A k-space method for acoustic propagation using coupled first-order equations in three dimensions.
A k-space method for acoustic propagation using coupled first-order equations in three dimensions.
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DOI：
10.1121/1.3158857
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发表时间：
2009-09
期刊：
影响因子：
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通讯作者：
J. Tillett;M. Daoud;J. Lacefield;R. Waag
中科院分区：
文献类型：
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作者：
J. Tillett;M. Daoud;J. Lacefield;R. Waag
以前描述的二维k空间方法用于大规模计算声波在组织中的传播被扩展到三维。三维方法包含了二维方法的所有特征，使传播计算准确稳定。这些特征是空间导数的光谱计算，在均匀介质中产生精确传播的时间校正，交错的空间和时间网格，以及完美匹配的边界层。空间导数的频谱评估是用三维的快速傅立叶变换来完成的。这种计算瓶颈需要全对全通信；因此，并行实现中的执行时间对节点互连延迟和带宽很敏感。通过与具有球面非均匀性介质的精确解的比较，评价了三维方法的精度。三维的大规模计算是通过在一组计算机上分配每个体素近50个变量来实现的。比较了用于评价方法准确性的两种计算机聚类。k空间计算与包括吸收在内的精确方法的比较突出了准确模拟介质色散关系的必要性，特别是在大尺度介质中。精确建模的介质允许k空间方法计算组织中数百个波长的声波传播。
A previously described two-dimensional k-space method for large-scale calculation of acoustic wave propagation in tissues is extended to three dimensions. The three-dimensional method contains all of the two-dimensional method features that allow accurate and stable calculation of propagation. These features are spectral calculation of spatial derivatives, temporal correction that produces exact propagation in a homogeneous medium, staggered spatial and temporal grids, and a perfectly matched boundary layer. Spectral evaluation of spatial derivatives is accomplished using a fast Fourier transform in three dimensions. This computational bottleneck requires all-to-all communication; execution time in a parallel implementation is therefore sensitive to node interconnect latency and bandwidth. Accuracy of the three-dimensional method is evaluated through comparisons with exact solutions for media having spherical inhomogeneities. Large-scale calculations in three dimensions were performed by distributing the nearly 50 variables per voxel that are used to implement the method over a cluster of computers. Two computer clusters used to evaluate method accuracy are compared. Comparisons of k-space calculations with exact methods including absorption highlight the need to model accurately the medium dispersion relationships, especially in large-scale media. Accurately modeled media allow the k-space method to calculate acoustic propagation in tissues over hundreds of wavelengths.