An hp-adaptive finite element method for electromagnetics. Part 3: A three-dimensional infinite element for Maxwell's equations
This paper is a continuation of Reference [26] (Cecot, Demkowicz and Rachowicz, Computer Methods in Applied Mechanics and Engineering 2000; 188: 625–643) and describes an implementation of the infinite element for three‐dimensional, time harmonic Maxwell's equations, proposed in Reference [15]...
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| Vydané v: | International journal for numerical methods in engineering Ročník 57; číslo 7; s. 899 - 921 |
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| Jazyk: | English |
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Chichester, UK
John Wiley & Sons, Ltd
21.06.2003
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| ISSN: | 0029-5981, 1097-0207 |
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| Abstract | This paper is a continuation of Reference [26] (Cecot, Demkowicz and Rachowicz, Computer Methods in Applied Mechanics and Engineering 2000; 188: 625–643) and describes an implementation of the infinite element for three‐dimensional, time harmonic Maxwell's equations, proposed in Reference [15] (Demkowicz and Pal, Computer Methods in Applied Mechanics and Engineering 1998; 164: 77–94). The element is compatible with the hp finite element discretizations for Maxwell's equations in bounded domains reported in References [16–18] (Computer Methods in Applied Mechanics and Engineering 1998; 152: 103–124, 1999; 169: 331–344, 2000; 187: 307–337). Copyright © 2003 John Wiley & Sons, Ltd. |
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| AbstractList | This paper is a continuation of Reference [26] (Cecot, Demkowicz and Rachowicz, Computer Methods in Applied Mechanics and Engineering 2000; 188: 625-643) and describes an implementation of the infinite element for three-dimensional, time harmonic Maxwell's equations, proposed in Reference [15] (Demkowicz and Pal, Computer Methods in Applied Mechanics and Engineering 1998; 164: 77-94). The element is compatible with the hp finite element discretizations for Maxwell's equations in bounded domains reported in This paper is a continuation of Reference [26] (Cecot, Demkowicz and Rachowicz, Computer Methods in Applied Mechanics and Engineering 2000; 188 : 625–643) and describes an implementation of the infinite element for three‐dimensional, time harmonic Maxwell's equations, proposed in Reference [15] (Demkowicz and Pal, Computer Methods in Applied Mechanics and Engineering 1998; 164 : 77–94). The element is compatible with the hp finite element discretizations for Maxwell's equations in bounded domains reported in References [16–18] ( Computer Methods in Applied Mechanics and Engineering 1998; 152 : 103–124, 1999; 169 : 331–344, 2000; 187 : 307–337). Copyright © 2003 John Wiley & Sons, Ltd. This paper is a continuation of Reference [26] (Cecot, Demkowicz and Rachowicz, Computer Methods in Applied Mechanics and Engineering 2000; 188: 625–643) and describes an implementation of the infinite element for three‐dimensional, time harmonic Maxwell's equations, proposed in Reference [15] (Demkowicz and Pal, Computer Methods in Applied Mechanics and Engineering 1998; 164: 77–94). The element is compatible with the hp finite element discretizations for Maxwell's equations in bounded domains reported in References [16–18] (Computer Methods in Applied Mechanics and Engineering 1998; 152: 103–124, 1999; 169: 331–344, 2000; 187: 307–337). Copyright © 2003 John Wiley & Sons, Ltd. This paper is a continuation of Reference [26] (Cecot, Demkowicz and Rachowicz, Computer Methods in Applied Mechanics and Engineering 2000; 188: 625-643) and describes an implementation of the infinite element for three-dimensional, time harmonic Maxwell's equations, proposed in Reference [15] (Demkowicz and Pal, Computer Methods in Applied Mechanics and Engineering 1998; 164: 77-94). The element is compatible with the hp finite element discretizations for Maxwell's equations in bounded domains reported in References [16-18] (Computer Methods in Applied Mechanics and Engineering 1998; 152: 103-124, 1999; 169: 331-344, 2000; 187: 307-337). |
