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2021 | OriginalPaper | Buchkapitel

1. Motivation: The Cavity Problem

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Abstract

This chapter gives a brief overview of the historircal context and the state-of-the-art relevant for the development of isogeometric boundary element methods for electromagnetic problems.

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Literatur
1.
Zurück zum Zitat Aune B, Bandelmann R, Bloess D, Bonin B, Bosotti A, Champion M, Crawford C, Deppe G, Dwersteg B, Edwards DA, Edwards HT, Ferrario M, Fouaidy M, Gall P-D, Gamp A, Gössel A, Graber J, Hubert D, Hüning M, Juillard M, Junquera T, Kaiser H, Kreps G, Kuchnir M, Lange R, Leenen M, Liepe M, Lilje L, Matheisen A, Möller W-D, Mosnier A, Padamsee H, Pagani C, Pekeler M, Peters H-B, Peters O, Proch D, Rehlich K, Reschke D, Safa H, Schilcher T, Schmuser P, Sekutowicz J, Simrock S, Singer W, Tigner M, Trines D, Twarowski K, Weichert G, Weisend J, Wojtkiewicz J, Wolff S, Zapfe K (2000) Superconducting TESLA cavities. Phys Rev Accel Beams 3(9):092001CrossRef Aune B, Bandelmann R, Bloess D, Bonin B, Bosotti A, Champion M, Crawford C, Deppe G, Dwersteg B, Edwards DA, Edwards HT, Ferrario M, Fouaidy M, Gall P-D, Gamp A, Gössel A, Graber J, Hubert D, Hüning M, Juillard M, Junquera T, Kaiser H, Kreps G, Kuchnir M, Lange R, Leenen M, Liepe M, Lilje L, Matheisen A, Möller W-D, Mosnier A, Padamsee H, Pagani C, Pekeler M, Peters H-B, Peters O, Proch D, Rehlich K, Reschke D, Safa H, Schilcher T, Schmuser P, Sekutowicz J, Simrock S, Singer W, Tigner M, Trines D, Twarowski K, Weichert G, Weisend J, Wojtkiewicz J, Wolff S, Zapfe K (2000) Superconducting TESLA cavities. Phys Rev Accel Beams 3(9):092001CrossRef
2.
Zurück zum Zitat Wiedemann H (2007) Particle accelerator physics, 3rd edn. Springer, Berlin Wiedemann H (2007) Particle accelerator physics, 3rd edn. Springer, Berlin
3.
Zurück zum Zitat Georg N, Ackermann W, Corno J, Schöps S (2019) Uncertainty quantification for Maxwell’s eigenproblem based on isogeometric analysis and mode tracking. Comput Methods Appl Mech Eng 350:228–244MathSciNetCrossRef Georg N, Ackermann W, Corno J, Schöps S (2019) Uncertainty quantification for Maxwell’s eigenproblem based on isogeometric analysis and mode tracking. Comput Methods Appl Mech Eng 350:228–244MathSciNetCrossRef
4.
Zurück zum Zitat Weiland T, Timm M, Munteanu I (2008) A practical guide to 3-D simulation. IEEE Microwave Mag 9(6):62–75CrossRef Weiland T, Timm M, Munteanu I (2008) A practical guide to 3-D simulation. IEEE Microwave Mag 9(6):62–75CrossRef
5.
Zurück zum Zitat Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195MathSciNetCrossRef Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195MathSciNetCrossRef
6.
Zurück zum Zitat Beyn W-J (2012) An integral method for solving nonlinear eigenvalue problems. Linear Algebra Appl 436(10):3839–3863. Special Issue dedicated to Heinrich Voss’s 65th birthday Beyn W-J (2012) An integral method for solving nonlinear eigenvalue problems. Linear Algebra Appl 436(10):3839–3863. Special Issue dedicated to Heinrich Voss’s 65th birthday
7.
Zurück zum Zitat Cheng AH-D, Cheng DT (2005) Heritage and early history of the boundary element method. Eng Anal with Bound Elem 29(3):268–302CrossRef Cheng AH-D, Cheng DT (2005) Heritage and early history of the boundary element method. Eng Anal with Bound Elem 29(3):268–302CrossRef
8.
