Parallel Matrix Processing with Overlapping Data for Algebraic Multigrid
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Solution Overview
Problem
Existing parallel processing methods face challenges in achieving high computational accuracy and fast calculation when the number of computers in parallel is increased, as they often result in a large number of iterations and potential failure to obtain a solution due to inadequate consideration of the connection relationships between grid points in hierarchical structures during algebraic multigrid method-based processing.
Innovation Solution
A parallel processing apparatus and method that generates divided matrix data with overlapping portions, allowing for evaluation-value matrix data exchange and C/F point determination across processors, ensuring accurate interpolation and coefficient matrix generation while considering the connection relationships between grid points, thereby improving computational accuracy and reducing the number of iterations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If matrix data is divided and processed in parallel across multiple computers, then processing speed increases, but computational accuracy deteriorates and the number of iterations increases
Solution Approach 1:
The patent divides the matrix data into multiple divided matrix data sets that can be processed in parallel across multiple computers. Each processor handles a specific portion of the matrix data, enabling parallel processing while maintaining the ability to integrate results through the overlapping portion mechanism.
Solution Approach 2:
The patent merges results from parallel processing by utilizing overlapping portions of divided matrix data. Each processor processes its assigned data and exchanges information through overlapping regions, allowing the system to combine results from multiple processors while maintaining computational accuracy and reducing iteration requirements.
2Productivity
If the number of parallel computers is increased, then processing capacity increases, but the number of iterations increases and convergence reliability deteriorates
Solution Approach 1:
The patent implements a feedback mechanism where processors exchange evaluation values through overlapping portions. This feedback allows each processor to adjust its processing based on information from neighboring processors, ensuring that the parallel processing maintains convergence properties and reliability even as the number of processors increases.
Solution Approach 2:
The patent performs preliminary setup by dividing the matrix data with intentionally created overlapping portions before parallel processing begins. This preliminary action ensures that all necessary information is available in the overlapping regions, preventing convergence issues that would otherwise arise when scaling to more processors.
3Productivity
If matrix data is divided without overlapping portions, then data distribution efficiency increases, but computational accuracy deteriorates due to loss of connection relationships
Solution Approach 1:
The patent applies local quality by creating overlapping portions at the boundaries of divided matrix data. These overlapping regions have special significance as they contain the connection relationship information that is lost in non-overlapping divisions. The overlapping portions enable accurate computation of evaluation values by preserving local connectivity information.
Data Source
AI summary
A parallel processing apparatus includes: processors; and a network switch, wherein a first processor: generates divided matrix data by dividing the matrix data in such a manner that an overlapping portion is present with each other; transmits the divided matrix data to a second processor; generates first evaluation-value matrix data from the divided matrix data; transmits, to the second processor, first elements in a first overlapping portion of the first evaluation-value matrix data; receives, from the second processor, second elements of a second overlapping portion of second evaluation-value matrix data; calculates first added evaluation data by adding the second elements to the first elements; transmits the first added evaluation data to the second processor; receives, from the second processor, second added evaluation data; and calculates a first C point or a first F point based on the first evaluation-value matrix data which is updated using the second added evaluation data.