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Recent study shows that the nonuniform thermal distribution not only has an impact on the substrate but also interconnects. Hence, three-dimensional (3-D) thermal analysis is crucial to analyze these effects. In this paper, the authors present and develop an efficient 3-D transient thermal simulator based on the alternating direction implicit (ADI) method for temperature estimation in a 3-D environment. Their simulator, 3D Thermal-ADI, not only has a linear runtime and memory requirement, but also is unconditionally stable. Detailed analysis of the 3-D nonhomogeneous cases and boundary conditions for on-chip VLSI applications are introduced and presented. Extensive experimental results show that our algorithm is not only orders of magnitude faster than the traditional thermal simulation algorithms but also highly accurate and memory efficient. The temperature profile of steady state can also be reached in several iterations. This software will be released via the web for public usage.