Zurück zum Zitat Townsend A (2014) On the spline: a brief history of the computational curve. Int J Inter Arch + Spatial Design 2(3):48–59 Townsend A (2014) On the spline: a brief history of the computational curve. Int J Inter Arch + Spatial Design 2(3):48–59
9.
Zurück zum Zitat Rautio J (2014) The long road to Maxwell’s equations. IEEE Spect 51(12):36–56CrossRef Rautio J (2014) The long road to Maxwell’s equations. IEEE Spect 51(12):36–56CrossRef
10.
Zurück zum Zitat Ritz W (1909) Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik. Journal für reine und angewandte Mathematik 135:1–61MathSciNetMATH Ritz W (1909) Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik. Journal für reine und angewandte Mathematik 135:1–61MathSciNetMATH
11.
Zurück zum Zitat Galerkin BG (1915) Rods and plates. Series occurring in various questions concerning the elasticequilibrium of rods and plates. Engineers Bulletin (Vestnik Inzhenerov) 19:897–908 In Russian Galerkin BG (1915) Rods and plates. Series occurring in various questions concerning the elasticequilibrium of rods and plates. Engineers Bulletin (Vestnik Inzhenerov) 19:897–908 In Russian
12.
Zurück zum Zitat Sobolev SL (1936) Méthode nouvelle à résoudre le problème de Cauchy pour les équations linéaires hyperboliques normales. Matematicheskiĭ Sbornik 1 43(1):39–72 Sobolev SL (1936) Méthode nouvelle à résoudre le problème de Cauchy pour les équations linéaires hyperboliques normales. Matematicheskiĭ Sbornik 1 43(1):39–72
13.
Zurück zum Zitat Courant R (1943) Variational methods for the solution of problems of equilibrium and vibrations. Bull Amer Math Soc 49:1–23MathSciNetCrossRef Courant R (1943) Variational methods for the solution of problems of equilibrium and vibrations. Bull Amer Math Soc 49:1–23MathSciNetCrossRef
15.
Zurück zum Zitat Green G (1828) An essay on the application of mathematical analysis to the theories of electricity and magnetism. George Green, Göteborg Green G (1828) An essay on the application of mathematical analysis to the theories of electricity and magnetism. George Green, Göteborg
16.
Zurück zum Zitat Stratton JA (1941) Electromagnetic theory. IEEE Press, PiscatawayMATH Stratton JA (1941) Electromagnetic theory. IEEE Press, PiscatawayMATH
17.
Zurück zum Zitat Rjasanow S (1998) The structure of the boundary element matrix for the threedimensional Dirichlet problem in elasticity. Numer Linear Algebra Appl 5(3):203–217MathSciNetCrossRef Rjasanow S (1998) The structure of the boundary element matrix for the threedimensional Dirichlet problem in elasticity. Numer Linear Algebra Appl 5(3):203–217MathSciNetCrossRef
18.
19.
Zurück zum Zitat Schoenberg IJ (1946) Contributions to the problem of approximation of equidistant data by analytic functions, Parts A and B. Appl Math 4:45–99 Schoenberg IJ (1946) Contributions to the problem of approximation of equidistant data by analytic functions, Parts A and B. Appl Math 4:45–99
20.
Zurück zum Zitat de Boor C (2001) A practical guide to splines, vol 27, Revised edn. Applied mathematical sciences. Springer, New York de Boor C (2001) A practical guide to splines, vol 27, Revised edn. Applied mathematical sciences. Springer, New York
21.
Zurück zum Zitat de Casteljau PdF (1963) Courbes et surfaces à Pôles. Technical Report, Paris, Citröen de Casteljau PdF (1963) Courbes et surfaces à Pôles. Technical Report, Paris, Citröen
22.
23.
Zurück zum Zitat Piegl L, Tiller W (1987) Curve and surface constructions using rational B-splines. Comput-Aided Design 19(9):485–498CrossRef Piegl L, Tiller W (1987) Curve and surface constructions using rational B-splines. Comput-Aided Design 19(9):485–498CrossRef
24.
Zurück zum Zitat Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis: toward integration of CAD and FEA. Wiley, New YorkCrossRef Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis: toward integration of CAD and FEA. Wiley, New YorkCrossRef
25.
