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In this article, a generalized alternating direction implicit (ADI) method for transient thermal simulation of two-dimensional structures with locally refined grids is proposed. First, a flexible approach is employed to generate the semistructured grids with local refinement. The generalized ADI method is then derived based on these semistructured grids, in which two new directions are added to deal with the grid points in the transition regions. By this means, the ADI scheme is successfully extended to handle the transient simulation of objects with locally refined grids while maintaining the property of linear complexity in computation. The accuracy and high efficiency of the proposed method are verified by several typical examples.

A generalized alternating direction implicit method for transient thermal simulation of 2-D structures with locally refined grids