Mathematical Sciences Computing Research Environment

圣路易斯华盛顿大学系统科学与数学系将购买Sun微系统图形工作站设备，该设备将专门用于支持数学科学研究。该设备将用于几个研究项目，具体包括：1。里卡第偏微分方程的计算理论，是非线性系统控制的基础，特别是用于经典爆炸和非线性激波的可视化；2. 概率系统的优化，目标函数的估计采用蒙特卡罗模拟，计算量大；3. 有限单元法的p-版本，在这里首创，现在被推广到非线性和时变问题；4. 非线性控制理论的符号代数计算，使用李代数和形式幂级数方法，以及由此产生的新的不变积分方法的数值实验，具有图形输出。

The Department of Systems Science and Mathematics at Washington University, St. Louis, will purchase Sun Microsystems Graphics Workstation equipment which will be dedicated to the support of research in the mathematical sciences. The equipment will be used for several research projects, including in particular: 1. Computational theory of Riccati partial differential equations, fundamental to the control of nonlinear systems, directed especially to a visualization of their classical blow- ups and nonlinear shock waves; 2. Optimization for probabilistic systems, in which the objective function is estimated by Monte Carlo simulation, which is computation intensive; 3. The p-version of the finite element method, pioneered here and now being extended to nonlinear and time-varying problems; 4. Symbolic algebraic computation for nonlinear control theory, using Lie algebra and formal power series methods, and numerical experimentation with resulting new invariant-preserving integration methods, with graphic output.