Dear Roy:

~The Degree of Freedom numbering is contiguous on each processor, and
~each processor stores the matrix rows for each DoF it "owns".
That is, generally, the user don't need to consider this problem although his problem includes multiple matrices and multiple variables. Regarding what you said, I guess that each processor will store the rows of multiple matrices, not store the whole or part rows of the single matrix in the multiple matrices and variables situation.

> In the system with multiple matrixes and multiple variables, in view of
> adaptive mesh refinment,
> how to make several variables guide adaptive mesh refinement?

By combining error estimates from multiple variables.  If you use the
same type of estimator for all variables, you may just need to set
ErrorEstimator::component_scale to normalize them.  If not, you'll
need to combine multiple ErrorVector results by hand.

> in view of parallel computation, what is the distribution of the
> matrixes in computer cluster when the user solves its problem?

> How can the user check the corresponding information?

You ought to look through the Class Docs pages.  I know I'm more user
friendly, but you can find answers there faster.