 year: 1997 end-page: 39 ident: BIB32 article-title: High-order boundary conditions and finite elements for infinite domains publication-title: Comput. Methods Appl. Mech. Engrg. – volume: 3 start-page: 507 year: 1983 end-page: 526 ident: BIB3 article-title: Wave envelope and infinite elements for acoustical radiation publication-title: Int. J. Numer. Methods Fluids – volume: 11 start-page: 53 year: 1977 end-page: 64 ident: BIB15 article-title: Infinite elements publication-title: Int. J. Numer. Methods Engrg. – volume: 171 start-page: 483 year: 1994 end-page: 508 ident: BIB30 article-title: A variable order infinite acoustic wave envelope element publication-title: J. Sound Vib. – volume: 44 start-page: 41 year: 1968 end-page: 58 ident: BIB56 article-title: Improved integral formulation for acoustic radiation problems publication-title: J. Acoust. Soc. Am. – volume: 170 start-page: 97 year: 1994 end-page: 118 ident: BIB5 article-title: Mapped wave envelope elements for acoustical radiation and scattering publication-title: J. Sound Vib. – volume: 34 start-page: 29 year: 1996 end-page: 34 ident: BIB36 article-title: Application of the infinite element method to acoustic scattering problems publication-title: AIAA J. – volume: 27 start-page: 129 year: 1974 end-page: 142 ident: BIB47 article-title: Integral equations for the exterior acoustic problem publication-title: Quart. J. Mech. Appl. Math. – volume: 88 start-page: 47 year: 1983 end-page: 64 ident: BIB7 article-title: Finite element formulations for acoustic radiation publication-title: J. Sound Vib. – volume: 146 start-page: 173 year: 1997 end-page: 196 ident: BIB53 article-title: Iterative solution of multiple radiation and scattering problems in structural acoustics using a block quasi-minimal residual algorithm publication-title: Comput. Methods Appl. Mech. Engrg. – volume: 31 start-page: 629 year: 1977 end-page: 651 ident: BIB37 article-title: Absorbing boundary conditions for the numerical simulation of waves publication-title: Math. Comput. – volume: 22 start-page: 1719 year: 1984 end-page: 1726 ident: BIB8 article-title: Wave envelope and infinite element schemes for fan noise radiation from turbofan inlets publication-title: Am. Instit. Aeronaut. Astronaut. J. – year: 1991 ident: BIB59 article-title: Finite Element Analysis – volume: 11 start-page: 734 year: 1995 end-page: 741 ident: BIB13 article-title: Solution of unbounded domain problems using elliptic artificial boundaries publication-title: Comm. Numer. Methods Engrg. – volume: 97 start-page: 77 year: 1992 end-page: 102 ident: BIB45 article-title: A cost comparison of boundary element and finite element methods for problems of time-harmonic acoustics publication-title: Comput. Methods Appl. Mech. Engrg. – year: 1992 ident: BIB2 article-title: Coupled Boundary and Finite Element Methods for the Solution of the Dynamic Fluid-Structure Interaction Problem – volume: 17 year: 1981 ident: BIB17 article-title: Operation counts for boundary integral and finite element methods publication-title: Int. J. Numer. Methods Engrg. – volume: 5 start-page: 95 year: 1997 end-page: 115 ident: BIB55 article-title: Non-reflecting finite element schemes for three-dimensional acoustic waves publication-title: J. Comput. Acoust. – volume: 43 start-page: 6 year: 1995 end-page: 10 ident: BIB33 article-title: Comparison of local radiation boundary conditions for the scalar Helmholtz equation with general boundary shapes publication-title: IEEE Trans. Antennas Propagation – volume: 