A previously described two-dimensional -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 -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 -space method to calculate acoustic propagation in tissues over hundreds of wavelengths.
David P. Duncan is thanked for discussions and code development. Jeffrey P. Astheimer and Jing Jin are thanked for participation in reviews throughout the duration of this work. Andrew J. Hesford is thanked for discussions during the final stages of the reported studies. Initial development of code used resources at Research Computing and the Department of Electrical Engineering, Multi-agent Bio-Robotics Lab, at the Rochester Institute of Technology. Gurcharan S. Khanna and Ferat Sahin are thanked for granting access to these resources. This research also used the SHARCNET facilities. Ge Baolai is thanked for technical assistance in the use of SHARCNET. Subsequent code development and computations used resources of the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. Consulting staff at NERSC are thanked for help compiling benchmark test programs on the Cray XT4 (Franklin). M.I.D. is a Scholar of the Canadian Institutes of Health Research/University of Western Ontario Strategic Training Initiative in Cancer Research and Technology Transfer and holds a NSERC PGS-D scholarship. This research was funded in part by NIH Grant Nos. HL 50855, CA 74050, and EB 00280, Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant Nos. 261323-03 and 261323-07, the Canadian Institutes of Health Research/University of Western Ontario Strategic Training Initiative in Cancer Research and Technology Transfer, and the University of Rochester Diagnostic Ultrasound Research Laboratory Industrial Associates.
II. MATHEMATICAL FORMULATION
A. Physical acoustic foundations
B. Inclusion of a PML
C. Solution for scattered pressure
III. NUMERICAL METHODS
A. Parameters of the PML
B. Investigation of smoothing
C. Inclusion of absorption
D. Accuracy and stability: vs CFL and PPW for a small sphere
E. Impact of inhomogeneity scale
F. Large-scale compound object
IV. NUMERICAL RESULTS
A. PML parameters
B. Medium smoothing
D. Accuracy vs PPW and CFL for a small sphere
E. Scaling results
A. Solutions for total pressure and scattered pressure
B. Scaling and accuracy
Data & Media loading...
Article metrics loading...
Full text loading...