This paper studies a class of variational problems which involving both bulk and surfaceenergies. The bulk energy is of Dirichlet type though it can be in very general forms allowingunknowns to be scalar or vectors.Th...This paper studies a class of variational problems which involving both bulk and surfaceenergies. The bulk energy is of Dirichlet type though it can be in very general forms allowingunknowns to be scalar or vectors.The surface energy is an arbitrary elliptic parametric integralwhich is defined on a free interface. One also allows other constraints such as volumes of partitioning sets. One establishes the existence and regularity theory, in particular, the regularityof the free interface of such problems.展开更多
In this work,a hybrid meta-model based design space differentiation（HMDSD）method is proposed for practical problems.In the proposed method,an iteratively reduced promising region is constructed using the expensive p...In this work,a hybrid meta-model based design space differentiation（HMDSD）method is proposed for practical problems.In the proposed method,an iteratively reduced promising region is constructed using the expensive points,with two different search strategies respectively applied inside and outside the promising region.Besides,the hybrid meta-model strategy applied in the search process makes it possible to solve the complex practical problems.Tested upon a serial of benchmark math functions,the HMDSD method shows great efficiency and search accuracy.On top of that,a practical lightweight design demonstrates its superior performance.展开更多
文摘This paper studies a class of variational problems which involving both bulk and surfaceenergies. The bulk energy is of Dirichlet type though it can be in very general forms allowingunknowns to be scalar or vectors.The surface energy is an arbitrary elliptic parametric integralwhich is defined on a free interface. One also allows other constraints such as volumes of partitioning sets. One establishes the existence and regularity theory, in particular, the regularityof the free interface of such problems.
基金Project supported by the Plan for the growth of young teachers,the National Natural Science Foundation of China(No.51505138)the National 973 Program of China(No.2010CB328005)+1 种基金Outstanding Youth Foundation of NSFC(No.50625519)Program for Changjiang Scholars
文摘In this work,a hybrid meta-model based design space differentiation（HMDSD）method is proposed for practical problems.In the proposed method,an iteratively reduced promising region is constructed using the expensive points,with two different search strategies respectively applied inside and outside the promising region.Besides,the hybrid meta-model strategy applied in the search process makes it possible to solve the complex practical problems.Tested upon a serial of benchmark math functions,the HMDSD method shows great efficiency and search accuracy.On top of that,a practical lightweight design demonstrates its superior performance.
