Mathematical Sciences: VLSI Modeling and Algorithms for Nonlinear Systems

本课程将对半导体性能数学模型解的存在性和稳定性进行基础性研究。我们将通过研究基本线性化的特征值结构来研究全局收敛的牛顿/连续方法。注意力集中在VLSI芯片设计中出现的偏微分方程式上。过程模拟扩散的某些方面(发生在自由边界/流动问题的背景下)将从数学建模的角度进行研究。

Fundamental studies of existence and stability of solutions to a mathematical model for semiconductor performance will be performed. Globally convergent Newton/continuation methods will be examined by studying the eigenvalue structure of the underlying linearizations. Attention will be focused on the partial differential equations that arise in VLSI chip design. Some aspects of process simulation diffusion (which occurs in the context of free boundary/flow problems) will be studied from the standpoint of mathematical modeling.