Zurück zum Zitat Harbrecht H (2011) Wavelet Galerkin schemes for the boundary element method in three dimensions. Dissertation. Technische Universität Chemnitz Harbrecht H (2011) Wavelet Galerkin schemes for the boundary element method in three dimensions. Dissertation. Technische Universität Chemnitz
26.
Zurück zum Zitat Boggs PT, Althsuler A, Larzelere AR, Walsh EJ, Clay RL, Hardwick MF (2005) DART system analysis. Technical report, Sandia National Laboratories Boggs PT, Althsuler A, Larzelere AR, Walsh EJ, Clay RL, Hardwick MF (2005) DART system analysis. Technical report, Sandia National Laboratories
27.
Zurück zum Zitat Bontinck Z, Corno J, De Gersem H, Kurz S, Pels A, Schöps S, Wolf F, de Falco C, Dölz J, Vázquez R, Römer U (2017) Recent advances of isogeometric analysis in computational electromagnetics. In: ICS Newsletter (International Compumag Society) 3. arXiv:1709.06004 Bontinck Z, Corno J, De Gersem H, Kurz S, Pels A, Schöps S, Wolf F, de Falco C, Dölz J, Vázquez R, Römer U (2017) Recent advances of isogeometric analysis in computational electromagnetics. In: ICS Newsletter (International Compumag Society) 3. arXiv:​1709.​06004
28.
Zurück zum Zitat Buffa A, Sangalli G, Vázquez R (2013) Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations. J Comput Phys 257(Part B.0):1291–1320 Buffa A, Sangalli G, Vázquez R (2013) Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations. J Comput Phys 257(Part B.0):1291–1320
29.
Zurück zum Zitat Corno J, de Falco C, De Gersem H, Schöps S (2016) Isogeometric simulation of Lorentz detuning in superconducting accelerator cavities. Comput Phys Commun 201:1–7MathSciNetCrossRef Corno J, de Falco C, De Gersem H, Schöps S (2016) Isogeometric simulation of Lorentz detuning in superconducting accelerator cavities. Comput Phys Commun 201:1–7MathSciNetCrossRef
30.
Zurück zum Zitat Beer G, Mallardo V, Ruocco E, Marussig B, Zechner J, Dunser C, Fries T-P (2017) Isogeometric boundary element analysis with elasto-plastic inclusions. Part 2: 3-D problems. Comput Methods Appl Mech Eng 315(Supplement C):418–433 Beer G, Mallardo V, Ruocco E, Marussig B, Zechner J, Dunser C, Fries T-P (2017) Isogeometric boundary element analysis with elasto-plastic inclusions. Part 2: 3-D problems. Comput Methods Appl Mech Eng 315(Supplement C):418–433
31.
Zurück zum Zitat Simpson RN, Bordas S, Trevelyan J, Rabczuk T (2012) A two-dimensional isogeometric boundary element method for elastostatic analysis. Comput Methods Appl Mech Eng 209(212):87–100MathSciNetCrossRef Simpson RN, Bordas S, Trevelyan J, Rabczuk T (2012) A two-dimensional isogeometric boundary element method for elastostatic analysis. Comput Methods Appl Mech Eng 209(212):87–100MathSciNetCrossRef
32.
Zurück zum Zitat Takahashi T, Matsumoto T (2012) An application of fast multipole method to isogeometric boundary element method for Laplace equation in two dimensions. Eng Anal Bound Elem 36(12):1766–1775MathSciNetCrossRef Takahashi T, Matsumoto T (2012) An application of fast multipole method to isogeometric boundary element method for Laplace equation in two dimensions. Eng Anal Bound Elem 36(12):1766–1775MathSciNetCrossRef
33.
Zurück zum Zitat Monk P (2003) Finite element methods for Maxwell’s equations. Oxford University Press, OxfordCrossRef Monk P (2003) Finite element methods for Maxwell’s equations. Oxford University Press, OxfordCrossRef
34.
