A finite-difference eigenvalue solver computes the fundamental frequency of a…

PHYSICS · Multi-part · Fermi University Physics · Computational Physics · Research software practice, verification and validation · Research software practice, verification and validation

Scientific Computing for Physicists, Ch Are they the right equations? Solution verification, benchmarks and validation

Problem

A finite-difference eigenvalue solver computes the fundamental frequency

f

of a vibrating square membrane on three meshes with refinement ratio

r=2

N=45

gives

f_3=119.040\ \mathrm{Hz}

N=90

gives

f_2=119.760\ \mathrm{Hz}

N=180

gives

f_1=119.940\ \mathrm{Hz}

(subscript 1 is the finest mesh). The run is in the asymptotic range of grid convergence. ((a)) Compute

\hat p

and the Richardson-extrapolated frequency

f_{\rm ext}

. ((b)) Report

\mathrm{GCI}_{\rm fine}

(relative, dimensionless), using

F_s=1.25

. ((c)) The finest-mesh run is timed using warm-up runs followed by repeated timed runs, reporting the median and interquartile range: after 3 discarded warm-up runs, the 9 measured times (ms), sorted, are

30.0, 30.2, 30.4, 30.6, 30.8, 31.0, 31.2, 31.6, 33.0

. Report the median and IQR (median-of-halves convention, median excluded from each half of four).

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