Variational-based finite element method for inverse shape design of heat conduction

摘要

An inverse shape design of heat conduction is considered for optimizing the geometrical shape from prescribed temperature distribution and heat flux distribution on the unknown surface. A variational theory is established by the semi-inverse method suggested by Ji-Huan He for the problem discussed; we make the obtained variational principle stationary with moving boundaries until the natural boundary conditions on the unknown shape meet the prescribed condition on the unknown boundary, making the problem well-posed and easy to incorporate with the finite element simulation. Numerical results show that the present technique is robust and convenient.