3 start-page: 77 year: 1987 end-page: 80 ident: BIB18 article-title: A simple wave envelope element example publication-title: Comm. Appl. Numer. Methods – year: 1995 ident: BIB57 article-title: Solution of exterior Helmholtz problems using finite and infinite elements publication-title: Ph.D. Thesis – volume: 5 start-page: 33 year: 1997 end-page: 51 ident: BIB44 article-title: High-order finite element methods for acoustic problems publication-title: J. Comput. Acoust. – volume: 12 start-page: 257 year: 1996 end-page: 267 ident: BIB4 article-title: FE mode-matching schemes for the exterior Helmholtz problem and their relationship to the FE-DtN approach publication-title: Comm. Numer. Methods Engrg. – volume: 119 start-page: 199 year: 1994 end-page: 213 ident: BIB41 article-title: Special finite elements for use with high-order boundary conditions publication-title: Comput. Methods Appl. Mech. Engrg. – volume: 20 start-page: 221 year: 1965 end-page: 226 ident: BIB54 article-title: On the question of the solvability of the exterior boundary-value problems for the wave equation and Maxwell's equations publication-title: Russian Math. Surveys – volume: 82 start-page: 172 year: 1989 end-page: 192 ident: BIB50 article-title: Exact non-reflecting boundary conditions publication-title: J. Comput. Phys. – volume: 11 start-page: 1271 year: 1977 end-page: 1290 ident: BIB14 article-title: Diffraction and refraction of surface waves using finite and infinite elements publication-title: Int. J. Numer. Methods Engrg. – volume: 74 start-page: 117 year: 1973 end-page: 125 ident: BIB60 article-title: On the exterior problems of acoustics publication-title: Proc. Cambridge Philosophical Soc. – reference: D.S. Burnett and R.L. Holford, An ellipsoidal infinite element for 3D radiation and scattering, Comput. Methods Appl. Mech. Engrg., submitted. – start-page: 1439 year: 1983 end-page: 1453 ident: BIB48 article-title: Finite element method and natural boundary reduction publication-title: Proc. Int. Congress of Mathematicians – volume: 14 start-page: 427 year: 1961 end-page: 434 ident: BIB49 article-title: A convergent ‘far-field’ expansion for two-dimensional radiation functions publication-title: Comm. Pure Appl. Math. – reference: D.S. Burnett, 3-D structural acoustic modeling using a new high accuracy acoustic infinite element: A cost comparison with the BEM, Private communication of prepublication results, in preparation. – volume: 97 start-page: 2028 year: 1995 end-page: 2040 ident: BIB31 article-title: On the use of variable order infinite wave envelope elements for acoustic radiation and scattering publication-title: J. Acoust. Soc. Am. – volume: 15 start-page: 1613 year: 1980 end-page: 1626 ident: BIB16 article-title: More on infinite elements publication-title: Int. J. Numer. Methods Engrg. – volume: 94 start-page: 1 year: 1991 end-page: 29 ident: BIB42 article-title: Non-reflecting boundary conditions publication-title: J. Comput. Phys. – year: 1972 ident: BIB1 publication-title: Handbook of mathematical functions – volume: 8 start-page: 125 year: 1991 end-page: 151 ident: BIB21 article-title: Infinite elements for dynamic problems: Part 2 publication-title: Engrg. Comput. – volume: 88 start-page: 918 year: 1990 end-page: 937 ident: BIB27 article-title: An effective method for solving the hypersingular integral equations in 3-D acoustics publication-title: J. Acoust. Soc. Am. – volume: 7 start-page: 271 year: 1956 end-page: 276 ident: BIB62 article-title: A generalization of