Many physical phenomena, governed by partial differential equations (PDEs), are second order in nature. This makes sense to pose the control on the second order derivatives of the field solution, in addition to zero and first order ones, to consistently control the underlaying process. However, this type of control is nontrivial and to the best of our knowledge there is nigher a theoretic nor a numeric work in this regard. The present work goals to do the first quest in this regard, examining a problem of this type using a numerical simulation.
A distributed parameter identification problem includes the control
on the diffusion coefficient of the Poisson equation and a functional includes the state's curvature is considered. A heuristic regularization tool is introduced to manage codimension-one singularities during the functional analysis. Based on the duality principles, the approximate necessary optimality conditions is found. The system of optimality conditions is solved using a globalized projected gradient method. Numerical results, in two- and three-dimensions, implied the possibility of posing control on the second order derivatives and success of the presented numerical method.
Electro-thermal topology optimization of an electric machine by the topological derivative considering drive cycles
RICAM, Austrian Academy of Sciences（奥地利科学院 RICAM）；Université Paris-Saclay, Centralesupélec, CNRS, GeePs（巴黎萨克雷大学、中央理工-苏佩莱克学院、法国国家科学研究中心 GeePs）；Computational Electromagentics Group, TU Darmstadt（达姆施塔特工业大学计算电磁学组）
A Unified Phase-Field Fourier Neural Network Framework for Topology Optimization
East China Normal University（华东师范大学）；The Hong Kong Polytechnic University（香港理工大学）；Shanghai Jiao Tong University（上海交通大学）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）
