Parallel Power Grid Analysis via Partitioning
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Solution Overview
Problem
The complexity of modern integrated circuit designs poses challenges in achieving a reasonable tradeoff between accuracy and performance in simulating large-scale power grids, particularly in microprocessor designs, due to the difficulty in efficiently analyzing resistive voltage drop, electromigration, and noise failures.
Innovation Solution
The method involves representing the power grid as a graph with nodes and edges, partitioning it based on predetermined criteria, and performing concurrent and independent transient analysis of the partitions using sparse vector decomposition and worst-case nodal sensitivity analysis to determine the size of each partition's shell, allowing for efficient simulation in parallel with multiple threads.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional time-domain circuit simulation techniques are applied to large-scale power grids, then accuracy in identifying IR drop, electromigration and noise failures is improved, but computational performance deteriorates
Solution Approach 1:
The power grid is partitioned into multiple independent sub-grids based on connectivity and electrical characteristics. Each sub-grid can be analyzed separately using time-domain simulation techniques, reducing the computational complexity from O(N^3) for the entire grid to O(n^3) for each sub-grid where n << N. This segmentation maintains accuracy for critical failure identification while improving overall computational performance.
Solution Approach 2:
The problem is transformed from a single large-scale time-domain simulation into multiple parallel frequency-domain analyses. By converting the time-domain differential equations into frequency-domain algebraic equations using Fourier transform, the computational burden is reduced and parallel processing becomes feasible, thereby improving performance while maintaining accuracy through proper frequency sampling.
2Measurement precision
If the power grid is analyzed as a single large-scale system, then comprehensive accuracy is maintained, but the complexity of the analysis process increases
Solution Approach 1:
The power grid analysis is divided into multiple independent partitions based on connectivity thresholds and electrical characteristics. Each partition is analyzed separately using simplified models, reducing the overall analysis complexity. The partitions are then recombined to provide comprehensive grid assessment, maintaining accuracy while making the analysis process more manageable and less complex.
Solution Approach 2:
Instead of analyzing the entire power grid with full complexity, the method applies partial analysis to each partition using simplified models and assumptions. This partial action approach reduces computational complexity significantly while still providing sufficient accuracy for failure identification, as each partition is analyzed with appropriate detail rather than exhaustive complexity.
Data Source
AI summary
A method for a power grid configured to supply current to a plurality of elements of a circuit. The method includes representing the power grid as a graph including a plurality of nodes and a plurality of edges, wherein each node of a portion of the plurality of nodes corresponds to an element of the plurality of elements each modeled as a current source, determining a characteristic matrix A of the power grid, wherein transient behavior of the power grid is represented by a set of linear equations of A*v=i, wherein v is a nodal voltage vector representing nodal voltages of at least a portion of the plurality of nodes and i is a current source vector representing currents supplied to at least a portion of the plurality of elements, identifying first and second partitions of the power grid based on a predetermined criterion, identifying first and second current source subvectors of the current source vector according to the first and second partitions of the power grid, identifying a first shell of the first partition based on worst case nodal voltage sensitivity analysis with respect to the first current source subvector, identifying a second shell of the second partition based on worst case nodal voltage sensitivity analysis with respect to the second current source subvector, and generating an analysis result of transient behavior of the power grid by analyzing, concurrently and independently, the first and second shells of the first and second partitions of the power grid, respectively.