The existing software for the handling of large linear systems of equations must be extended for the combination and solution of huge heterogeneous systems whose matrix consists of blocks with different storage schemes, because the matrices will soon reach a size for which the conventional complete storage isn’t any more controllable.
First of all, partitions with block-diagonal or band structure (e.g. for the orientation parameters of the Earth) must be treatable together with dense blocks in conventional storage (e.g. for the coordinates of the stations in an observation campaign).
Probably the existing possibilities for the identification of parameter groups are not sufficient. Then the group of variables appendant on a matrix block must achieve a unique name by which it is accessible in a command language. Routines must be created for the transformation of the storage form of a matrix block, for the combination of blocks with different storage structures, and for the split-up of blocks. Therefore a benchmark function for the effectiveness of a storage scheme is necessary to decide whether a sparse structure can be transformed into a dense structure or vice versa.
Finally a unique set of rules for the addition of matrix blocks must have been generated so that two block-partitioned systems of equations with non identical vectors of variables can be added automatically.
Different methods for the solution of such heterogeneous systems of equations shall be tested: direct and iterative inversion, and mixed methods. Also a parallel inversion on clusters of computers is worth to be realized.