Hardware accelerator for 3D method of moments based parasitic extraction

Abstract

A Field Programmable Gate Array (FPGA) based hardware accelerator for multi-conductor parasitic capacitance extraction, using Method of Moments (MoM), is presented in this paper. Due to the prohibitive cost of solving a dense algebraic system formed by MoM, linear complexity fast solver algorithms have been developed in the past to expedite the matrix-vector product computation in a Krylov sub-space based iterative solver framework. However, as the number of conductors in a system increases leading to a corresponding increase in the number of right-hand-side (RHS) vectors, the computational cost for multiple matrix-vector products present a time bottleneck, especially for ill-conditioned system matrices. In this work, an FPGA based hardware implementation is proposed to parallelize the iterative matrix solution for multiple RHS vectors in a lowrank compression based fast solver scheme. The method is applied to accelerate electrostatic parasitic capacitance extraction of multiple conductors in a Ball Grid Array (BGA) package. Speed-ups up to 13x over equivalent software implementation on an Intel Core i5 processor for dense matrix-vector products and 12x for QR compressed matrix-vector products is achieved using a Virtex-6 XC6VLX240T FPGA on Xilinx's ML605 board.

Accelerating method of moments based package‐board 3D parasitic extraction using FPGA

“…Although there have been some efforts in FPGA‐based acceleration of the 3D Finite Difference Time Domain (FDTD) and the Finite Element Method (FEM) , to the best of our knowledge, MoM acceleration on FPGA was first attempted in Ref. .…”

“…In this study, building on , an algorithm is implemented on Virtex‐6 XC6VLX240T FPGA on Xilinx's ML605 board to expedite the matrix‐vector products such that significant (>10×) speed‐up is observed in the entire solve process. The algorithm is architected to scale almost linearly with FPGA resource utilization.…”

Choosing order of operations to accelerate strip structure analysis in parameter range

“…An example of such problem is the time-consuming computation of the capacitance matrix for strip structures with varied parameters (A k is a square and dense matrix of N order) [9] with boundary element methods [10], also called the method of moments in electromagnetics [11], and the panel method in fluid dynamics. The linear system matrix in the method of moments has a much smaller order in comparison with the time-domain finite-difference, finite element, finite integration, and transmission line matrix methods, which are also used in electromagnetic tasks.…”