On Design and Implementation of Parallel Algorithms for Solving Inverse Problems

A new strategy for design and optimization of parallel algorithms is proposed. This strategy is based on an abstract machine model that allows the programmer to focus on the inherent parallelism of the problems at hand rather than on the parallelism of the target machines. It is possible to transform a subclass of these parallel algorithms into programs running efficiently on a great variety of parallel machines, including workstation clusters. From a practical point of view, this subclass is large. It includes e.g. conjugate gradient methods for which we discuss the transformation. The proposed method is also applicable to more complex problems like inverse problems in partial differential equations. We demonstrate this for an identification problem arising from hydrology.