The following kernel performs a portion of the finite-difference time-domain (FDTD) method for computing Maxwell’s equations in a three-dimensional space, part of one of the SPEC06fp benchmarks:

Assume that dH1, dH2, Hy, Hz, dy, dz, Ca, Cb, and Ex are all singleprecision floating-point arrays. Assume IDx is an array of unsigned int.

a. What is the arithmetic intensity of this kernel?

b. Is this kernel amenable to vector or SIMD execution? Why or why not?

c. Assume this kernel is to be executed on a processor that has 30 GB/s of memory bandwidth. Will this kernel be memory bound or compute bound?

d. Develop a roofline model for this processor, assuming it has a peak computational throughput of 85 GFLOP/s.

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