A Parallel Solution Method for Lower Triangular Equations Oriented to Structured Mesh Sparse Matrix

Abstract

A method for optimizing inter-processor communication and cache space utilization in solving structured grid sparse lower triangular equations in high-performance parallel computing, including: receiving the solution vector of structured grid, etc., starting multiprocessors to start parallel execution ;Decompose the solution vector into multiple sub-blocks, divide each sub-block into multiple columns, treat multiprocessors as a rectangular array, each processor is responsible for computing a column, and the processors open up storage dependent data in their own caches Buffer, get the data required for calculation from neighbors or its own memory and store it in the buffer, complete its own column calculation, and send the calculated data to other processors that depend on the data; the rectangular array of processors traverses all sub-blocks, and completes Calculate the required data communication, and perform calculations for each sub-block until the entire solution calculation is completed. The dependent data of each operation is transmitted through fast communication between processors, minimizing memory access overhead and maximizing resource utilization.

Description

technical field [0001] The invention relates to the fields of numerical calculation and high-performance calculation, in particular to a method for solving a lower triangular sparse matrix in the form of a structured grid under the environment of a high-performance parallel computer. Background technique [0002] With the development of computer technology, the demand for large-scale scientific computing is gradually increasing. Many fields of scientific computing, such as numerical weather prediction simulation, fluid dynamics calculation, etc., need to solve large-scale sparse linear equations. A structured grid is one in which all internal points within a grid region have the same adjacent cells. As a special form of grid, it has the advantages of simple data structure, fast generation speed, and suitable for fluid calculation, so it widely exists in many real applications. [0003] Therefore, Structured Sparse Triangular Solver plays a very important role in the field ...

AI Technical Summary

Problems solved by technology

For the structured grid SpTRSV, there is still a lack of an algorithm to solve the structured sparse lower triangular matrix by effectively using the inter-processor communication method

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