Postdoctoral Research Associateship in Computer Science: Parallel Conjugate Gradient and Multilevel Algorithms for PDEs

一种新的对称化方法 偏微分方程在新兴并行计算机上的应用 将被研究。 该方法的算法发展， 将强调大规模并行化的上下文。 的 对称化的方法是有吸引力的椭圆偏 微分算子，A=S+BT，因为它将问题 在A中到一个自伴算子中， 类似于S，自伴部分。 因此，通过调用对称性 即使对于非自伴问题，它也允许使用有效的 以及多级共轭梯度法的稳健版本 的线性系统的解决方案的算法， 方程 使用多级和共轭梯度算法， 该方法在并行计算机上的实现将 提供了在上下文中研究并行化的机会， 其中多级算法本身被用作内部求解器 对于由内迭代和外迭代组成的算法。 的 算法将在大规模并行环境中进行测试 由连接机器提供。

A new symmetrization method for the numerical solution of partial differential equations on emerging parallel computers will be studied. The algorithmic development of the method in the context of massive parallelization will be emphasized. The method of symmetrization is attractive for an elliptic partial differential operator, A=S+BT in that it transforms the problem in A to one in an operator that is self-adjoint and that closely resembles S, the self-adjoint part. Thus, by invoking symmetry even for nonself-adjoint problems, it allows the use of efficient and robust versions of multilevel and conjugate gradient algorithms for the solution of the arising linear systems of equations. The use of multilevel and conjugate gradient algorithms in the implementation of the method on a parallel computer will provide the opportunity to study parallelization in a context where a multilevel algorithm itself is used as in inner solver for an algorithm composed of inner and outer iterations. The algorithms will be tested in a massively parallel environment offered by the Connection Machine.