ALGORITHMS: Multiscale, Multicolor, Multigrid-Like Solvers for High Performance Technical Computing

While there are several acceptable algebraic multigrid algorithms for symmetric positive definite problems (or ones with an M-matrix), there is very little known that works, much less works robustly, for general nonsymmetric, indefinite problems. In fact, none of the three basic principles for developing algebraic multigrid methods apply except under special circumstances. For nonsymmetric, indefinite problems we will develop principles, algorithms, and serial and parallel codes that work well with applications when little or no, some, or a lot of application information is provided to make multiscale and multilevel solvers robust. Both symbolic and numeric tools will be developed to make prototyping new algorithms relatively painless. Memory caches will be exploited portably with little tuning necessary from the users. Two diverse applications will motivate the new algorithms and software: ocean and flame modeling. The results should have impact on any area of science or engineering in which nonsymmetric, indefinite problems result. At the same time, material from the project can be integrated into a first course in computational sciences (UKy CS521), which is taken by seniors and graduate students. Minority students already are half of the PI's research group (half are female, one is of color). Almost all of the UKy CS grad students are minority students. Dissemination will be through web sites including http://www.mgnet.org and Douglas' home page http://www.ccs.uky.edu/~douglas.