This paper presents a new parallel ILU preconditioned It is based on the technique of Sequential Staging of Tasks (SST) which overcomes the difficulty of recursiveness arising from ILU factorization. This new parallel ILU preconditioner is easy to reconstruct from the sequential version. The only requirement is to insert the synchronization codes of stages of tasks into the sequential version, and any other modifications to the original serial codes are not needed. The characteristic of matching various ordering schemes is still maintained, and the new merit of handling different numbers of processors is obtained. Numerical results were obtained using a thermal model with different grid system. The parallel speedup is satisfactory.

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