Geodesic
Lower estimates for the equivalence constant of the torsional rigidity and the moment of inertia about a boundary
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 4, pp. 59-66

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In this paper, we consider the problem of approximate computation of the torsional rigidity coefficient for simply-connected domains. An approach to the distance function determination is defined; a numerical method for calculating the moment of inertia about a boundary is proposed. Using a numerical experiment, the estimate for the equivalence constant of the torsional rigidity coefficient and the moment of inertia about a boundary is improved.
Keywords: torsional rigidity, moment of inertia about a boundary, conjugate gradients method, Dirichlet problem. 
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     author = {D. A. Abramov},
     title = {Lower estimates for the equivalence constant of the torsional rigidity and the moment of inertia about a~boundary},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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     publisher = {mathdoc},
     volume = {153},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2011_153_4_a5/}
}
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D. A. Abramov. Lower estimates for the equivalence constant of the torsional rigidity and the moment of inertia about a boundary. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 4, pp. 59-66. http://geodesic.mathdoc.fr/item/UZKU_2011_153_4_a5/