A finite-difference Poisson solver computes the electrostatic potential at the centre…

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 Poisson solver computes the electrostatic potential

V

at the centre of a grounded box on three successive grids, each with twice the linear resolution of the last:

N=25

gives

V_3 = 0.993600\ \mathrm{V}

N=50

gives

V_2 = 0.998400\ \mathrm{V}

, and

N=100

gives

V_1 = 0.999600\ \mathrm{V}

(subscript 1 is the finest grid). The grid refinement ratio is

r=2

and the run is in the asymptotic range of grid convergence. ((a)) Compute the observed order of convergence

\hat p

and the Richardson-extrapolated value

V_{\rm ext}

. ((b)) Report the fine-grid grid convergence index

\mathrm{GCI}_{\rm fine}

(relative, dimensionless) using the safety factor

F_s = 1.25

. ((c)) The same solver, run on the finest grid, is timed by discarding 3 warm-up runs and then measuring 9 further times (in milliseconds), sorted in increasing order:

8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.9, 9.4

. Using the convention that the median is the middle value and each of

Q_1

Q_3

is the average of the two middle values of the lower and upper halves of four values (median excluded), report the median and the interquartile range (IQR

= Q_3 - Q_1

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