theorems of Rellich and Atkinson publication-title: Proc. Am. Math. Soc. – year: 1992 ident: BIB39 publication-title: LAPACK User's Guide – volume: 42 start-page: 430 year: 1982 end-page: 451 ident: BIB11 article-title: Solution of elliptic equations in exterior regions publication-title: SIAM J. Appl. Math. – volume: 16 start-page: 325 year: 1965 end-page: 329 ident: BIB22 article-title: Über das Dirichletsche Aussenraumproblem für die Helmholtzsche Schwingungsgleichung publication-title: Arch. Math. – volume: 137 start-page: 239 year: 1997 end-page: 273 ident: BIB40 article-title: Solution of 3D Laplace and Helmholtz equations in exterior domains using publication-title: Comput. Methods Appl. Mech. Engrg. – volume: 76 start-page: 595 year: 1981 end-page: 601 ident: BIB6 article-title: A note on the utility of a wave envelope approach in finite element duct transmission studies publication-title: J. Sound Vib. – volume: 16 start-page: 322 year: 1971 end-page: 333 ident: BIB10 article-title: Error-bounds for finite element method publication-title: Numer. Math. – year: May 1995 ident: BIB34 article-title: Convergence of the infinite element methods for the Helmholtz equation publication-title: Technical Report 95-07 – year: November 1996 ident: BIB35 article-title: Analysis of a coupled finite-infinite element method for exterior Helmholtz problems publication-title: Technical Report 96-11 – volume: 33 start-page: 707 year: 1980 end-page: 725 ident: BIB12 article-title: Radiation boundary conditions for wave-like equations publication-title: Comm. Pure Appl. Math. – reference: A.A. Oberai, M. Malhotra and P.M. Pinsky, On the uyse of infinite elements and the DtN condition for solving large-scale problems in acoustics, to be submitted. – volume: 19 start-page: 29 year: 1991 end-page: 30 ident: BIB29 article-title: Numerical methods for solving acoustic radiation problems publication-title: Can. Acoust. – reference: R.L. Holford, A multipole expansion for the acoustic field exterior to a prolate or oblate spheroid, AT&T Bell Laboratories, Whippany, NJ., J. Acoust. Soc. Am., to be submitted. – volume: 88 start-page: 47 year: 1983 ident: 10.1016/S0045-7825(98)00050-4_BIB7 article-title: Finite element formulations for acoustic radiation publication-title: J. Sound Vib. doi: 10.1016/0022-460X(83)90678-8 – volume: 11 start-page: 53 year: 1977 ident: 10.1016/S0045-7825(98)00050-4_BIB15 article-title: Infinite elements publication-title: Int. J. Numer. Methods Engrg. doi: 10.1002/nme.1620110107 – year: 1991 ident: 10.1016/S0045-7825(98)00050-4_BIB59 – volume: 5 start-page: 33 issue: 1 year: 1997 ident: 10.1016/S0045-7825(98)00050-4_BIB44 article-title: High-order finite element methods for acoustic problems publication-title: J. Comput. Acoust. doi: 10.1142/S0218396X97000046 – year: 1995 ident: 10.1016/S0045-7825(98)00050-4_BIB57 article-title: Solution of exterior Helmholtz problems using finite and infinite elements – ident: 10.1016/S0045-7825(98)00050-4_BIB25 – year: 1992 ident: 10.1016/S0045-7825(98)00050-4_BIB19 – volume: 82 start-page: 172 year: 1989 ident: 10.1016/S0045-7825(98)00050-4_BIB50 article-title: Exact non-reflecting boundary conditions publication-title: J. Comput. Phys. doi: 10.1016/0021-9991(89)90041-7 – volume: 74 start-page: 117 year: 1973 ident: 10.1016/S0045-7825(98)00050-4_BIB60 article-title: On the exterior problems of acoustics – volume: 16 start-page: 325 year: 1965 ident: 10.1016/S0045-7825(98)00050-4_BIB22 article-title: Über das Dirichletsche