Real-Time Linear Equation Solver for Tokamak Plasma Control
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Solution Overview
Problem
Current techniques are inadequate for solving systems of linear equations in real-time, particularly in applications like tokamak nuclear fusion where fast and accurate plasma control is required, as they are computationally demanding and cannot meet the stringent time constraints of modern tokamak systems.
Innovation Solution
A two-stage approach is implemented, where an off-line stage pre-computes data based on constant problem parameters to determine a partitioning strategy and calculate coefficients, and a real-time stage uses these pre-computed values with current input data to solve linear equations quickly, allowing for recursive partitioning and solution generation within tight time frames.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If current techniques are used to solve systems of linear equations, then computational accuracy can be maintained, but the solution time exceeds real-time constraints
Solution Approach 1:
The patent pre-calculates and stores inverse matrix elements offline before real-time operation. During real-time control, the pre-computed inverse elements are directly applied to solve linear equations, eliminating the need for time-consuming matrix inversion during critical operations and enabling solutions within millisecond constraints
Solution Approach 2:
The patent divides the large coefficient matrix into smaller block matrices through partitioning. This segmentation allows the inverse to be computed from smaller sub-matrices offline, reducing real-time computational burden while maintaining solution accuracy through systematic block matrix operations
2Measurement precision
If the spatial resolution of the PDE grid is increased to improve plasma control accuracy, then the computational complexity increases significantly
Solution Approach 1:
The patent partitions the high-resolution PDE grid into smaller block matrices, allowing the system to handle fine spatial resolution without proportionally increasing real-time computational complexity. The block structure enables efficient memory access patterns and parallel computation
Solution Approach 2:
The patent performs offline pre-computation of inverse matrix elements for high-resolution grids, storing these pre-computed values for rapid retrieval during real-time plasma control. This separates the heavy computational burden from the real-time control loop, enabling high spatial resolution without real-time complexity penalties
3Productivity
If offline HPC is used to pre-calculate Grad-Shafranov parameters, then real-time approximation speed improves, but the computational demand remains high
Solution Approach 1:
The patent pre-calculates and stores inverse matrix elements offline in detail, then uses these pre-computed elements directly during real-time operation. This approach achieves exact solutions (not just approximations) at real-time speeds, reducing the need for heavy offline HPC resources compared to iterative approximation methods
Solution Approach 2:
The patent creates a compressed representation of the inverse matrix that can be stored in limited memory and rapidly applied during real-time control. This copied inverse structure enables exact solutions without requiring access to the full computational power needed for original matrix inversion
Data Source
AI summary
System and method for controlling/analyzing a process by solving a system of linear equations in real-time. Linear equations that model the process are stored. In an off-line stage a partitioning strategy is determined based on the linear equations, including determining groups of values for recursively partitioning a set of values measured and/or computed from the process. In an on-line stage: current process data are received from the process, including measurements from the process, and composing a set of values; the linear equations are recursively solved for a first group of the set, where the first group partitions the set into respective subsets of values, and where the recursively solving produces solved values for respective first groups of the set/subset of values; the linear equations are solved for remaining unsolved values in the set, thereby producing solved values for the set, which are stored and are useable to control/analyze the process.