数学与系统科学研究院

计算数学所学术报告

报告人：        Prof.Ronald H.W. Hoppe

Universitaet Augsburg, Germany

报告题目 Primal-Dual Newton Interior-Point Methods in Structural Optimization

Abstract: The optimization of the shape and the topology of continuum mechanical structures by means of a systematic, physically consistent design methodology is referred to as structural optimization. The design criteria are chosen according to a goal oriented operational behavior of the structures under consideration and typically lead to nonlinear objective functionals depending on the state variables describing the operational mode and the design variables determining the shape and the topology. The state variables are assumed to satisfy di erential equations reflecting the underlying physical laws whereas technological aspects may give rise to further equality and inequality constraints on both the state and the design variables.

After discretization the resulting nonlinear programming problem is usually solved by what is called an alternating iteration where the discretized state equations and the optimization are carried out sequentially. Here, we advocate the use of recently developed ”all-at-once” approaches featuring the numerical solution of the state equations as an integral part of the optimization routine. In particular, we focus on primal-dual Newton interior-point methods. Special emphasis is given on the e±cient solution of the primal-dual Hessian system and on convergence monitoring by a hierarchy of two merit functions. Applications include the structural optimization of microcellular biomorphic ceramics based on homogenization, the shape optimization of electrorheological shock absorbers, and the topology optimization of high power electromotors,.

报告时间：2004年5月31日  下午4：00

报告地点：科技综合楼三层报告厅