Numerical simulations in 3D heat conduction: Minimizing the quadratic mean temperature gradient by an optimality criteria method

摘要

We analyze an optimal design problem in three-dimensional (3D) heat conduction: Given fixed amounts of two isotropic conducting materials, decide how we are to mix them in a 3D domain to minimize the quadratic mean temperature gradient. By using an optimality criteria method, we provide some numerical evidence that Tartar's result ( see [ in Calculus of Variations, Homogenization and Continuum Mechanics, G. Buttazzo, G. Bouchitte, and P. Suquet, eds., World Scientific, River Edge, NJ, 1994, pp. 279-296]) is verified in three dimensions when the target vector field is zero.