Aussenraumproblem für die Helmholtzsche Schwingungsgleichung publication-title: Arch. Math. doi: 10.1007/BF01220037 – volume: 44 start-page: 41 year: 1968 ident: 10.1016/S0045-7825(98)00050-4_BIB56 article-title: Improved integral formulation for acoustic radiation problems publication-title: J. Acoust. Soc. Am. doi: 10.1121/1.1911085 – year: 1992 ident: 10.1016/S0045-7825(98)00050-4_BIB2 – volume: 42 start-page: 430 year: 1982 ident: 10.1016/S0045-7825(98)00050-4_BIB11 article-title: Solution of elliptic equations in exterior regions publication-title: SIAM J. Appl. Math. doi: 10.1137/0142032 – volume: 14 start-page: 427 year: 1961 ident: 10.1016/S0045-7825(98)00050-4_BIB49 article-title: A convergent ‘far-field’ expansion for two-dimensional radiation functions publication-title: Comm. Pure Appl. Math. doi: 10.1002/cpa.3160140318 – volume: 122 start-page: 231 issue: 2 year: 1995 ident: 10.1016/S0045-7825(98)00050-4_BIB43 article-title: On nonreflecting boundary conditions publication-title: J. Comput. Phys. doi: 10.1006/jcph.1995.1210 – volume: 33 start-page: 707 year: 1980 ident: 10.1016/S0045-7825(98)00050-4_BIB12 article-title: Radiation boundary conditions for wave-like equations publication-title: Comm. Pure Appl. Math. doi: 10.1002/cpa.3160330603 – volume: 21 start-page: 309 year: 1912 ident: 10.1016/S0045-7825(98)00050-4_BIB58 article-title: Die Greensche funktion der Schwingungsgleichung publication-title: Jber. Deutsch. Math. Verein. – volume: 97 start-page: 77 year: 1992 ident: 10.1016/S0045-7825(98)00050-4_BIB45 article-title: A cost comparison of boundary element and finite element methods for problems of time-harmonic acoustics publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/0045-7825(92)90108-V – volume: 43 start-page: 6 issue: 1 year: 1995 ident: 10.1016/S0045-7825(98)00050-4_BIB33 article-title: Comparison of local radiation boundary conditions for the scalar Helmholtz equation with general boundary shapes publication-title: IEEE Trans. Antennas Propagation doi: 10.1109/8.366346 – volume: 5 start-page: 95 issue: 1 year: 1997 ident: 10.1016/S0045-7825(98)00050-4_BIB55 article-title: Non-reflecting finite element schemes for three-dimensional acoustic waves publication-title: J. Comput. Acoust. doi: 10.1142/S0218396X97000071 – year: 1995 ident: 10.1016/S0045-7825(98)00050-4_BIB34 article-title: Convergence of the infinite element methods for the Helmholtz equation – volume: 27 start-page: 129 year: 1974 ident: 10.1016/S0045-7825(98)00050-4_BIB47 article-title: Integral equations for the exterior acoustic problem publication-title: Quart. J. Mech. Appl. Math. doi: 10.1093/qjmam/27.1.129 – ident: 10.1016/S0045-7825(98)00050-4_BIB46 – volume: 40 start-page: 645 year: 1949 ident: 10.1016/S0045-7825(98)00050-4_BIB9 article-title: On Sommerfled's ‘radiation condition’ publication-title: The Philosophical Mag. doi: 10.1080/14786444908561291 – volume: 22 start-page: 1719 year: 1984 ident: 10.1016/S0045-7825(98)00050-4_BIB8 article-title: Wave envelope and infinite element schemes for fan noise radiation from turbofan inlets publication-title: Am. Instit. Aeronaut. Astronaut. J. doi: 10.2514/3.8843 – volume: 8 start-page: 99 year: 1991 ident: 10.1016/S0045-7825(98)00050-4_BIB20 article-title: Infinite elements for dynamic problems: Part 1 publication-title: Engrg. Comput. doi: 10.1108/eb023829 – volume: 88 start-page: 918 year: 1990 ident: 10.1016/S0045-7825(98)00050-4_BIB27 article-title: An effective method for solving the hypersingular integral equations in 