Parallel LU Factorization Panel Integration Load Balancing
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Solution Overview
Problem
The existing techniques for solving simultaneous linear equations using parallel computer systems face challenges in reducing processing time due to non-uniform block allocation among nodes, which affects computational efficiency and load balancing, especially when increasing block size for faster matrix products.
Innovation Solution
A parallel computer system configuration where each processor generates and integrates row and column panels of a matrix for LU factorization, computes matrix products, and exchanges panels between processors to maintain efficient computation and load balancing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If block size is increased to improve computational efficiency for matrix products, then processing speed improves, but load balancing deteriorates due to non-uniform block allocation among nodes
Solution Approach 1:
The matrix is divided into panels (row panels and column panels) instead of traditional blocks, allowing for more flexible distribution. Each processor handles specific panels, and the panel-based segmentation enables better load balancing while maintaining computational efficiency through integrated panel operations.
Solution Approach 2:
The system dynamically adjusts panel allocation and integration strategies based on processor capabilities and workload distribution. By integrating multiple row panels and column panels dynamically, the system optimizes both computational efficiency and load balancing adaptively during execution.
2Adaptability or versatility
If non-uniform block allocation is used among nodes, then adaptability to different problem sizes improves, but processing time increases due to load imbalance
Solution Approach 1:
Different processors can handle different types of panels (row panels vs. column panels) with specialized optimization. Each processor is assigned specific panel integration tasks based on its local capabilities, allowing adaptive problem size handling while maintaining balanced workload distribution through targeted panel allocation.
Data Source
AI summary
A parallel computer system including a plurality of processors configured to perform LU factorization in parallel, the system is configured to cause each of the plurality of processors to execute processing including: generating a first panel by integrating a plurality of row panels among panels of a matrix to be subjected to the LU-factorization, the plurality of row panels being processed by the processor, generating a second panel by integrating a plurality of column panels among the panels of the matrix, the plurality of column panels being processed by the processor, and computing a matrix product of the first panel and the second panel. In parallel with the computation of the matrix product, each processor is configured to receive or transmit a column panel to be used for computation of a subsequent matrix product from or to another processor among the plurality of processors.