﻿ Sample Problems > Usage > Accuracy > sine3d

# sine3d

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# sine3d   { SINE3D.PDE

This problem compares the solution accuracy for three different levels of ERRLIM.

}

title '3D Accuracy Test - Sine'

coordinates

cartesian3

select

ngrid = 5

errlim = staged(1e-2, 3e-3, 1e-3, 3e-4, 1e-4)

variables

u

definitions

long = 1

wide = 1

z1 = -1

z2 = 1

w=0.1

rs = r/w

uex = sin(rs)/rs

s = -(dxx(uex)+dyy(uex)+dzz(uex))

RMS_error = sqrt(integral((u-uex)^2)/sqrt(integral(uex^2)))

equations

U:    div(grad(u)) + s = 0

extrusion z = z1,z2

boundaries

surface 1 value(u)=uex     { fix bottom surface temp }

surface 2 value(u)=uex     { fix top surface temp }

Region 1               { define full domain boundary in base plane }

start(-wide,-wide)

value(u) = uex         { fix all side temps }

line to (wide,-wide)   { walk outer boundary in base plane }

to (wide,wide)

to (-wide,wide)

to close

monitors

grid(x,z) on y=0 as "Grid on X-Z cut"

contour(uex) on y=0 as "Exact Solution Uex"

contour(u) on y=0 as "Numerical Solution U"

contour(u-uex) on y=0 as "Actual error U-Uex"

plots

grid(x,z) on y=0 as "Grid on X-Z cut"

contour(uex) on y=0 as "Exact Solution Uex"

contour(u) on y=0 as "Numerical Solution U"

contour(u-uex) on y=0 as "Actual error U-Uex"

summary

report(errlim) as "Requested error"

report(RMS_error)

histories

history(RMS_error, errlim) LOG

end