Zurück zum Zitat Buffa A, Sangalli G, Vázquez R (2010) Isogeometric analysis in electromagnetics: B-splines approximation. Comp Methods Appl Mech Eng 199:1143–1152MathSciNetCrossRef Buffa A, Sangalli G, Vázquez R (2010) Isogeometric analysis in electromagnetics: B-splines approximation. Comp Methods Appl Mech Eng 199:1143–1152MathSciNetCrossRef
35.
Zurück zum Zitat Weggler L (2011) High order boundary element methods. Dissertation. Universitat des Saarlandes, Saarbrücken Weggler L (2011) High order boundary element methods. Dissertation. Universitat des Saarlandes, Saarbrücken
36.
Zurück zum Zitat Hiptmair R, Kielhorn L (2012) BETL-a generic boundary element template library. Technical Report, Seminar for Applied Mathematics, ETH Zurich, pp 2012–36 Hiptmair R, Kielhorn L (2012) BETL-a generic boundary element template library. Technical Report, Seminar for Applied Mathematics, ETH Zurich, pp 2012–36
37.
Zurück zum Zitat Śmigaj W, Betcke T, Arridge S, Phillips J, Schweiger M (2015) Solving boundary integral problems with BEM++. ACM Trans Math Softw 41(2):1–40MathSciNetCrossRef Śmigaj W, Betcke T, Arridge S, Phillips J, Schweiger M (2015) Solving boundary integral problems with BEM++. ACM Trans Math Softw 41(2):1–40MathSciNetCrossRef
38.
Zurück zum Zitat Li J, Dault D, Zhao R, Liu B, Tong Y, Shanker B (2015) Isogeometric analysis of integral equations using subdivision. In: 2015 IEEE international symposium on antennas and propagation USNC/URSI national radio science meeting, pp 153–154 Li J, Dault D, Zhao R, Liu B, Tong Y, Shanker B (2015) Isogeometric analysis of integral equations using subdivision. In: 2015 IEEE international symposium on antennas and propagation USNC/URSI national radio science meeting, pp 153–154
39.
Zurück zum Zitat Catmull E, Clark J (1978) Recursively generated B-spline surfaces on arbitrary topological meshes. Comput Aided Design 10(6):350–355CrossRef Catmull E, Clark J (1978) Recursively generated B-spline surfaces on arbitrary topological meshes. Comput Aided Design 10(6):350–355CrossRef
40.
Zurück zum Zitat Simpson R, Scott M, Taus M, Thomas D, Lian H (2014) Acoustic isogeometric boundary element analysis. Comput Methods Appl Mech Eng 269:265–290MathSciNetCrossRef Simpson R, Scott M, Taus M, Thomas D, Lian H (2014) Acoustic isogeometric boundary element analysis. Comput Methods Appl Mech Eng 269:265–290MathSciNetCrossRef
41.
Zurück zum Zitat Dölz J, Harbrecht H, Kurz S, Schöps S, Wolf F (2018) A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems. Comput Methods Appl Mech Eng 330(Supplement C):83–101 Dölz J, Harbrecht H, Kurz S, Schöps S, Wolf F (2018) A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems. Comput Methods Appl Mech Eng 330(Supplement C):83–101
42.
Zurück zum Zitat Simpson R, Liu Z, Vázquez R, Evans J (2018) An isogeometric boundary element method for electromagnetic scattering with compatible B-spline discretizations. J Comput Phys 362:264–289MathSciNetCrossRef Simpson R, Liu Z, Vázquez R, Evans J (2018) An isogeometric boundary element method for electromagnetic scattering with compatible B-spline discretizations. J Comput Phys 362:264–289MathSciNetCrossRef
43.
Zurück zum Zitat Dölz J, Kurz S, Schöps S, Wolf F (2019) Isogeometric boundary elements in electromagnetism: rigorous analysis, fast methods, and examples. SIAM J Sci Comput 41(5):B983–B1010MathSciNetCrossRef Dölz J, Kurz S, Schöps S, Wolf F (2019) Isogeometric boundary elements in electromagnetism: rigorous analysis, fast methods, and examples. SIAM J Sci Comput 41(5):B983–B1010MathSciNetCrossRef
44.
Zurück zum Zitat Kurz S, Schöps S, Wolf F (2019) Towards a spectral method of moments using computer aided design Kurz S, Schöps S, Wolf F (2019) Towards a spectral method of moments using computer aided design
45.
