Unstructured N-Dimensional Grid Table Model for Circuit Simulation
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Solution Overview
Problem
Current circuit simulation methods spend a significant amount of computation time constructing circuit equations, particularly when evaluating device models, and lack a straightforward approach to preserve monotonicity and continuity while reducing computation time.
Innovation Solution
A method for generating and evaluating a table model using an unstructured N-dimensional grid that performs accuracy partitioning, continuity partitioning, and grid refinement to ensure monotonic and continuous solutions, thereby reducing computation time and preserving model properties.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If a table model is used to reduce computation time, then device model evaluation speed is improved, but it is difficult and time consuming to extract a good model for a complex device
Solution Approach 1:
The function domain is segmented into multiple partitions using a tree-based model approximation method. The root partition is split recursively into sub-partitions, allowing the complex device model to be divided into manageable segments that can be processed independently, thus reducing the overall complexity of model extraction while maintaining evaluation speed.
2Ease of operation
If structured grids are used with regular connectivity, then interpolation and neighbor calculation are simplified, but accuracy is limited by available computer memory
Solution Approach 1:
The patent employs a dynamic partitioning approach where the grid structure is not fixed but adaptively created through recursive partitioning of the function domain. This dynamic structure allows the model to achieve higher accuracy by creating finer partitions in regions requiring more precision, while still maintaining computational efficiency through the tree-based organization that simplifies neighbor identification and interpolation operations.
Data Source
AI summary
A method for generating and evaluating a table model for circuit simulation in N dimensions employing mathematical expressions for modeling a device. The table model uses an unstructured N-dimensional grid for approximating the expressions. The method includes the steps of: (a) establishing a function domain having boundary limits in the N dimensions; (b) performing an accuracy partitioning operation to establish accuracy partitions; the mathematical expressions being satisfied within each accuracy partition within a predetermined error criteria; (c) performing a continuity partitioning operation to establish continuity partitions ensuring continuity of solutions of the mathematical expressions across boundaries separating adjacent accuracy partitions; (d) performing a grid refining operation to configure the continuity partitions to assure monotonic solutions of the mathematical expressions in the continuity partitions; (e) if a continuity partition is altered during the grid refining operation, returning to step (c), else proceeding to next step; (f) ending the method.