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On Detecting the Shape of an Unknown Object in an Electric Field

Tutkimustuotosvertaisarvioitu

Standard

On Detecting the Shape of an Unknown Object in an Electric Field. / Humaloja, Jukka-Pekka; Hämäläinen, Timo; Pohjolainen, Seppo.

Progress in Industrial Mathematics at ECMI 2014. toim. / G. Russo; V. Capasso; G. Nicosia; V. Romano. Springer International Publishing, 2016. (Mathematics in Industry; Vuosikerta 22).

Tutkimustuotosvertaisarvioitu

Harvard

Humaloja, J-P, Hämäläinen, T & Pohjolainen, S 2016, On Detecting the Shape of an Unknown Object in an Electric Field. julkaisussa G Russo, V Capasso, G Nicosia & V Romano (toim), Progress in Industrial Mathematics at ECMI 2014. Mathematics in Industry, Vuosikerta. 22, Springer International Publishing, 1/01/00. https://doi.org/10.1007/978-3-319-23413-7

APA

Humaloja, J-P., Hämäläinen, T., & Pohjolainen, S. (2016). On Detecting the Shape of an Unknown Object in an Electric Field. teoksessa G. Russo, V. Capasso, G. Nicosia, & V. Romano (Toimittajat), Progress in Industrial Mathematics at ECMI 2014 (Mathematics in Industry; Vuosikerta 22). Springer International Publishing. https://doi.org/10.1007/978-3-319-23413-7

Vancouver

Humaloja J-P, Hämäläinen T, Pohjolainen S. On Detecting the Shape of an Unknown Object in an Electric Field. julkaisussa Russo G, Capasso V, Nicosia G, Romano V, toimittajat, Progress in Industrial Mathematics at ECMI 2014. Springer International Publishing. 2016. (Mathematics in Industry). https://doi.org/10.1007/978-3-319-23413-7

Author

Humaloja, Jukka-Pekka ; Hämäläinen, Timo ; Pohjolainen, Seppo. / On Detecting the Shape of an Unknown Object in an Electric Field. Progress in Industrial Mathematics at ECMI 2014. Toimittaja / G. Russo ; V. Capasso ; G. Nicosia ; V. Romano. Springer International Publishing, 2016. (Mathematics in Industry).

Bibtex - Lataa

@inproceedings{c0deb0cfab654576ba59c79c84d153f1,
title = "On Detecting the Shape of an Unknown Object in an Electric Field",
abstract = "The problem discussed in this paper is detecting the shape of an unknown object in a 2-dimensional static electric field. For simplicity, the problem is defined in a partially rectangular domain, where on a part of the boundary the potential and/or its normal derivative are known. On the other part of the boundary the boundary curve is unknown, and this curve is to be determined. The unknown part of the boundary curve describes the shape of the unknown object.The problem is defined in the complex plane by an analytic function w=f(z) = u(x,y)+iv(x,y) with the potential u as its real part. Then the inverse function is given as f^{-1}(w) = x(u,v)+iy(u,v), where the functions x and y are harmonic in a rectangle with an unknown boundary condition on one boundary. The alternating-field technique is used to solve the unknown boundary condition.",
keywords = "free boundary problem, industrial mathematics",
author = "Jukka-Pekka Humaloja and Timo H{\"a}m{\"a}l{\"a}inen and Seppo Pohjolainen",
note = "Embargo avoinna, koska ei viel{\"a} julkaistu (Due May 3, 2017) HO / 2.5.2016",
year = "2016",
doi = "10.1007/978-3-319-23413-7",
language = "English",
isbn = "978-3-319-23412-0",
series = "Mathematics in Industry",
publisher = "Springer International Publishing",
editor = "G. Russo and V. Capasso and G. Nicosia and V. Romano",
booktitle = "Progress in Industrial Mathematics at ECMI 2014",

}

RIS (suitable for import to EndNote) - Lataa

TY - GEN

T1 - On Detecting the Shape of an Unknown Object in an Electric Field

AU - Humaloja, Jukka-Pekka

AU - Hämäläinen, Timo

AU - Pohjolainen, Seppo

N1 - Embargo avoinna, koska ei vielä julkaistu (Due May 3, 2017) HO / 2.5.2016

PY - 2016

Y1 - 2016

N2 - The problem discussed in this paper is detecting the shape of an unknown object in a 2-dimensional static electric field. For simplicity, the problem is defined in a partially rectangular domain, where on a part of the boundary the potential and/or its normal derivative are known. On the other part of the boundary the boundary curve is unknown, and this curve is to be determined. The unknown part of the boundary curve describes the shape of the unknown object.The problem is defined in the complex plane by an analytic function w=f(z) = u(x,y)+iv(x,y) with the potential u as its real part. Then the inverse function is given as f^{-1}(w) = x(u,v)+iy(u,v), where the functions x and y are harmonic in a rectangle with an unknown boundary condition on one boundary. The alternating-field technique is used to solve the unknown boundary condition.

AB - The problem discussed in this paper is detecting the shape of an unknown object in a 2-dimensional static electric field. For simplicity, the problem is defined in a partially rectangular domain, where on a part of the boundary the potential and/or its normal derivative are known. On the other part of the boundary the boundary curve is unknown, and this curve is to be determined. The unknown part of the boundary curve describes the shape of the unknown object.The problem is defined in the complex plane by an analytic function w=f(z) = u(x,y)+iv(x,y) with the potential u as its real part. Then the inverse function is given as f^{-1}(w) = x(u,v)+iy(u,v), where the functions x and y are harmonic in a rectangle with an unknown boundary condition on one boundary. The alternating-field technique is used to solve the unknown boundary condition.

KW - free boundary problem

KW - industrial mathematics

U2 - 10.1007/978-3-319-23413-7

DO - 10.1007/978-3-319-23413-7

M3 - Conference contribution

SN - 978-3-319-23412-0

T3 - Mathematics in Industry

BT - Progress in Industrial Mathematics at ECMI 2014

A2 - Russo, G.

A2 - Capasso, V.

A2 - Nicosia, G.

A2 - Romano, V.

PB - Springer International Publishing

ER -