卷积完全匹配层在两维声波有限元计算中的应用  

Application of convolution perfectly matched layer in finite element method calculation for 2D acoustic wave

作　　者：李义丰[1] 李国峰[2] 王云[3] 

机构地区：[1]南京工业大学电子与信息工程学院,南京210009 [2]廊坊师范学院物理与电子信息学院,廊坊065000 [3]廊坊师范学院数学与信息科学学院,廊坊065000

出　　处：《声学学报》2010年第6期601-607,共7页Acta Acustica

摘　　要：将基于复坐标变换和复频移扩展坐标变量的卷积完全匹配层Convolution Perfectly Machted Layer(CPML)引入到两维声波方程的有限元(FEM)计算中,该匹配层作为一种吸收边界条件Absorbing Boundary Condition(ABC)应用在有限元计算的边界截断上。文中分别给出了频域和时域的CPML方程的表达形式,并在有限元计算软件COMSOL中完成数值计算。相对于经典的PML,CPML最大的优势在于它不需要把场分裂开,这使其具有更好的稳定性和更高的吸收性能,且更易于实现。数值计算结果表明,CPML边界层有着比PML更好的吸收效果,其更有效的吸收了进入其中的声场能量。A method is presented to extend the Convolution Perfectly Matched Layer（CPML）,which bases on the complex coordinates transformation and complex frequency shifted stretched-coordinate metrics,to the 2D acoustic equation calculated with the method of Finite Element Method（FEM）.This non-physical layer is used at the computational edge of a FEM as an Absorbing Boundary Condition（ABC） to truncate unbounded media.In this paper,the CPML equations have been presented in frequency domain and in time domain,respectively,and the calculations have been realized in the FEM software of COMSOL.The main advantage of CPML over the classical PML layer is that it is based on the unsplit components of the wave field leading to a more stable,highly effective absorption and a more facility to realize.The results of numerical simulation demonstrate that CPML has better absorbability than PML and it absorbs the outgoing energy more effectively.

关 键 词：有限元计算软件 卷积完全匹配层 声波方程 应用 吸收边界条件 复坐标变换 数值计算 吸收性能 

分 类 号：O422.2[理学—声学] O411[理学—物理]