| Author | Cecot, W. Demkowicz, L. Rachowicz, W. |
| Author_xml | – sequence: 1 givenname: W. surname: Cecot fullname: Cecot, W. organization: Texas Institute for Computational and Applied Mathematics, The University of Texas at Austin, Austin, TX 78712, U.S.A – sequence: 2 givenname: W. surname: Rachowicz fullname: Rachowicz, W. organization: Texas Institute for Computational and Applied Mathematics, The University of Texas at Austin, Austin, TX 78712, U.S.A – sequence: 3 givenname: L. surname: Demkowicz fullname: Demkowicz, L. email: leszek@ticam.utexas.edu organization: Texas Institute for Computational and Applied Mathematics, The University of Texas at Austin, Austin, TX 78712, U.S.A |
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| Cites_doi | 10.1109/20.34362 10.1016/S0168-9274(98)00020-8 10.1006/jsvi.1994.1048 10.1090/S0025-5718-02-01411-4 10.1016/0045-7825(89)90129-1 10.1090/S0025-5718-00-01229-1 10.1007/BF01389668 10.1016/S0168-9274(98)00025-7 10.1016/S0045-7825(98)00047-4 10.1007/978-3-663-10649-4 10.1002/nme.396 10.1016/0045-7825(95)00987-6 10.1007/PL00005440 10.1006/jcph.1994.1159 10.1016/S0045-7825(98)00161-3 10.1016/S0898-1221(00)00062-6 10.1007/BF02736182 10.1016/S0045-7825(99)00290-X 10.1007/BF01396415 10.1142/2938 10.1016/S0045-7825(97)00184-9 10.1006/jsvi.1994.1136 10.1121/1.411286 10.1016/S0045-7825(99)00137-1 10.1007/978-3-662-02835-3 |
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| References | Demkowicz L, Ihlenburg F. Analysis of a coupled finite-infinite element method for exterior helmholtz problems. Numerische Mathematik 2001; 88:43-73. Bérenger J-P. A perfectly matched layer for the absorption of electromagnetic waves. Journal of Computational Physics 1994; 114:185-200. Demkowicz L, Pal M. An infinite element for Maxwell's equations. Computer Methods in Applied Mechanics and Engineering 1998; 164:77-94. Rachowicz W, Demkowicz L. An hp-adaptive finite element method for electromagnetics. Part 2: A 3D implementation. International Journal for Numerical Methods in Engineering 2002; 53:147-180. Astley RJ, Macaulay GJ, Coyette JP. Mapped wave envelope elements for acoustical radiation and scattering. Journal of Sound and Vibration 1994; 170(1):97-118. Harrington RF. Time-Harmonic Electromagnetic Fields. McGraw-Hill Book Co.: New York, 1961. Demkowicz L, Oden LJT, Rachowicz W, Hardy O. Toward a universal hp adaptive finite element strategy, Part 1. Constrained approximation and data structure. Computer Methods in Applied Mechanics and Engineering 1989; 77:79-112. Vardapetyan L, Demkowicz L. Full-wave analysis of dielectric waveguides at a given frequency. Mathematics of Computation 2003; 72:105-129. Nedelec JC. Mixed finite elements in ℝ3. Numerische Mathematik 1980; 35:315-341. Givoli D, Patlashenko I. Optimal local non-reflecting boundary conditions. Applied Numerical Mathematics 1998; 27:367-384. Leis R. Initial Boundary Value Problems in Mathematical Physics. Teubner: Stuttgart, 1986. Demkowicz L, Vardapetyan L. Modeling of electromagnetic absoption/scattering problems using hp-adaptive finite elements. Computer Methods in Applied Mechanics and Engineering 1998; 152(1-2):103-124. Cecot W, Demkowicz L, Rachowicz W. A two-dimensional infinite element for Maxwell's equations. Computer Methods in Applied