Adaptive Solution of Partial Differential Equations on Parallel Computers Using an Equational Language

该项目将开发自动自适应的软件工具， 偏微分方程组的并行求解 矢量计算机自适应技术将能够解决 使用有限元的各种偏微分系统 包含网格移动、局部细化和 误差估计程序。 将开发自适应软件 使用等式语言系统MODEL。 这个复杂的系统 包含方便描述复杂 数学系统和自动检测并行性， 并行处理器的调度。 该研究将有必要（i）改善网格移动，局部 改进和误差估计技术;（ii）动态调度 添加了用于将处理器分配为计算单元的算法， 或从网格中删除;（iii）平衡网格上的计算负载， 处理器的并行系统，以及（iv）开发一个多重网格 求解线性代数系统的求解策略。 由此产生的软件将使科学家和工程师能够解决一个 在多种计算环境下的各种复杂问题。

This project will develop software tools for the automatic adaptive solution of systems of partial differential equations on parallel and vector computers. The adaptive techniques will be capable of solving a wide variety of partial differential systems using finite element methods that contain combinations of mesh moving, local refinement, and error estimation procedures. The adaptive software will be developed using the equational language system MODEL. This sophisticated system contains facilities for the convenient description of complex mathematical systems and for the automatic detection of parallelism and the scheduling of parallel processors. The research will necessitate (i) improving the mesh moving, local refinement, and error estimation techniques; (ii) dynamic scheduling algorithms for assigning processors as computational cells are added to or deleted from a mesh; (iii) balancing the computational load on the processors of the parallel system, and (iv) developing a multigrid solution strategy for solving linear algebraic systems. The resulting software will enable scientists and engineers to solve a wide variety of complex problems on several computing environments.