Theoretical and numerical study of a free boundary problem by boundary integral methods

Michel Crouzeix; Philippe Féat; Francisco-Javier Sayas

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 35, Issue: 6, page 1137-1158
  • ISSN: 0764-583X

Abstract

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In this paper we study a free boundary problem appearing in electromagnetism and its numerical approximation by means of boundary integral methods. Once the problem is written in a equivalent integro-differential form, with the arc parametrization of the boundary as unknown, we analyse it in this new setting. Then we consider Galerkin and collocation methods with trigonometric polynomial and spline curves as approximate solutions.

How to cite

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Crouzeix, Michel, Féat, Philippe, and Sayas, Francisco-Javier. "Theoretical and numerical study of a free boundary problem by boundary integral methods." ESAIM: Mathematical Modelling and Numerical Analysis 35.6 (2010): 1137-1158. <http://eudml.org/doc/197491>.

@article{Crouzeix2010,
abstract = { In this paper we study a free boundary problem appearing in electromagnetism and its numerical approximation by means of boundary integral methods. Once the problem is written in a equivalent integro-differential form, with the arc parametrization of the boundary as unknown, we analyse it in this new setting. Then we consider Galerkin and collocation methods with trigonometric polynomial and spline curves as approximate solutions. },
author = {Crouzeix, Michel, Féat, Philippe, Sayas, Francisco-Javier},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Free boundary; spline; trigonometric polynomial.; electromagnetic shaping; boundary integral methods; collocation methods with trigonometric polynomial and spline curves},
language = {eng},
month = {3},
number = {6},
pages = {1137-1158},
publisher = {EDP Sciences},
title = {Theoretical and numerical study of a free boundary problem by boundary integral methods},
url = {http://eudml.org/doc/197491},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Crouzeix, Michel
AU - Féat, Philippe
AU - Sayas, Francisco-Javier
TI - Theoretical and numerical study of a free boundary problem by boundary integral methods
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 6
SP - 1137
EP - 1158
AB - In this paper we study a free boundary problem appearing in electromagnetism and its numerical approximation by means of boundary integral methods. Once the problem is written in a equivalent integro-differential form, with the arc parametrization of the boundary as unknown, we analyse it in this new setting. Then we consider Galerkin and collocation methods with trigonometric polynomial and spline curves as approximate solutions.
LA - eng
KW - Free boundary; spline; trigonometric polynomial.; electromagnetic shaping; boundary integral methods; collocation methods with trigonometric polynomial and spline curves
UR - http://eudml.org/doc/197491
ER -

References

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  12. S. Mikhlin and S. Prößdorf, Singular Integral Operators. Springer-Verlag, Berlin (1986).  Zbl0612.47024
  13. X. Pelgrin, Un problème de frontière libre. Thèse de l'Université de Rennes I, France (1994).  
  14. M. Pierre and J.R. Roche, Numerical simulation of tridimensional electromagnetic shaping of liquid metals. Numer. Math.65 (1993) 203-217.  Zbl0792.65096
  15. S. Prößdorf and B. Silbermann, Numerical Analysis for Integral and Related Operator Equations. Akademie-Verlag, Berlin (1991).  Zbl0763.65102
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  17. Y. Yan and I.H. Sloan, On integral equations of the first kind with logarithmic kernels. J. Integral Equations. Appl.1 (1988) 549-579.  Zbl0682.45001

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