Shape optimization and optimal control for transient heat conduction problems using an isogeometric approach. (June 2017) - Wang, Zhen-Pei; Turteltaub, Sergio; Abdalla, Mostafa
Highlights: Continuous adjoint shape sensitivity of objective functionals for transient problems. Sensitivity analysis for objective functionals with discontinuities in space and time. Isogeometric shape optimization with two-level discretizations for analysis and design. Applications of passive optimal thermal management for transient heat conduction. Abstract: This work is concerned with the development of a framework to solve shape optimization problems for transient heat conduction problems within the context of isogeometric analysis (IGA). A general objective functional is used to accommodate both shape optimization and passive control problems under transient conditions. An adjoint sensitivity analysis, which accounts for possible discontinuities in the objective functional, is performed analytically and subsequently discretized within the context of IGA. The gradient of the objective functional is used in a descent algorithm to solve optimization problems. Numerical examples are presented to validate and demonstrate the capacity to manage thermal fields under transient conditions.