Mathematical Sciences: Algorithms and Numerical Analysis forDifferential Equations

这项研究将在制定算法 偏微分方程的数值解 定常和非定常问题以及 方法进行分析。 具体议题包括建设 的先决条件，用于在迭代算法的并行 计算机体系结构，区域分解技术，问题 奇异摄动结构，角点处理 奇异性，现有有限的超收敛近似 元素，抛物方程与时间相关的系数， 对流占优问题流线扩散法 具有转折点、自适应网格细化和污染 效果等 科学和工程中的技术问题是如此 复杂的今天，最现实的将需要数字 在计算机和超级计算机的帮助下， 的 这里的研究是设计准确和高效的 用于当前和未来计算机环境的算法。

The research will be in the formulation of algorithms for the numerical solutions of partial differential equations for stationary and non-stationary problems and the development of methods for their analysis. Specific topics include construction of preconditions for use in iterative algorithms for parallel computer architectures, domain decomposition techniques, problems with singular perturbation structures, treatment of corner singularities, superconvergent approximations for existing finite elements, parabolic equations with time dependent coefficients, streamline diffusion method for convection dominated problems with turning points, adaptive mesh refinements and pollution effects etc. Technical problems in science and engineering are so complex today that most realistic ones will require numerical solutions with the help of computers and supercomputer. The research here is central to the design of accurate and efficient algorithms for use in present and future computer environments.