Path-following primal-dual interior-point methods for shape optimization of stationary flow problems

被引：0

作者：

Department of Mathematics, University of Houston, United States ^{[1
]}

不详 ^{[2
]}

机构：

[1] Department of Mathematics, University of Houston

[2] Institute of Mathematics, University of Augsburg

来源：

J. Numer. Math. | 2007年 / 2卷 / 81-100期

基金：

美国国家科学基金会;

关键词：

Central path; Continuation methods; PDE constrained optimization; Primal-dual interior-point methods; Shape optimization; Stokes flow;

D O I：

10.1515/jnma.2007.005

中图分类号：

学科分类号：

摘要：

We consider shape optimization of Stokes flow in channels where the objective is to design the lateral walls of the channel in such a way that a desired velocity profile is achieved. This amounts to the solution of a PDE constrained optimization problem with the state equation given by the Stokes system and the design variables being the control points of a Bézier curve representation of the lateral walls subject to bilateral constraints. Using a finite element discretization of the problem by Taylor-Hood elements, the shape optimization problem is solved numerically by a path-following primal-dual interior-point method applied to the parameter dependent nonlinear system representing the optimality conditions. The method is an all-at-once approach featuring an adaptive choice of the continuation parameter, inexact Newton solves by means of right-transforming iterations, and a monotonicity test for convergence monitoring. The performance of the adaptive continuation process is illustrated by several numerical examples. © de Gruyter 2007.

引用

页码：81 / 100

页数：19

共 44 条

[1] Allaire G., Shape Optimization by the Homogenization Method, (2002)
[2] Bendsoe M.P., Optimization of Structural Topology, Shape, and Material, (1995)
[3] Bendsoe M.P., Sigmund O., Topology Optimization: Theory, Methods and Applications, (2003)
[4] Large-scale PDE-constrained optimization, Lecture Notes in Computational Science and Engineering, 30, (2003)
[5] Biegler L.T., Nocedal J., Schmid C., A reduced Hessian method for large-scale constrained optimization, SIAM J. Optimization, 5, pp. 314-347, (1995)
[6] Biros G., Ghattas O., Parallel Lagrange-Newton-Krylov-Schur methods for PDE-constrained optimization. Parti: The Krylov-Schur solver, SIAM J. Sci. Comp, 27, pp. 687-713, (2005)
[7] Biros G., Ghattas O., Parallel Lagrange-Newton-Krylov-Schur methods for PDE-constrained optimization. Part II: The Lagrange-Newton solver and its application to optimal control of steady viscous flows, SIAM J. Sci. Comp, 27, pp. 714-739, (2005)
[8] Boggs P.T., Tolle J.W., Sequential quadratic programming, Acta Numerica, 4, pp. 1-50, (1995)
[9] Bonnans J.F., Gilbert J.C., Lemarechal C., Sagastizabal C.A., Numerical Optimization. Theoretical and Practical Aspects, (2003)
[10] Brezzi F., Fortin M., Mixed and Hybrid Finite Element Methods, (1991)

← 1 2 3 4 5 →