一种求解地震波方程的高效并行谱元格式

An Efficient Parallel Spectral Element Scheme for Solving Seismic Wave Equation

地震波数值模拟在地震学和地震勘探中扮演着非常重要角色.在已有工作的基础上,提出1种高效并行的地震波PML方程谱元格式.PML被引入地震波方程以吸收外向波进而模拟无界区域.进一步,为了适应复杂地形同时允许时间显式推进,谱元方法被用来离散地震波PML方程.由此得到地震波PML方程谱元格式.在此基础上,阐述了单元刚度矩阵分解性质,并说明了利用单元刚度矩阵分解可以大幅减少刚度矩阵存储量同时显著加速刚度矩阵与向量乘积,进而显著减少格式的计算量和存储量.此外,算法复杂性分析表明格式无论在计算量上还是在存储量上都优于几种已知的1阶地震波PML方程谱元格式.结合并行技术,给出了高效并行的地震波PML方程谱元格式.数值实验验证了格式的正确性、良好的强弱并行可扩展性以及对复杂地形的适应性.

Numerical simulation of seismic waves plays an essential role in seismology and seismic exploration .We propose here an efficient parallel spectral element scheme for seismic wave equation with perfectly matched layer （PML） .PML is integrated into the seismic wave equation to absorb out-going waves and mimic unbounded domain .Ulteriorly ,to enable adapting complex topography and explicit time stepping ,the spectral element method （SEM ） is used to discretize seismic wave equation with PML ,which results in a spectral element scheme .In addition ,we demonstrate that element stiffness matrices can be decomposed ,which can be used to greatly reduce the storage of stiffness matrix and accelerate stiffness matrix-vector multiplication and thus remarkably speed up the scheme and cut down memory cost .Furthermore ,we study several spectral element schemes known and show that our scheme is superior to others in both calculation and storage . Combined with parallel technique ,an efficient parallel spectral element solver for seismic wave equation with PML is present . Numerical experiments show that our scheme is correct ,well strongly/weakly scalable and of good adaptation to complex topography .