Lengendre spectral element method elastic wave propagation parallel simulation method based on element-by-element technology

Abstract

The invention discloses a Lengendre spectral element method elastic wave propagation parallel simulation method based on an element-by-element technology, which is based on a Lengendre-expanding spectral element method and adopts the element-by-element technology to realize the method for simulating wave propagation in parallel in such a way that a main node controls a plurality of independent computing nodes. The method comprises the following steps: (1) firstly, rewriting an elastic wave propagation equation by adopting the Lengendre spectral element method; carrying out the task allocation of each computing node according to an equilibrium principle after the space of the whole computing area is dispersed; computing an element mass matrix and an element stiffness matrix which are contained by the respective task of each computing node by each computing node, and storing in the storage of each computing node; and (2) then, computing the overall lattice vector of the whole iteration time slot at the main node by adopting a time domain iteration method, and simultaneously, converting the overall matrix and the vector product of the equally distributed task by each parallel computing node by adopting the element-by-element technology into an element matrix and a vector product. The invention also discloses how to apply the element-by-element technology to the Lengendre spectral element method and lays foundation for realizing parallel methods.

Description

technical field [0001] The invention relates to the field of elastic wave propagation simulation, in particular to a method for parallel simulation of elastic wave propagation based on Lengendre spectral element method based on element-by-element technology. Background technique [0002] The simulation of elastic wave propagation plays an important role in the fields of geophysics, engineering seismology and computational acoustics. How to find a numerical simulation method that is more accurate, faster, and more suitable for parallelization has always been the goal and focus of researchers in related fields at home and abroad. [0003] Currently, the numerical methods commonly used in the simulation of elastic wave equations mainly include finite difference method, finite element method and spectral method. They have their own advantages and disadvantages and are applied in different fields. [0004] The finite difference method can be regarded as a configuration point met...

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Problems solved by technology

Considering the sparse nature of the global matrix, the global matrix and phasor multiplication consumes a lot of computing time

These have greatly hindered the application of the spectral element method in specific problems

[0011] In addition, due to the existence of the global stiffness matrix and mass matrix in the traditional spectral element method, the efficiency of its parallelization is limited in the algorithm

This is a great defect for the large-scale practical application of the spectral element method in the fields of geophysics, engineering seismology, computational acoustics, etc.

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