GBEM: Galerkin Boundary Element Method for 3-D Capacitance Extraction

TL;DR

This paper introduces GBEM, a Galerkin boundary element method that significantly speeds up 3-D capacitance extraction in IC design by reducing boundary elements while maintaining accuracy.

Contribution

The paper presents a novel GBEM approach that decreases computational complexity in capacitance extraction, integrating mathematical theorems to enhance efficiency and accuracy.

Findings

Reduces boundary elements for faster computation

Maintains low error with fewer boundary elements

Proven efficiency through experiments

Abstract

For modern IC design, electromagnetic coupling among interconnect wires plays an increasingly important role in signoff analysis. The requirement of fast and accurate capacitance extraction is becoming more and more urgent.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. To improve computational efficiency, we propose a Galerkin boundary element method (GBEM) to extract capacitance. The advantage of this method is that it can greatly reduce the number of boundary elements on the premise of ensuring that the error is small enough. As a consequence, the matrix order of the discretization equation will also decrease. The experiments in this paper have proved this advantage of our algorithm. Moreover, we have took advantage of some mathematical theorems in this paper. Our attempt shows that there will be more connections between the capacitance extraction and some mathematical conception so that we can use more mathematical tools to solve the problems of capacitance extraction.