We compared the performance of our new scheme with the standard finite difference schemes and found the new scheme is much more accurate and computationally more efficient than the standard ones. The performance of the iterative solvers based on multigrid and multilevel methods is impressive. Very difficult problems have been solved and the results are very encouraging. All above high performance calculation are conducted on SPP supercomputer. Our approach and study span all three solution seeking steps mentioned previously in a coherent fashion.
Graded mesh ensures boundary layers be represented.
Grid transformation makes fourth order compact schemes applicable. Fourth order compact scheme yields high accuracy approximation and linear systems with good property. Fast iterative methods compute high accuracy solution efficiently. My research project is in the area of extremal graph theory. I wish to find the maximum weight of a weighted graph on n vertices having no subgraph on m vertices of a given weight.