Zurück zum Zitat Dölz J, Kurz S, Schöps S, Wolf F (2019) A numerical comparison of an isogeometric and a parametric higher order Raviart-Thomas approach to the electric field integral equation. IEEE Trans Antennas Propag 68(1):593–597CrossRef Dölz J, Kurz S, Schöps S, Wolf F (2019) A numerical comparison of an isogeometric and a parametric higher order Raviart-Thomas approach to the electric field integral equation. IEEE Trans Antennas Propag 68(1):593–597CrossRef
46.
Zurück zum Zitat Dölz J, Harbrecht H, Kurz S, Multerer M, Schöps S, Wolf F (2019) Bembel. The C++ boundary element engineering library. Official website, www.bembel.eu. Accessed 20 Aug 2019 Dölz J, Harbrecht H, Kurz S, Multerer M, Schöps S, Wolf F (2019) Bembel. The C++ boundary element engineering library. Official website, www.​bembel.​eu. Accessed 20 Aug 2019
48.
Zurück zum Zitat Dölz J, Harbrecht H, Kurz S, Multerer M, Schöps S, Wolf F (2020) Bembel: the fast isogeometric boundary element C++ library for laplace, Helmholtz, and Electric Wave Equation. In: SoftwareX 11, p 10476 Dölz J, Harbrecht H, Kurz S, Multerer M, Schöps S, Wolf F (2020) Bembel: the fast isogeometric boundary element C++ library for laplace, Helmholtz, and Electric Wave Equation. In: SoftwareX 11, p 10476
49.
Zurück zum Zitat Schobert DT, Eibert TF (2010) A multilevel interpolating fast integral solver with fast Fourier transform acceleration. In: 2010 URSI international symposium on electromagnetic theory, pp 520–523 Schobert DT, Eibert TF (2010) A multilevel interpolating fast integral solver with fast Fourier transform acceleration. In: 2010 URSI international symposium on electromagnetic theory, pp 520–523
50.
Zurück zum Zitat Schobert DT, Eibert TF (2012) Fast integral equation solution by multilevel Green’s function interpolation combined with multilevel fast multipole method. IEEE Trans Antennas Propag 60(9):4458–4463MathSciNetCrossRef Schobert DT, Eibert TF (2012) Fast integral equation solution by multilevel Green’s function interpolation combined with multilevel fast multipole method. IEEE Trans Antennas Propag 60(9):4458–4463MathSciNetCrossRef
51.
Zurück zum Zitat Dölz J, Harbrecht H, Peters M (2016) An interpolation-based fast multipole method for higher-order boundary elements on parametric surfaces. Int J Numer Methods Eng 108(13):1705–1728MathSciNetCrossRef Dölz J, Harbrecht H, Peters M (2016) An interpolation-based fast multipole method for higher-order boundary elements on parametric surfaces. Int J Numer Methods Eng 108(13):1705–1728MathSciNetCrossRef
52.
Zurück zum Zitat Hackbusch W (2015) Hierarchical matrices: algorithms and analysis. Springer, BerlinCrossRef Hackbusch W (2015) Hierarchical matrices: algorithms and analysis. Springer, BerlinCrossRef
53.
Zurück zum Zitat Harbrecht H, Peters M (2013) Comparison of fast boundary element methods on parametric surfaces. Comput Methods Appl Mech Eng 261:39–55MathSciNetCrossRef Harbrecht H, Peters M (2013) Comparison of fast boundary element methods on parametric surfaces. Comput Methods Appl Mech Eng 261:39–55MathSciNetCrossRef
54.
Zurück zum Zitat Marussig B, Zechner J, Beer G, Fries T-P (2015) Fast isogeometric boundary element method based on independent field approximation. Comput Methods Appl Mech Eng 284:458–488. Isogeometric Analysis Special Issue Marussig B, Zechner J, Beer G, Fries T-P (2015) Fast isogeometric boundary element method based on independent field approximation. Comput Methods Appl Mech Eng 284:458–488. Isogeometric Analysis Special Issue
55.
