Abstract
The importance of the optimal shape design has been increasing in the present industrial design due to the request to make their production more efficient.
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References
Allaire, G.: Shape optimization by the homogenization method. Applied Mathematical Sciences, vol. 146, Springer (2002)
Azegami, H., Takeuchi, K.: A smoothing method for shape optimization: traction method using the Robin condition. Int. J. Comput. Methods 3(1), 21–33 (2006)
Hecht, F.: New development in FreeFem++. J. Numer. Math. 20(3-4), 251–265 (2012)
Henrot, A.: Subsolutions and supersolutions in a free boundary problem. Ark. Mat. 32, 78–98 (1994)
Henrot, A., Pierre, M.: About existence of equilibria in electromagnetic casting. Q. Appl. Math. 49(3), 563–575 (1991)
Kawarada, H., Sawaguri, T., Imai, H.: An approximate resolution of a free boundary problem appearing in the equilibrium plasma by means of conformal mapping. Jpn. J. Appl. Math. 6, 331–340 (1989)
Kimura, M.: Geometry of hypersurfaces and moving hypersurfaces in \(R^m\)—for the study of moving boundary problems—. Jindřich Nečas Center for Mathematical Modeling Lecture notes Volume IV, Topics in Mathematical Modeling, pp. 39–93 (2008)
Maharani, A.U., Kimura, M., Azegami, H., Ohtsuka, K., Armanda, I.: Shape optimization approach to a free boundary problem. Recent Dev. Comput. Sci. 6, 42–55 (2015)
Morisue, T., Yajima, T., Kume, T., Fujimori, S.: Analysis of electromagnetic force for shaping the free surface of a molten metal in a cold crucible. IEEE Trans. Magn. 29(2), 1562–1565 (1993)
Onodera, M.: Geometric flows for quadrature identities. Math. Ann. 361, 77–106 (2015)
Pironneau, O.: Optimal Shape Design for Elliptic Systems. Springer (1984)
Sokolowski, J., Zolésio, J.-P.: Introduction to shape optimization: shape sensitivity analysis. Springer (1992)
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Shioda, S., Maharani, A.U., Kimura, M., Azegami, H., Ohtsuka, K. (2017). Shape Optimization Approach by Traction Method to Inverse Free Boundary Problems. In: Itou, H., Kimura, M., Chalupecký, V., Ohtsuka, K., Tagami, D., Takada, A. (eds) Mathematical Analysis of Continuum Mechanics and Industrial Applications. Mathematics for Industry, vol 26. Springer, Singapore. https://doi.org/10.1007/978-981-10-2633-1_8
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