Mechanics and Engineering 2000; 188:625-643. Demkowicz L, Rachowicz W, Devloo Ph. A fully automatic hp-adaptivity. Journal of Scientific Computing 2002; 17(1-3):127-155. Colton D, Kress R. Inverse Acoustic and Electromagnetic Scattering. Springer Verlag: Berlin, 1992. Zdunek A, Rachowicz W, Sehlstedt N. Toward hp-adaptive solution of 3D electromagnetic scattering from cavities. IEEE Transactions on Antennas and Propagation, submitted. Gerdes K, Demkowicz L. Solution of 3D-laplace and helmholtz equation in exterior domains using hp infinite elements. Computer Methods in Applied Mechanics and Engineering 1996; 137:239-274. Cremers L, Fyfe KR, Coyette JO. A variable order infinite acoustic wave envelope element. Journal of Sound and Vibrations 1994; 17(4):483-508. Givoli D. Numerical Methods for Problems in Infinite Domains. Elsevier: Amsterdam, 1992. Babuška I, Szabo B. The Finite Element Method. Wiley: New York, 1991. Givoli D. Recent advances in the DtN FE method. Archives of Computational Methods in Engineering 1999; 6(2):71-116. Burnett DS. A three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion. Journal of the Acoustical Society of America 1994; 96:2798-2816. Demkowicz L, Monk P, Vardapetyan L, Rachowicz W. De Rham diagram for hp finite element spaces. Computers and Mathematics with Applications 2000; 39(7-8):29-38. Nedelec JC. A new family of mixed finite elements in ℝ3. Numerische Mathematik 1986; 50:57-81. d'Angelo J, Mayergoyz ID. On the use of local absorbing boundary conditions for RF scattering problems. IEEE Transactions on Magnetics 1989; 25(4):3038-3042. Bettess P. Infinite Elements. Penshaw Press: Sunderland, 1992. Rachowicz W, Demkowicz L. An hp-adaptive finite element method for electromagnetics. Part 1: data structure and constrained approximation. Computer Methods in Applied Mechanics and Engineering 2000; 187(1-2):307-337. Vardapetyan L, Demkowicz L. hp-Adaptive finite elements in electromagnetics. Computer Methods in Applied Mechanics and Engineering 1999; 169:331-344. Monk P, Demkowicz L. Discrete compactness and the approximation of Maxwell's equations in ℝ3. Mathematics of Computation 2001; 70:507-523. Tsynkov SV. Numerical solution of problems on unbounded domains. A review. Applied Numerical Mathematics 1998; 27:465-532. Cessenat M. Mathematical Methods in Electromagnetism. Linear Theory and Applications. World Scientific: London, 1996. 1998; 27 2001; 70 2002; 17 1994; 114 1986; 50 1994; 170 2002; 53 1998 1996 1999; 169 1992 2002 1991 2001; 88 2003; 72 1999; 6 1989; 25 1998; 152 1999 1989; 77 2000; 39 2001 1980; 35 1986 1999; II 1961 2000; 187 2000; 188 1994; 17 1996; 137 1994; 96 1998; 164 Bettess P (e_1_2_1_9_2) 1992 Babuška I (e_1_2_1_36_2) 1991 Demkowicz L (e_1_2_1_37_2) 2002; 17 e_1_2_1_40_2 e_1_2_1_23_2 e_1_2_1_20_2 e_1_2_1_21_2 Rachowicz W (e_1_2_1_22_2) 1999 e_1_2_1_26_2 e_1_2_1_27_2 e_1_2_1_24_2 e_1_2_1_25_2 Givoli D (e_1_2_1_4_2) 1992 e_1_2_1_28_2 e_1_2_1_29_2 Harrington RF (e_1_2_1_33_2) 1961 Zdunek A (e_1_2_1_39_2) e_1_2_1_6_2 e_1_2_1_30_2 e_1_2_1_7_2 e_1_2_1_5_2 e_1_2_1_2_2 e_1_2_1_11_2 e_1_2_1_34_2 e_1_2_1_3_2 e_1_2_1_12_2 e_1_2_1_32_2 e_1_2_1_10_2 e_1_2_1_31_2 e_1_2_1_15_2 e_1_2_1_38_2 e_1_2_1_16_2 e_1_2_1_13_2 e_1_2_1_14_2 e_1_2_1_35_2 e_1_2_1_19_2 e_1_2_1_8_2 e_1_2_1_17_2 e_1_2_1_18_2 |