3-D acoustics publication-title: J. Acoust. Soc. Am. doi: 10.1121/1.399743 – year: 1992 ident: 10.1016/S0045-7825(98)00050-4_BIB39 – volume: 32 start-page: 313 year: 1979 ident: 10.1016/S0045-7825(98)00050-4_BIB38 article-title: Radiation boundary conditions for acoustic and elastic wave calculations publication-title: Comm. Pure Appl. Math. doi: 10.1002/cpa.3160320303 – volume: 20 start-page: 221 year: 1965 ident: 10.1016/S0045-7825(98)00050-4_BIB54 article-title: On the question of the solvability of the exterior boundary-value problems for the wave equation and Maxwell's equations publication-title: Russian Math. Surveys – volume: 97 start-page: 2028 year: 1995 ident: 10.1016/S0045-7825(98)00050-4_BIB31 article-title: On the use of variable order infinite wave envelope elements for acoustic radiation and scattering publication-title: J. Acoust. Soc. Am. doi: 10.1121/1.411994 – volume: 12 start-page: 257 issue: 4 year: 1996 ident: 10.1016/S0045-7825(98)00050-4_BIB4 article-title: FE mode-matching schemes for the exterior Helmholtz problem and their relationship to the FE-DtN approach publication-title: Comm. Numer. Methods Engrg. doi: 10.1002/(SICI)1099-0887(199604)12:4<257::AID-CNM977>3.0.CO;2-8 – ident: 10.1016/S0045-7825(98)00050-4_BIB52 – volume: 16 start-page: 322 year: 1971 ident: 10.1016/S0045-7825(98)00050-4_BIB10 article-title: Error-bounds for finite element method publication-title: Numer. Math. doi: 10.1007/BF02165003 – volume: A323 start-page: 201 year: 1971 ident: 10.1016/S0045-7825(98)00050-4_BIB26 article-title: The application of integral equation methods to the numerical solution of some exterior boundary value problems – volume: 171 start-page: 483 year: 1994 ident: 10.1016/S0045-7825(98)00050-4_BIB30 article-title: A variable order infinite acoustic wave envelope element publication-title: J. Sound Vib. doi: 10.1006/jsvi.1994.1136 – volume: 15 start-page: 1613 year: 1980 ident: 10.1016/S0045-7825(98)00050-4_BIB16 article-title: More on infinite elements publication-title: Int. J. Numer. Methods Engrg. doi: 10.1002/nme.1620151105 – year: 1972 ident: 10.1016/S0045-7825(98)00050-4_BIB1 – volume: 17 year: 1981 ident: 10.1016/S0045-7825(98)00050-4_BIB17 article-title: Operation counts for boundary integral and finite element methods publication-title: Int. J. Numer. Methods Engrg. doi: 10.1002/nme.1620170214 – volume: 19 start-page: 29 issue: 4 year: 1991 ident: 10.1016/S0045-7825(98)00050-4_BIB29 article-title: Numerical methods for solving acoustic radiation problems publication-title: Can. Acoust. – volume: 11 start-page: 734 issue: 9 year: 1995 ident: 10.1016/S0045-7825(98)00050-4_BIB13 article-title: Solution of unbounded domain problems using elliptic artificial boundaries publication-title: Comm. Numer. Methods Engrg. – volume: 7 start-page: 271 year: 1956 ident: 10.1016/S0045-7825(98)00050-4_BIB62 article-title: A generalization of theorems of Rellich and Atkinson – year: 1996 ident: 10.1016/S0045-7825(98)00050-4_BIB35 article-title: Analysis of a coupled finite-infinite element method for exterior Helmholtz problems – year: 1972 ident: 10.1016/S0045-7825(98)00050-4_BIB51 – volume: 34 start-page: 29 issue: 1 year: 1996 ident: 10.1016/S0045-7825(98)00050-4_BIB36 article-title: Application of the infinite element method to acoustic scattering problems publication-title: AIAA J. doi: 10.2514/3.13017 – volume: 119 start-page: 199 issue: 3–4 year: 1994 ident: 10.1016/S0045-7825(98)00050-4_BIB41 article-title: Special finite elements for use with