Abstract
In this paper we derive rigorously the derivative of the Dirichlet to Neumann map and of the Neumann to Dirichlet map of the conductivity equation with respect to movements of vertices of triangular conductivity inclusions. We apply this result to formulate an optimization problem based on a shape derivative approach.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 756-776 |
| Number of pages | 21 |
| Journal | SIAM Journal on Mathematical Analysis |
| Volume | 49 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jan 1 2017 |
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Keywords
- Conductivity equation
- Dirichlet to Neumann map
- Polygonal inclusion
- Shape derivative
ASJC Scopus subject areas
- Analysis
- Computational Mathematics
- Applied Mathematics
Cite this
Differentiability of the Dirichlet to Neumann map under movements of polygonal inclusions with an application to shape optimization. / Beretta, Elena; Francini, Elisa; Vessella, Sergio.
In: SIAM Journal on Mathematical Analysis, Vol. 49, No. 2, 01.01.2017, p. 756-776.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Differentiability of the Dirichlet to Neumann map under movements of polygonal inclusions with an application to shape optimization
AU - Beretta, Elena
AU - Francini, Elisa
AU - Vessella, Sergio
PY - 2017/1/1
Y1 - 2017/1/1
N2 - In this paper we derive rigorously the derivative of the Dirichlet to Neumann map and of the Neumann to Dirichlet map of the conductivity equation with respect to movements of vertices of triangular conductivity inclusions. We apply this result to formulate an optimization problem based on a shape derivative approach.
AB - In this paper we derive rigorously the derivative of the Dirichlet to Neumann map and of the Neumann to Dirichlet map of the conductivity equation with respect to movements of vertices of triangular conductivity inclusions. We apply this result to formulate an optimization problem based on a shape derivative approach.
KW - Conductivity equation
KW - Dirichlet to Neumann map
KW - Polygonal inclusion
KW - Shape derivative
UR - http://www.scopus.com/inward/record.url?scp=85018790436&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85018790436&partnerID=8YFLogxK
U2 - 10.1137/16M1082160
DO - 10.1137/16M1082160
M3 - Article
AN - SCOPUS:85018790436
VL - 49
SP - 756
EP - 776
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
SN - 0036-1410
IS - 2
ER -