Rapid numerical simulation method for element-by-element parallel strong ground motion

Abstract

The invention discloses a rapid numerical simulation method for element-by-element parallel strong ground motion. The method comprises the following steps: 1) transforming a hexahedron unit into a standard cube unit through isoparametric transformation; 2) averagely distributing hexahedron units obtained by spatial discretization to a plurality of calculation cores for parallel calculation; 3) adopting high-order Lagrange interpolation on each unit to obtain an interpolation polynomial, and directly performing approximation on the spatial differential operator by utilizing interpolation multiple terms to form a unit stiffness matrix; 4) performing product operation of the element stiffness matrix and the solution vector on the calculation core; and 5) realizing communication between the process pairs according to a product operation result in a cache communication mode. In the theoretical framework of the spectral element method, the element-by-element parallel algorithm for directly solving the seismic wave motion equation is developed, the calculation amount of seismic wave numerical simulation is effectively reduced by improving the spatial discrete format of the traditional spectral element method and adopting a more efficient parallel calculation communication mode, the seismic wave parallel calculation efficiency is improved, and high-efficiency and high-precision strong ground movement becomes reality.

Description

technical field [0001] The invention belongs to the technical field of seismic data processing, for example, analysis, interpretation, and correction, and in particular relates to a fast numerical simulation method for element-by-element parallel strong ground motion in the field of earthquake disaster emergency response. Background technique [0002] Fast numerical simulation of strong ground motion is crucial for disaster judgment and emergency rescue in earthquake areas; the commonly used strong ground motion method is the stochastic method, which superimposes the dynamic inflection point spectrum on random noise, and considers the attenuation of seismic waves along the path and geometric diffusion effect, so as to quickly synthesize strong ground motion. Although the stochastic method has achieved good results in the practical application of strong ground motion and provided key reference information for earthquake disaster assessment, this method lacks mathematical logic...

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Problems solved by technology

Among these commonly used methods, the finite difference method directly uses finite difference operators to discretize the differential terms of the seismic equation, which has the advantages of intuitive algorithm, minimum calculation amount, and easy program implementation; but the finite difference method has obvious shortcomings, which are mainly reflected in Two aspects: First, the finite difference method is difficult to approximate the free boundary conditions or the approximation accuracy of the free boundary conditions is limited, so that the simulation accuracy of the finite difference method for surface waves is low; secondly, the finite difference method is difficult to use unstructured network The numerical description of the complex model by the lattice makes it difficult for the finite difference method to simulate the strong ground motion in the complex actual geological model; the pseudospectral method is used to approximate the spatial differential operator of the seismic wave motion equation through fast Fourier transform. This method has high precision, The advantage of small numerical dispersion, but the pseudo-spectral method has similar defects to the finite difference method, that is, the surface wave simulation accuracy is low, and the grid is not flexible; compared with the finite difference method and the pseudo-spectral method, the finite element method can accurately simulate the surface wave propagation, and has the ability to adapt to complex models, but the finite element method needs to store a large-scale stiffness matrix, which requires a lot of computer memory. At the same time, the element stiffness matrix formed by the discrete seismic wave motion equation of the finite element method is a dense matrix. When calculating the product of the element stiffness matrix and the solution vector, the amount of calculation is large; because the calculation efficiency of the finite element method is low, it is difficult to meet the needs of fast calculation of strong ground motion; the spectral element method is similar to the finite element method, and has surface wave simulation accuracy High, strong adaptability to the model, etc.; because the spectral element method uses orthogonal polynomial interpolation in space, the spectral element method has the accuracy of the spectral method, so the calculation accuracy is high when used for strong ground motion simulation; but the spectral element method Also, the calculation efficiency is low, and it is difficult to quickly obtain the simulation results of near-field strong ground motion after the earthquake occurs

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