Zurück zum Zitat Jensen TK, Christensen O, Pedersen M (2003) On adaptive wavelet-based methods for the Maxwell equations. Technical University of Denmark, Kongens Lyngby, Denmark Jensen TK, Christensen O, Pedersen M (2003) On adaptive wavelet-based methods for the Maxwell equations. Technical University of Denmark, Kongens Lyngby, Denmark
56.
Zurück zum Zitat Dahmen W, Harbrecht H, Schneider R (2006) Compression techniques for boundary integral equations. Asymptotically optimal complexity estimates. SIAM J Numer Anal 43(6):2251–2271 Dahmen W, Harbrecht H, Schneider R (2006) Compression techniques for boundary integral equations. Asymptotically optimal complexity estimates. SIAM J Numer Anal 43(6):2251–2271
57.
Zurück zum Zitat Buffa A, Vázquez RH, Sangalli G, da Veiga LB (2015) Approximation estimates for isogeometric spaces in multipatch geometries. Numer Methods Partial Diff Equ 31(2):422–438MathSciNetCrossRef Buffa A, Vázquez RH, Sangalli G, da Veiga LB (2015) Approximation estimates for isogeometric spaces in multipatch geometries. Numer Methods Partial Diff Equ 31(2):422–438MathSciNetCrossRef
58.
Zurück zum Zitat Buffa A, Dölz J, Kurz S, Schöps S, Vázquez R, Wolf F (2020) Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis. Numerische Mathematik 144:201–236MathSciNetCrossRef Buffa A, Dölz J, Kurz S, Schöps S, Vázquez R, Wolf F (2020) Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis. Numerische Mathematik 144:201–236MathSciNetCrossRef
59.
Zurück zum Zitat Xin J (2011) Boundary element approximation for Maxwell’s eigenvalue problem. Dissertation. Karlsruhe Institute of Technology, Karlsruhe, Germany Xin J (2011) Boundary element approximation for Maxwell’s eigenvalue problem. Dissertation. Karlsruhe Institute of Technology, Karlsruhe, Germany
60.
Zurück zum Zitat Mehrmann V, Voss H (2004) Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods. GAMM-Mitteilungen 27(2):121–152MathSciNetCrossRef Mehrmann V, Voss H (2004) Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods. GAMM-Mitteilungen 27(2):121–152MathSciNetCrossRef
61.
Zurück zum Zitat Asakura J, Sakurai T, Tadano H, Ikegami T, Kimura K (2009) A numerical method for nonlinear eigenvalue problems using contour integrals. JSIAM Lett 1:52–55MathSciNetCrossRef Asakura J, Sakurai T, Tadano H, Ikegami T, Kimura K (2009) A numerical method for nonlinear eigenvalue problems using contour integrals. JSIAM Lett 1:52–55MathSciNetCrossRef
62.
Zurück zum Zitat Imakura A, Du L, Sakurai T (2016) Relationships among contour integral-based methods for solving generalized eigenvalue problems. Jpn J Ind Appl Math 33(3):721–750MathSciNetCrossRef Imakura A, Du L, Sakurai T (2016) Relationships among contour integral-based methods for solving generalized eigenvalue problems. Jpn J Ind Appl Math 33(3):721–750MathSciNetCrossRef
63.
Zurück zum Zitat Elasmi M (2017) Boundary element method for Maxwell’s eigenvalue problems in TESLA cavities using the contour integral method. Master’s Thesis. Universität des Saarlandes, Saarbrücken Elasmi M (2017) Boundary element method for Maxwell’s eigenvalue problems in TESLA cavities using the contour integral method. Master’s Thesis. Universität des Saarlandes, Saarbrücken
64.
Zurück zum Zitat Unger G (2017) Convergence analysis of a Galerkin boundary element method for electromagnetic eigenvalue problems. Technical Report 2017/2, Institute of Computational Mathematics, Graz University of Technology Unger G (2017) Convergence analysis of a Galerkin boundary element method for electromagnetic eigenvalue problems. Technical Report 2017/2, Institute of Computational Mathematics, Graz University of Technology
Metadaten
Titel
Motivation: The Cavity Problem
verfasst von
Dr. Felix Wolf
Copyright-Jahr
2021
DOI
https://doi.org/10.1007/978-3-030-61939-8_1

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