high-order boundary conditions publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/0045-7825(94)90089-2 – start-page: 1439 year: 1983 ident: 10.1016/S0045-7825(98)00050-4_BIB48 article-title: Finite element method and natural boundary reduction – year: 1983 ident: 10.1016/S0045-7825(98)00050-4_BIB28 article-title: Integral equation methods in scattering theory – volume: 146 start-page: 173 issue: 1–2 year: 1997 ident: 10.1016/S0045-7825(98)00050-4_BIB53 article-title: Iterative solution of multiple radiation and scattering problems in structural acoustics using a block quasi-minimal residual algorithm publication-title: Comput. Methods Appl. Mech. Engrg. – ident: 10.1016/S0045-7825(98)00050-4_BIB23 – volume: 170 start-page: 97 year: 1994 ident: 10.1016/S0045-7825(98)00050-4_BIB5 article-title: Mapped wave envelope elements for acoustical radiation and scattering publication-title: J. Sound Vib. doi: 10.1006/jsvi.1994.1048 – volume: 31 start-page: 629 year: 1977 ident: 10.1016/S0045-7825(98)00050-4_BIB37 article-title: Absorbing boundary conditions for the numerical simulation of waves publication-title: Math. Comput. doi: 10.1090/S0025-5718-1977-0436612-4 – volume: 94 start-page: 1 year: 1991 ident: 10.1016/S0045-7825(98)00050-4_BIB42 article-title: Non-reflecting boundary conditions publication-title: J. Comput. Phys. doi: 10.1016/0021-9991(91)90135-8 – volume: 11 start-page: 1271 year: 1977 ident: 10.1016/S0045-7825(98)00050-4_BIB14 article-title: Diffraction and refraction of surface waves using finite and infinite elements publication-title: Int. J. Numer. Methods Engrg. doi: 10.1002/nme.1620110808 – volume: 3 start-page: 77 year: 1987 ident: 10.1016/S0045-7825(98)00050-4_BIB18 article-title: A simple wave envelope element example publication-title: Comm. Appl. Numer. Methods doi: 10.1002/cnm.1630030113 – volume: 8 start-page: 125 year: 1991 ident: 10.1016/S0045-7825(98)00050-4_BIB21 article-title: Infinite elements for dynamic problems: Part 2 publication-title: Engrg. Comput. doi: 10.1108/eb023830 – volume: 96 start-page: 2798 year: 1994 ident: 10.1016/S0045-7825(98)00050-4_BIB24 article-title: A three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion publication-title: J. Acoust. Soc. Am. doi: 10.1121/1.411286 – volume: 76 start-page: 595 year: 1981 ident: 10.1016/S0045-7825(98)00050-4_BIB6 article-title: A note on the utility of a wave envelope approach in finite element duct transmission studies publication-title: J. Sound Vib. doi: 10.1016/0022-460X(81)90273-X – volume: 137 start-page: 239 issue: 3–4 year: 1997 ident: 10.1016/S0045-7825(98)00050-4_BIB40 article-title: Solution of 3D Laplace and Helmholtz equations in exterior domains using hp-infinite elements publication-title: Comput. Methods Appl. Mech. Engrg. – volume: 3 start-page: 507 year: 1983 ident: 10.1016/S0045-7825(98)00050-4_BIB3 article-title: Wave envelope and infinite elements for acoustical radiation publication-title: Int. J. Numer. Methods Fluids doi: 10.1002/fld.1650030506 – volume: 9 start-page: 115 year: 1956 ident: 10.1016/S0045-7825(98)00050-4_BIB61 article-title: An expansion theorem for electromagnetic fields publication-title: Comm. Pure Appl. Math. doi: 10.1002/cpa.3160090202 – volume: 143 start-page: 13 year: 1997 ident: 10.1016/S0045-7825(98)00050-4_BIB32 article-title: High-order boundary conditions and finite elements for infinite domains publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/S0045-7825(96)01150-4 |
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