The parallel computing based on the domain deson-position method is used for solving this problem. A mumber of PCs are used to form a network unber the Liux operafing system. A parallel algoxithm of the domain decomposition is fut forvavd by means of the plysical coneption. i.e. the continuous ondition of heat flux in the interace. Another parallel algorthm is Caalled as modiffed tridagrnmal matrix algorithm (mTDMA). In this algraithm, the equation set for a subregion in the domain are elininared to a single equation, and the collection of these equations (ion per slave processor) from a small set of equations. This equation set is solved by using the classical tridiagonal matrix algocithm (TDMA), but by sending and receiving data among the master and slaves. The impliementation of thes domain decomposition paralled algorithm are made in PVM envirment. (to be rewrituen.)