load balancing in variable-order expansion

In variable-order expansion, the weight of element in mesh partition is the element DOFs or boundary DOFs. But as Chris @ccantwel mentioned, the complexity of matrix operation is square DOFs.

I did a small test case (65 low order elements + 1 high order elements) wing_15.xml. Results are as follows:

Serial running,

Time-integration : 84.3741s; Total Computation Time = 86s

Two cores parallel, WEIGHTPARTITIONS=DOF,

Time-integration : 37.5043s; Total Computation Time = 80s

Two cores paralled, WEIGHTPARTITIONS=BOUNDARY,

Time-integration : 37.9102s; Total Computation Time = 80s

Two cores parallel, WEIGHTPARTITIONS=DOF^2,

Time-integration : 32.6387s; Total Computation Time = 35s

Two cores parallel, WEIGHTPARTITIONS=BOUNDARY^2,

Time-integration : 32.7864s; Total Computation Time = 35s

If the DOFs is not squared, time-integration is halved, but total computation time changes little. After using DOFs^2, both time-integration and total computation time are halved.

The difference between WEIGHTPARTITIONS=DOF and WEIGHTPARTITIONS=BOUNDARY is little.