Difference Graphs of Block ADI Method

The block alternating direction implicit (ADI) method is the parallelization of the well-known ADI method, which is suitable for the distributed memory multiprocessors with a minimal cost of communications. The difference graphs of the block ADI method are introduced in this paper, and a general procedure is obtained to design a block ADI method, and at the same time a new proof of unconditional stability of the block ADI method is given.