SplineTable

{SPLINETABLE.PDE}

{

This problem employs a 2D data table named 'stable.tbl' to create a spline table.

The file format is the same for TABLE or SPLINETABLE input.

The SPLINETABLE operator can be used to build spline tables of one or two dimensions.

The resulting interpolation is third order in the coordinates, with continuous values and derivatives.

First or second derivatives of the interpolated function may be computed.

Here the table is used as source and diffusivity in a fictitious heat equation, merely to

show the use of the table variable.

The SAVE function is used to construct a Finite Element interpolation of the data from the

spline table, for comparison of derivatives.  Cubic FEM basis is used so that the second derivative

is meaningful.

}

title 'Table Input Test'

select

regrid=off

surfacegrid=100

contourgrid=100

cubic

variables

u

definitions

alpha = splinetable('stable.tbl')  ! construct spline fit of table

k = 1/alpha

femalpha = save(alpha)        ! save a FEM interpolation of table

equations

div(k*grad(u)) + alpha = 0

boundaries

region 1

   start(0,10)

   value(u) = 0

   line to (0,0) to (10,0) to (10,10) to close

monitors

contour(u)

plots

grid(x,y)

contour(u)

contour(k)

surface(u)

contour(alpha) as 'table'

contour(dx(alpha)) as 'dx(table)'

contour(dy(alpha)) as 'dy(table)'

vector(grad(alpha)) as 'grad(table)'

surface(alpha) as 'table'

contour(dxx(alpha)) as 'dxx(table)'

contour(dxy(alpha)) as 'dxy(table)'

contour(dyy(alpha)) as 'dyy(table)'

contour(dxx(alpha)+dyy(alpha))  as "Table Curvature"

contour(div(grad(femalpha)))  as "FEM Curvature"

end