Sparse matrix plots

The upper color bar in the right-hand side of the matrix plot indicates the relative magnitude of the matrix elements and the lower bar their incidence. Notice, that the scale is not the same for all plots.

The purpose of these plots is to demonstrate the difference of the structure of the matrix and its inverse in the analysis of heat transfer and stress analysis of shells. Stiffness matrices in the analysis of shell problems are far from being diagonally dominant and the decay of the entriens in its inverse is slow. Thus it is difficult to construct sparse approximate inverse preconditioners for shell problems.

Cylindrical shell -- 4x4 mesh (110 unknowns) R/t = 1000

Unscaled matrix

Symmetric diagonal scaling

Inverse of the unscaled matrix

Heat transfer analysis -- 10x10mesh (81 unknowns)

Unscaled matrix

Inverse of the unscaled matrix