Threshold-Crossing Event Processing in Circuit Simulation
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Solution Overview
Problem
Current circuit simulators face computational inefficiencies when processing threshold-crossing events during transient analysis, as they require multiple time points and iterative predictions to accurately locate crossing times, leading to increased computational expense.
Innovation Solution
A method that detects violations of cross conditions by solving the equations jointly with discretized differential algebraic equations as a coupled nonlinear system, treating the crossing time step as an unknown, and using polynomial interpolation to refine solutions, thereby directly converging to the crossing time point without requiring multiple potential solutions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional iterative prediction methods are used to detect threshold-crossing events, then crossing time points can be located, but computational expense increases due to requiring multiple time points and iterations
Solution Approach 1:
The patent transforms the detection problem by changing the parameter being solved for - instead of iteratively searching for the crossing time point through multiple time steps, the method directly solves for the crossing time step as an unknown variable in the discretized differential algebraic equations. This parameter transformation eliminates the need for multiple iterative predictions while maintaining detection accuracy.
Solution Approach 2:
The patent adds the crossing time step as an additional unknown dimension to the system of equations. By treating the time step itself as a variable to be solved rather than a predetermined parameter, the method transforms a sequential iterative search into a simultaneous solution problem, reducing computational iterations.
2Reliability
If multiple time points are used to iteratively predict crossing events, then accurate crossing detection is achieved, but the number of iterations and computational burden increase
Solution Approach 1:
The patent performs preliminary action by incorporating the crossing detection condition directly into the system of equations before solution. By formulating the crossing time step as an unknown in the initial discretized equations, the method eliminates the need for subsequent iterative predictions and multiple time point evaluations, reducing total computation time while maintaining reliable detection.
Solution Approach 2:
The patent merges the crossing detection process with the main system of equations solution. Instead of treating crossing detection as a separate iterative process that requires multiple time points, the method combines the crossing condition into the discretized differential algebraic equations, allowing simultaneous solution of both the system state and the crossing time step in a unified computational framework.
Data Source
AI summary
Methods, computer systems, and computer readable media are provided for simulation of a model of a system by detecting a violation of a cross condition while iteratively refining a first solution of a system of nonlinear algebraic equations at a current time point, and responsive to the detecting, predicting a crossing time step, projecting an initial guess for a second solution of the system of nonlinear algebraic equations at the crossing time point, and iteratively refining the second solution and the crossing time step by jointly solving an equation for the cross condition with the system of nonlinear algebraic equations as a coupled nonlinear system in which the crossing time step is treated as an unknown to compute changes to the second solution and the crossing time step in each iteration.