We have developed a robust, efficient, and accurate tool, which integrates inductance extraction and simulation, called INDUCTWISE. This paper advances the state-of-the-art inductance extraction and simulation techniques and contains two major parts. In the first part, INDUCTWISE extractor, we discovered that the recently proposed inductance matrix sparsification algorithm, the K-method, albeit its great benefit of efficiency, has a major flaw in the stability. We provide both a counter example and a remedy for it. A window section algorithm is also presented to preserve the accuracy of the sparsification method. The second part, the INDUCTWISE simulator, demonstrates great efficiency of integrating the nodal analysis formulation with the improved K-method. Experimental results show that INDUCTWISE has over 250× speedup compared to SPICE3. The proposed sparsification algorithm accelerates the simulator another 175× and speeds up the extractor 23.4× within 0.1% of error. INDUCTWISE can extract and simulate an 118K-conductor RKC circuit within 18 minutes.