| References_xml | – reference: Burnett DS. A three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion. Journal of the Acoustical Society of America 1994; 96:2798-2816. – reference: Bettess P. Infinite Elements. Penshaw Press: Sunderland, 1992. – reference: Givoli D. Numerical Methods for Problems in Infinite Domains. Elsevier: Amsterdam, 1992. – reference: Demkowicz L, Oden LJT, Rachowicz W, Hardy O. Toward a universal hp adaptive finite element strategy, Part 1. Constrained approximation and data structure. Computer Methods in Applied Mechanics and Engineering 1989; 77:79-112. – reference: Vardapetyan L, Demkowicz L. hp-Adaptive finite elements in electromagnetics. Computer Methods in Applied Mechanics and Engineering 1999; 169:331-344. – reference: Leis R. Initial Boundary Value Problems in Mathematical Physics. Teubner: Stuttgart, 1986. – reference: Demkowicz L, Ihlenburg F. Analysis of a coupled finite-infinite element method for exterior helmholtz problems. Numerische Mathematik 2001; 88:43-73. – reference: Rachowicz W, Demkowicz L. An hp-adaptive finite element method for electromagnetics. Part 1: data structure and constrained approximation. Computer Methods in Applied Mechanics and Engineering 2000; 187(1-2):307-337. – reference: Vardapetyan L, Demkowicz L. Full-wave analysis of dielectric waveguides at a given frequency. Mathematics of Computation 2003; 72:105-129. – reference: Nedelec JC. A new family of mixed finite elements in ℝ3. Numerische Mathematik 1986; 50:57-81. – reference: d'Angelo J, Mayergoyz ID. On the use of local absorbing boundary conditions for RF scattering problems. IEEE Transactions on Magnetics 1989; 25(4):3038-3042. – reference: Demkowicz L, Monk P, Vardapetyan L, Rachowicz W. De Rham diagram for hp finite element spaces. Computers and Mathematics with Applications 2000; 39(7-8):29-38. – reference: Cecot W, Demkowicz L, Rachowicz W. A two-dimensional infinite element for Maxwell's equations. Computer Methods in Applied Mechanics and Engineering 2000; 188:625-643. – reference: Demkowicz L, Pal M. An infinite element for Maxwell's equations. Computer Methods in Applied Mechanics and Engineering 1998; 164:77-94. – reference: Bérenger J-P. A perfectly matched layer for the absorption of electromagnetic waves. Journal of Computational Physics 1994; 114:185-200. – reference: Tsynkov SV. Numerical solution of problems on unbounded domains. A review. Applied Numerical Mathematics 1998; 27:465-532. – reference: Colton D, Kress R. Inverse Acoustic and Electromagnetic Scattering. Springer Verlag: Berlin, 1992. – reference: Rachowicz W, Demkowicz L. An hp-adaptive finite element method for electromagnetics. Part 2: A 3D implementation. International Journal for Numerical Methods in Engineering 2002; 53:147-180. – reference: Babuška I, Szabo B. The Finite Element Method. Wiley: New York, 1991. – reference: Demkowicz L, Rachowicz W, Devloo Ph. A fully automatic hp-adaptivity. Journal of Scientific Computing 2002; 17(1-3):127-155. – reference: Harrington RF. Time-Harmonic Electromagnetic Fields. McGraw-Hill Book Co.: New York, 1961. – reference: Astley RJ, Macaulay GJ, Coyette JP. Mapped wave envelope elements for acoustical radiation and scattering. Journal of Sound and Vibration 1994; 170(1):97-118. – reference: Givoli D. Recent advances in the DtN FE method. Archives of Computational Methods in Engineering 1999; 6(2):71-116. – reference: Cessenat M. Mathematical Methods in Electromagnetism. Linear Theory and Applications. World Scientific: London, 1996. – reference: Cremers L, Fyfe KR, Coyette JO. A variable order infinite acoustic wave envelope element. Journal of Sound and Vibrations 1994; 17(4):483-508. – reference: Gerdes K, Demkowicz L. Solution of 3D-laplace and helmholtz equation in exterior domains using hp infinite elements. Computer Methods in Applied Mechanics and Engineering 1996; 137:239-274. – reference: Zdunek A, Rachowicz W, Sehlstedt N. Toward hp-adaptive solution of 3D electromagnetic scattering from cavities. IEEE Transactions on Antennas and Propagation, submitted. – reference: Demkowicz L, Vardapetyan L. Modeling of electromagnetic absoption/scattering problems using hp-adaptive finite elements. Computer