Collection of abstracts 14th GAMM-Seminar Kiel on Concepts of Numerical Software January 23rd to 25th, 1998.

Sunday, January 25th, 1998

Parallel linear algebra and the application to multigrid methods

We introduce an abstract model for linear algebra computations on distributed overlapping partitions of indices on different levels. Local refinement can be modeled by active sets of indices and the identification of indices on successive levels.

We show that the specification of the parallel linear algebra is important for the performance of the resulting algorithms. Furthermore, in the implementation most parallel modifications of the algorithms are hidden in the linear algebra module. In particular, nearly all other numerical algorithms such as assembling, smoothing and linear, nonlinear and time dependent solvers can be implemented without any parallel extensions. At least, the model can check the required consistency and indicates, where the model is violated.

Finally, we demonstrate that the specification of the parallel linear algebra yields parallel realizations of geometrical multigrid methods, algebraic multigrid methods and multigrid methods for mortar elements.