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Numerical modelling of nonlinear electromechanical coupling of an atomic force microscope with finite element method.

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Title: Numerical modelling of nonlinear electromechanical coupling of an atomic force microscope with finite element method.
Authors: Freitag, J.1 freitag@tet.uni-hannover.de, Mathis, W.1
Source: Advances in Radio Science. 2010, Vol. 8, p33-36. 4p. 5 Diagrams.
Subjects: Finite element method, Newton-Raphson method, Differential equations, Numerical analysis, Electromechanical technology
Abstract: In this contribution, an atomic force microscope is modelled and in this context, a non-linear coupled 3-D-boundary value problem is solved numerically using the finite element method. The coupling of this system is done by using the Maxwell stress tensor. In general, an iterative weak coupling is used, where the two physical problems are solved separately. However, this method does not necessarily guarantee convergence of the nonlinear computation. Hence, this contribution shows the possibility of solving the multiphysical problem by a strong coupling, which is also referred to as monolithic approach. The electrostatic field and the mechanical displacements are calculated simultaneously by solving only one system of equation. Since the Maxwell stress tensor depends nonlinearly on the potential, the solution is solved iteratively by the Newton method. [ABSTRACT FROM AUTHOR]
Copyright of Advances in Radio Science is the property of Copernicus Gesellschaft mbH and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Numerical modelling of nonlinear electromechanical coupling of an atomic force microscope with finite element method.
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  Data: <searchLink fieldCode="AR" term="%22Freitag%2C+J%2E%22">Freitag, J.</searchLink><relatesTo>1</relatesTo><i> freitag@tet.uni-hannover.de</i><br /><searchLink fieldCode="AR" term="%22Mathis%2C+W%2E%22">Mathis, W.</searchLink><relatesTo>1</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22Advances+in+Radio+Science%22">Advances in Radio Science</searchLink>. 2010, Vol. 8, p33-36. 4p. 5 Diagrams.
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  Data: <searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Newton-Raphson+method%22">Newton-Raphson method</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+equations%22">Differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Electromechanical+technology%22">Electromechanical technology</searchLink>
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  Data: In this contribution, an atomic force microscope is modelled and in this context, a non-linear coupled 3-D-boundary value problem is solved numerically using the finite element method. The coupling of this system is done by using the Maxwell stress tensor. In general, an iterative weak coupling is used, where the two physical problems are solved separately. However, this method does not necessarily guarantee convergence of the nonlinear computation. Hence, this contribution shows the possibility of solving the multiphysical problem by a strong coupling, which is also referred to as monolithic approach. The electrostatic field and the mechanical displacements are calculated simultaneously by solving only one system of equation. Since the Maxwell stress tensor depends nonlinearly on the potential, the solution is solved iteratively by the Newton method. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Advances in Radio Science is the property of Copernicus Gesellschaft mbH and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.5194/ars-8-33-2010
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        Text: English
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      – SubjectFull: Newton-Raphson method
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      – SubjectFull: Differential equations
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      – SubjectFull: Numerical analysis
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      – SubjectFull: Electromechanical technology
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