高效优化非分裂PML边界二阶标量波方程数值模拟方法

Efficient Optimization of Second Order Scalar Wave Equation Numerical Simulationfor Non-Splitting PML Boundary

卷积完全匹配层(convolution perfectly matched layer,CPML)吸收边界是一种高效处理波动方程数值模拟中人工边界反射波的方法。本文基于传统的一阶系统CPML吸收边界条件推广并推导了新的二阶系统CPML边界条件(NCPML)。与常规二阶系统CPML边界条件不同,新边界条件推导的核心思想是在复数频率域中忽略部分衰减因子空间变化特性,避免其在时间域产生复杂卷积算子,然后反变换至时间域得到基于CPML吸收条件的二阶标量波方程,并应用于二阶标量波方程数值模拟。均匀介质模型测试验证了NCPML吸收条件在内存使用上相对于常规二阶系统CPML与SPML(split PML)吸收条件更少。在对人工边界反射的吸收效果上,NCPML稍逊色于常规二阶系统CPML,但二者均相对于SPML优势明显。最后通过层状模型和Marmousi模型测试验证了NCPML的稳定性及其在效率上的优势。

Convolutional perfectly matched layer(CPML)absorbing boundary is a method for efficiently processing artificial boundary reflection waves in numerical simulation of wave equations.Based on the traditional first-order system CPML absorption boundary conditions,the authors generalized and deduced the new CPML boundary conditions of the second-order system.Different from the CPML boundary conditions of the conventional second-order system,the core idea of the new boundary is to ignore the space-varying characteristics of partial attenuation factors in the complexfrequency dom ain,so as to avoid of the generation of complex convolution in the time domain,and then to obtain a second-order scalar wave equation based on CPML absorption conditions,which is then applied to the second-order scalar wave numerical simulation.Through the uniform medium model te s t,the memory usage of the new second-order system CPML absorbing boundary is less than that of the conventional second-order system CPML and SPM L,and the effect of absorbing boundary of the new second-order system CPML is slightly inferior to the conventional second-order system CPM L,but they all have obvious advantages over SPML.The stability of the new boundary conditions and the advantages in efficiency are verified by the test of layered model and Marmousi model.