Finite element parallel computing method based on node overlapping type region decomposition without Schwarz alternation

Abstract

The invention provides a finite element parallel computing method based on node overlapping type region decomposition without Schwarz alternation. The finite element parallel computing method comprises the following steps that all processes cooperatively decompose a global grid; wherein each process establishes a data exchange area of an overlapped layer; wherein the processes cooperate to establish a regional communication topology and an overlapping region ghost point transceiving structure; and unit matrix assembly is finished by the process according to the local numbers of the finite element nodes in the units, and then completing region vector and matrix assembly according to mapping from the local numbers of the finite element nodes in the units to the numbers in the regions. The finite element parallel computing method without Schwarz alternate iteration based on node ParMetis overlapping region decomposition can be universally applied to multiple physical fields and coupling fields of complex structures, electromagnetism, sound, heat, fluid and the like, and convergence performance is kept consistent with that of serialization.

Description

technical field [0001] The present invention relates to the technical field of parallel computing, in particular to a finite element parallel computing method based on node overlapping domain decomposition without Schwarz alternation. Background technique [0002] The Domain Decomposition Method (DDM) is a numerical method for partial differential equations. Its central idea is to decompose the solution area of ​​the problem to be solved into multiple sub-areas, and coordinate each sub-area by using the transmission conditions on the common boundary to achieve in-sub-areas. The purpose of solving on the domain. The domain decomposition method (DDM) was only a serial algorithm in the early stage, and could not adapt to parallel computing applications. In recent years, with the rapid development of parallel computers and parallel algorithms, finite element parallel computing based on domain decomposition is becoming a powerful tool for solving complex domains or complex proce...

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Problems solved by technology

At this time, the scale and condition number of the interface equation will increase sharply with the increase of the number of sub-regions, so it is not suitable to use the direct method to solve it, and it will also cause the iterative method to need more iterations to converge.

The poor iterative convergence of interface equations and the substantial increase in communication overhead will seriously reduce the efficiency of solving interface equations, which will inevitably lead to a substantial increase in the total time of solving interface equations and the total time of system solving, thus seriously affecting the overall parallel computing efficiency of the system

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