CAPLET: A Highly Parallelized Field Solver for Capacitance Extraction Using Instantiable Basis Functions

Parallelization of traditional accelerated techniques for integral equation solvers has been shown to be inefficient and to scale poorly with the number of parallel computing nodes. This is because traditional methods typically represent the solution using piecewise constant (PWC) basis functions, resulting in gigantic systems of linear equations to solve. In this paper, we propose instantiable basis functions, which generate smaller systems than PWC basis functions for the same accuracy. Furthermore, they redistribute computation from the system solving step to the embarrassingly parallelizable system setup step, hence enabling highly scalable and efficient parallelization. In the examples, we tested, our new solver is six to ten times faster than FASTCAP in serial execution and achieves 90% parallel efficiency in a ten-core distributed-memory system. We developed a toolkit that automates a complete extraction flow from GDSII layout files to capacitance matrices. Our code has been released in the public domain.