Time required to execute a three-dimensional FFT on a single computer compared to the time to execute a three-dimensional FFT on a cluster of 32 computers for a grid size of , 128, 256, or 512. Each point is the average of ten trials. The single-computer architecture is a 64-bit AMD Opteron having 16 Gbytes of random access memory (RAM) running Windows XP x64 and a 64-bit version of MATLAB. The cluster of computers consists of Pentium-III 1.4 GHz processors each having 0.5 Gbyte of RAM, running Linux, and connected via a 1-Gbit/s Ethernet switched network.
Spatially staggered grid.
Left panel: Behavior of a PML as the maximum attenuation per cell is varied with the number of PML layers fixed at 10. Right panel: Behavior of a PML as the number of PML layers is varied and the maximum attenuation per PML cell is fixed at 3 Np.
The scattered waves from a filtered (left) and unfiltered (right) 1-mm radius sphere. The horizontal axes in each panel span 360° in the plane with measurements taken at a distance of 3 mm from the sphere center and waveforms are shown on a bipolar logarithmic scale over a ±60 dB range. The vertical axes span approximately .
Temporal-frequency dependence of sound speed (left) and attenuation (right) in the high-frequency band.
error resulting from scattering of clinical pulse waveforms by a 4-mm diameter sphere.
Scattering from sets of spheres with progressively larger radii.
Scattering from a 24-mm diameter compound sphere with properties similar to those of human breast in a background of water is shown in three orthogonal planes. At the top are time frames recorded at . In the middle are time frames recorded at . At the bottom are time frames recorded at . The six frames are recorded at times 4.8, 9.6, 10.4, 11.2, 12.4, and . The incident illumination is a plane-wave pulse offset at at time with center frequency of 2.5 MHz and a Gaussian envelope with a −3 dB bandwidth of 1.7 MHz. The medium sound speed is overlayed on the pressure field with brighter areas corresponding to higher sound speed.
Execution times for the three-dimensional FFT on the Franklin and SHARCNET clusters.
Properties of background and spheres for large-scale compound medium.
Positions and radii of spheres forming the large-scale compound medium.
errors of propagation calculations for each radius sphere in the large-scale compound medium.
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