Efficient representations of Green’s functions for some elliptic equations with piecewise-constant coefficients

Yuri Melnikov

Open Mathematics (2010)

  • Volume: 8, Issue: 1, page 53-72
  • ISSN: 2391-5455

Abstract

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Convenient for immediate computer implementation equivalents of Green’s functions are obtained for boundary-contact value problems posed for two-dimensional Laplace and Klein-Gordon equations on some regions filled in with piecewise homogeneous isotropic conductive materials. Dirichlet, Neumann and Robin conditions are allowed on the outer boundary of a simply-connected region, while conditions of ideal contact are assumed on interface lines. The objective in this study is to widen the range of effective applicability for the Green’s function version of the boundary integral equation method making the latter usable for equations with piecewise-constant coefficients.

How to cite

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Yuri Melnikov. "Efficient representations of Green’s functions for some elliptic equations with piecewise-constant coefficients." Open Mathematics 8.1 (2010): 53-72. <http://eudml.org/doc/268950>.

@article{YuriMelnikov2010,
abstract = {Convenient for immediate computer implementation equivalents of Green’s functions are obtained for boundary-contact value problems posed for two-dimensional Laplace and Klein-Gordon equations on some regions filled in with piecewise homogeneous isotropic conductive materials. Dirichlet, Neumann and Robin conditions are allowed on the outer boundary of a simply-connected region, while conditions of ideal contact are assumed on interface lines. The objective in this study is to widen the range of effective applicability for the Green’s function version of the boundary integral equation method making the latter usable for equations with piecewise-constant coefficients.},
author = {Yuri Melnikov},
journal = {Open Mathematics},
keywords = {Green’s function; Elliptic equations; Piecewise-constant coefficients; Green's function; elliptic equations; piecewise-constant coefficients},
language = {eng},
number = {1},
pages = {53-72},
title = {Efficient representations of Green’s functions for some elliptic equations with piecewise-constant coefficients},
url = {http://eudml.org/doc/268950},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Yuri Melnikov
TI - Efficient representations of Green’s functions for some elliptic equations with piecewise-constant coefficients
JO - Open Mathematics
PY - 2010
VL - 8
IS - 1
SP - 53
EP - 72
AB - Convenient for immediate computer implementation equivalents of Green’s functions are obtained for boundary-contact value problems posed for two-dimensional Laplace and Klein-Gordon equations on some regions filled in with piecewise homogeneous isotropic conductive materials. Dirichlet, Neumann and Robin conditions are allowed on the outer boundary of a simply-connected region, while conditions of ideal contact are assumed on interface lines. The objective in this study is to widen the range of effective applicability for the Green’s function version of the boundary integral equation method making the latter usable for equations with piecewise-constant coefficients.
LA - eng
KW - Green’s function; Elliptic equations; Piecewise-constant coefficients; Green's function; elliptic equations; piecewise-constant coefficients
UR - http://eudml.org/doc/268950
ER -

References

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