Bivariate Splines for Geometric Modeling

聚合物制品的最终性能在很大程度上取决于工艺条件，如低速率、加工模具形状和冷却温度，这些都用数学模型中的条件参数来表示。从这个意义上说，对粘弹性流体行为的建模提供了对聚合物产品（如纤维和薄膜）结构的基本解释。用于模拟纤维和薄膜过程的有限元计算方法的进展是聚合物工业的最新发展。本工作的目的是将数学优化技术引入粘弹性流体的数值模拟，以确定聚合物产品的最佳工艺条件。提案涉及两个研究项目：薄膜铸造和涡量最小化问题。总体策略将是整合最近开发的粘弹性模型和优化技术，以便通过各种控制机制（如形状控制和边界控制）实现目标。作为薄膜铸造问题的方程求解器，将使用商业软件包Poly ow，它可以模拟各种设置下的薄膜和纤维加工。对于另一个问题，将使用目前正在开发的有限元代码。在解决优化问题时，当前研究的最新成果将扩展到更一般的高维粘弹性体系。

ABSTRACT0204174Marian NeamtuVerderbilt UniversityThe final properties of polymer products are largely determined by process conditions such a low rate, shape of processing die and cooling temperature, which are represented as condition parameters in mathematical models. In this sense, modeling viscoelastic fluid behavior provides a fundamental explanation of the structure of polymer products such as fibers and films. Advances in the finite element computational methodologies for simulating the fiber and film process is a recent development in polymer industries.The goal of this work is to introduce mathematical optimization techniques into the nu-merical simulation of viscoelastic fluid, in order to determine optimal process conditions for polymer products. Two research projects are involved in the proposal: film casting and a vorticity minimization problem. The overall strategy will be to integrate recently developed viscoelastic models and optimization techniques in order to meet objectives through various control mechanisms such as shape control and boundary control. As an equation solver for the film casting problem, the commercial software package Poly ow, which simulates film and fiber processing in various settings, will be used. For the other problem, a finite element codecurrently under development will be used. In solving the optimization problems, recent resultsfrom current research will be extended to the more general and high dimensional viscoelasticregime.