Abstract
The skew-derivative problem for harmonic functions in the exterior of an open arc in a plane is considered. This problem models the electric current in a semiconductor film from an electrode of arbitrary shape in the presence of a magnetic field. A numerical method for solving the problem is proposed. The method is based on a boundary-integral-equation approach. The proposed numerical method is tested. The numerical simulation is presented for different values of the parameters and different shapes of the electrode. Physical effects found in numerical experiments are discussed.
Similar content being viewed by others
References
Lifanov IK (1996) Singular integral equations and discrete vortices. Zeist. VSP, International Sceience Publishers, The Netherlands
Lifanov IK, Poltavskii LN, Vainikko GM (2004) Hypersingular integral equations and their applications. CRC Press, Boca Raton
Hall EH (1879) On a new action of the magnet on electric currents. Am J Maths 2:287
Putley EH (1960) The Hall effect and related phenomena. Butterworth, London
Seeger K (1973) Semiconductor physics. Springer, NY
Sze SM (1981) Physics of semiconductor devices. Wiley, NY
Krutitskii PA, Krutitskaya NCh, Malysheva GYu (1999) A problem related to the Hall effect in a semiconductor with an electrode of an arbitrary shape. Math Prob Eng 5:83–95
Gabov SA (1977) An angular potential and its applications. Math USSR Sbornik 32:423–436
Krutitskii PA (1994) Dirichlet problem for the Helmholtz equation outside cuts in a plane. Comp Maths Math Phys 34:1073–1090
Muskhelishvili NI (1968) Singular Integral Equations. Nauka, Moscow and Noordhoff, Groningen (1972)
Krutitskii PA (1994) Neumann problem for the Helmholtz equation outside cuts in a plane. Comp Maths Math Phys 34:1421–1431
Belotserkovskii SM, Lifanov IK (1993) Method of discrete vortices. CRC Press, Boca Raton
Vainikko G (2001) Fast solvers of generalized airfoil equation of index 1. Operator theory: advances and applications 121:498–516
Saranen J, Vainikko G (2002) Periodic integral and pseudodifferential equations with numerical approximation. Springer, Berlin
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Krutitskii, P.A., Kwak, D.Y. & Hyon, Y.K. Numerical treatment of a skew-derivative problem for the Laplace equation in the exterior of an open arc. J Eng Math 59, 25–60 (2007). https://doi.org/10.1007/s10665-006-9058-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10665-006-9058-x