Methods in Applied Mechanics and Engineering 1998; 152(1-2):103-124. – reference: Givoli D, Patlashenko I. Optimal local non-reflecting boundary conditions. Applied Numerical Mathematics 1998; 27:367-384. – reference: Nedelec JC. Mixed finite elements in ℝ3. Numerische Mathematik 1980; 35:315-341. – reference: Monk P, Demkowicz L. Discrete compactness and the approximation of Maxwell's equations in ℝ3. Mathematics of Computation 2001; 70:507-523. – volume: 17 start-page: 483 issue: 4 year: 1994 end-page: 508 article-title: A variable order infinite acoustic wave envelope element publication-title: Journal of Sound and Vibrations – volume: 39 start-page: 29 issue: 7–8 year: 2000 end-page: 38 article-title: De Rham diagram for hp finite element spaces publication-title: Computers and Mathematics with Applications – article-title: Toward ‐adaptive solution of 3D electromagnetic scattering from cavities publication-title: IEEE Transactions on Antennas and Propagation – volume: 70 start-page: 507 year: 2001 end-page: 523 article-title: Discrete compactness and the approximation of Maxwell's equations in ℝ publication-title: Mathematics of Computation – volume: 96 start-page: 2798 year: 1994 end-page: 2816 article-title: A three‐dimensional acoustic infinite element based on a prolate spheroidal multipole expansion publication-title: Journal of the Acoustical Society of America – volume: 35 start-page: 315 year: 1980 end-page: 341 article-title: Mixed finite elements in ℝ publication-title: Numerische Mathematik – volume: 187 start-page: 307 issue: 1–2 year: 2000 end-page: 337 article-title: An hp‐adaptive finite element method for electromagnetics. Part 1: data structure and constrained approximation publication-title: Computer Methods in Applied Mechanics and Engineering – volume: 164 start-page: 77 year: 1998 end-page: 94 article-title: An infinite element for Maxwell's equations publication-title: Computer Methods in Applied Mechanics and Engineering – year: 2001 – volume: 50 start-page: 57 year: 1986 end-page: 81 article-title: A new family of mixed finite elements in ℝ publication-title: Numerische Mathematik – volume: 27 start-page: 465 year: 1998 end-page: 532 article-title: Numerical solution of problems on unbounded domains. A review publication-title: Applied Numerical Mathematics – year: 1996 – volume: 152 start-page: 103 issue: 1–2 year: 1998 end-page: 124 article-title: Modeling of electromagnetic absoption/scattering problems using ‐adaptive finite elements publication-title: Computer Methods in Applied Mechanics and Engineering – volume: 25 start-page: 3038 issue: 4 year: 1989 end-page: 3042 article-title: On the use of local absorbing boundary conditions for RF scattering problems publication-title: IEEE Transactions on Magnetics – volume: 27 start-page: 367 year: 1998 end-page: 384 article-title: Optimal local non‐reflecting boundary conditions publication-title: Applied Numerical Mathematics – year: 1992 – volume: 188 start-page: 625 year: 2000 end-page: 643 article-title: A two‐dimensional infinite element for Maxwell's equations publication-title: Computer Methods in Applied Mechanics and Engineering – volume: 53 start-page: 147 year: 2002 end-page: 180 article-title: An hp‐adaptive finite element method for electromagnetics. 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| SubjectTerms | Compatibility Computer simulation Discretization Finite element method hp finite elements infinite elements Mathematical analysis Mathematical models Maxwell's equations Three dimensional |
| Title | An hp-adaptive finite element method for electromagnetics. Part 3: A three-dimensional infinite element for Maxwell's equations |
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