Parallel Numerical Methods For Initial Value Problems

该项目将探讨的理论和实践方面， 新发展的波形共轭方向法 初值问题（IVP）。 波形松弛（WR），一种基于波形的迭代技术， 是一种越来越流行的IVP并行解决方案方法。 共轭方向波形方法大大改善了 MOS器件瞬态模拟的WR收敛特性。 该项目将为更广泛地应用这些技术奠定基础。 方法通过开发精细的收敛估计和建立 并测试并行实现。 在共轭方向上，将寻求新的收敛结果 波形方法适用于线性和非线性系统的常微分方程和 DAE。 离散化和多速率积分的影响将 也被研究。 逐点和基于波形的IVP解算器将在 ASIM、Alewife模拟器和Alewife并行计算机。 它们对于各种ODE和DAE问题的行为， 将比较硬件配置。 波形共轭方向法似乎是一种有效的 和实用类的并行技术的各种 应用. 总之，理论结果和实践 实施将证明其价值和适用性。

This project will explore theoretical and practical aspects of newly-developed waveform conjugate-direction methods for parallel solution of initial value problems (IVPs). Waveform relaxation (WR), a waveform-based iterative technique, is an increasingly popular parallel solution approach for IVPs. Conjugate-direction waveform methods have dramatically improved the convergence properties of WR for transient simulation of MOS devices. The project will establish the basis for broader application of these methods by developing refined convergence estimates and by building and testing a parallel implementation. New convergence results will be sought for conjugate-direction waveform methods applied to linear and nonlinear systems of ODEs and DAEs. The effects of discretization and multirate integration will also be studied. Pointwise and waveform-based IVP solvers will be implemented on ASIM, the Alewife simulator, and on the Alewife parallel computer. Their behavior for a variety of ODE and DAE problems on various hardware configuration will be compared. Waveform conjugate-direction methods appear to be an efficient and practical class of parallel techniques for a variety of applications. Together, the theoretical results and practical implementations will demonstrate their value and applicability.