Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Inverse Problems Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

10. Some Numerical Methods

verfasst von : Victor Isakov

Erschienen in: Inverse Problems for Partial Differential Equations

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this chapter, we will briefly review some popular numerical methods widely used in practice. Of course it is not a comprehensive collection. We will demonstrate certain methods that are simple and widely used or, in our opinion, interesting and promising both theoretically and numerically. We observe that most of these methods have not been justified and in some cases even not rigorously tested numerically.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Inverse Parabolic Problems
Literatur
[ADN]
Agmon, S., Douglis, A., Nirenberg, L. Estimates near the boundary for the solutions of elliptic differential equations satisfying general boundary values, I. Comm. Pure Appl. Math., 12 (1959), 623–727.MathSciNetCrossRefMATH
[Be3]
[BDGM]
Borcea, L., Druskin, V., Guevara Vasquez, F., Mamonov, A. Resistor network approaches to electrical impedance tomography. In “Inside Out II”, MSRI Publ., Cambridge Univ. Press, 60 (2012), 54–118.
[BuO]
Burger, M., Osher, S. A survey on level set methods for inverse problems and optimal design. Eur. J. Appl. Math., 16 (2005), 263–301.MathSciNetCrossRefMATH
[C]
Calderon, A.P. On an inverse boundary value problem. “Seminar on numerical Analysis and Its Applications to Continuum Physics”, Rio de Janeiro, 1980, 65–73.
[ChIN]
Cheney, M., Isaacson, D., Newell, J.C. Electrical impedance tomography SIAM Rew., 41 (1999), 85–101.
[CoHP]
Colton, D., Haddar, H., Piana, M. The linear sampling method in inverse electromagnetic scattering theory. Inverse Problems, 19 (2003), S105–137.MathSciNetCrossRefMATH
[CoK]
Colton, D., Kirsch, A. A simple method for solving inverse scattering problems in the resonance region. Inverse Problems, 12 (1996), 383–395.MathSciNetCrossRefMATH
[CoKr]
Colton, D., Kress, R. Inverse Acoustic and Electromagnetic Scattering Theory. Appl. Math. Sc., 93, Springer Verlag, 2013.
[CuM]
Curtis, E., Morrow, J. Inverse Problems for electrical networks. World Scientific, 2000.CrossRefMATH
[DIVW]
DeLillo, T., Isakov, V., Valdivia, N., Wang, L. The detection of surface vibrations from interior acoustic measurements. Inverse Problems, 19 (2003), 507–525.MathSciNetCrossRefMATH
[DoS]
Dobson, D., Santosa, F. Resolution and stability analysis of an inverse problem in electrical impedance tomography. SIAM J. Appl. Math., 54 (1994), 1542–1560.MathSciNetCrossRefMATH
[DrK]
Druskin, V., Knizhnerman, L. Gaussian spectral rules for the three-point second differences. I. A two-point positive definite problem in a semiinfinite domain. SIAM J. Numer. Anal., 37 (2000), 403–422.
[ET]
Ekeland, I., Temam, R. Convex Analysis and Variational Problems. North-Holland, 1976.MATH
[ElI2]
[HrI]
Hrycak, T., Isakov, V. Increased stability in the continuation of solutions of the Helmholtz equation. Inverse Problems, 20 (2004), 697–712.MathSciNetCrossRefMATH
[Ik]
[Is3]
Isakov, V. On uniqueness of recovery of a discontinuous conductivity coefficient. Comm. Pure Appl. Math. 41 (1988), 865–877.MathSciNetCrossRefMATH
[Is4]
Isakov, V. Inverse Source Problems. Math. Surveys and Monographs Series, Vol. 34, AMS, Providence, R.I., 1990.
[Is5]
[IsK]
Isakov, V., Kindermann, S. Subspaces of stability in the Cauchy problem for the Helmholtz equation. Meth. Appl. Anal., 18 (2011), 1–30.MathSciNetMATH
[IsLW]
Isakov, V., Lai, R.-Y., Wang, J.-N. Increasing stability for the Conductivity and Attenuation Coefficients. SIAM J. Math. Anal, 48 (2016), 569–594.MathSciNetCrossRefMATH
[IsLQ]
Isakov, V., Leung, S., Qian, J. A three-dimensional inverse gravimetry problem for ice with snow caps. Inv. Probl. Imag., 7 (2013), 523–545.MathSciNetCrossRefMATH
[KirK]
[KirG]
Kirsch, A., Grinberg, N. The Factorization Method for Inverse Problems. Oxford Univ. Press, New York, 2008.MATH
[KlR]
Klibanov, M.V., Rakesh. Numerical solution of a time- like Cauchy problem for the wave equation. Math. Meth. Appl. Sc., 15 (1992), 559–570.
[KlT]
Klibanov, M.V., Timonov, A. Carleman Estimates for Coefficient Inverse Problems and Numerical Applications. VSP, Utrecht, The Netherlands, 2004.CrossRefMATH
[KoM]
Kohn, R., McKenney, A. Numerical implementation of a variational method for electrical impedance tomography. Inverse Problems, 9 (1990), 389–414.MathSciNetCrossRefMATH
[KoV3]
Kohn, R., Vogelius, M. Relaxation of a variational method for impedance computed tomography. Comm. Pure Appl. Math., 40 (1987), 745–777.MathSciNetCrossRefMATH
[KozM]
Kozlov, V.A., Maz’ya, V.G. On iterative procedures for solving ill-posed problems that preserve differential equations. Leningrad Math. J., 1 (1990), 1207–1228.MathSciNetMATH
[Kr]
Krein, M. On inverse problems for an inhomogeneous string. Dokl. Akad. Nauk SSSR, 82 (1952), 669–672.
[KuS]
[KwSY]
Kwon, O., Seo, J.K., Yoon, J.-R. A Real-Time Algorithm for Location Search of Discontinuous Conductivities with One Measurement. Comm. Pure Appl. Math., 55 (2002), 1–29.MathSciNetCrossRefMATH
[McL]
McLean, W. Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, 2000.MATH
[Mor]
Morrey, C.B., Jr. Multiple Integrals in the Calculus of Variations. Springer, 1966.MATH
[Po]
Potthast, R. Point Sources and Multi poles in Inverse Scattering Theory. London, Chapman and Hill, 2001.CrossRefMATH
[PoSK]
Potthast, R., Sylvester, J., Kusiak, S. A ’range test’ for determining scatterers with unknown physical properties. Inverse Problems, 19 (2003), 533–547.MathSciNetCrossRefMATH
[SaV]
Santosa, F., Vogelius, M. A Back projection Algorithm for Electrical Impedance Tomography. SIAM J. of Appl Math., 50 (1990), 216–244.CrossRefMATH
[SoCII]
Somersalo, E., Cheney, M., Isaacson, D., Isaacson, E. Layer-stripping: a direct numerical method for impedance imaging. Inverse Problems, 7 (1991), 899–926.MathSciNetCrossRefMATH
[Sy2]
Sylvester, J. A Convergent Layer Stripping Algorithm for the Radially Symmetric Impedance Tomography Problem. Comm. Part. Diff. Equat., 17 (1992), 1955–1994.MathSciNetCrossRefMATH
[Wu]
Wu, S. The Helmholtz Equation Least Squares Theory for Reconstructing and Predicting Acoustic Radiation. Springer, 2015.MATH
Metadaten
Titel
Some Numerical Methods
verfasst von
Victor Isakov
Copyright-Jahr
2017
Buch
Inverse Problems for Partial Differential Equations

Print ISBN: 978-3-319-51657-8

Electronic ISBN: 978-3-319-51658-5

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-51658-5_10