An object-oriented framework for block preconditioning

General software for preconditioning the iterative solution of linear syste ms is greatly lagging behind the literature. This is partly because specifi c problems need specific matrix and preconditioner data structures in order to be solved efficiently, i.e., multiple implementations of a precondition er with specialized data structures are required. This article presents a f ramework to support preconditioning with various, possibly user-defined, da ta structures for matrices that are partitioned into blocks. The main idea is to define data structures for the blocks, and an upper layer of software which uses these blocks transparently of their data structure. This transp arency can be accomplished by using an object-oriented language. Thus, vari ous preconditioners, such as block relaxations and block-incomplete factori zations, only need to be defined once and will work with any block type. In addition, it is possible to transparently interchange various approximate or exact techniques for inverting pivot blocks, or solving systems whose co efficient matrices are diagonal blocks. This leads to a rich variety of pre conditioners that can be selected. Operations with the blocks are performed with optimized libraries or fundamental data types. Comparisons with an op timized Fortran 77 code on both workstations and Gray supercomputers show t hat this framework can approach the efficiency of Fortran 77, as long as su itable block sizes and block types are chosen.