An Adaptive Partition Strategy of Galerkin Boundary Element Method for Capacitance Extraction

In advanced process, electromagnetic coupling among interconnect wires plays an increasingly important role in signoff analysis. For VLSI chip design, the requirement of fast and accurate capacitance extraction is becoming more and more urgent. And the critical step of extracting capacitance among interconnect wires is solving electric field. However, due to the high computational complexity, solving electric field is extreme timing-consuming. The Galerkin boundary element method (GBEM) was used for capacitance extraction in [2]. In this paper, we are going to use some mathematical theorems to analysis its error. Furthermore, with the error estimation of the Galerkin method, we design a boundary partition strategy to fit the electric field attenuation. It is worth to mention that this boundary partition strategy can greatly reduce the number of boundary elements on the promise of ensuring that the error is small enough. As a consequence, the matrix order of the discretization equation will also decrease. We also provide our suggestion of the calculation of the matrix elements. Experimental analysis demonstrates that, our partition strategy obtains a good enough result with a small number of boundary elements.