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{ EDGE_DISTANCE.PDE

 This script demonstrates the EDGE_DISTANCE function by constructing a

 gaussian curve based on the distance along the boundary path 'outer'.

}

Title 'Edge Distance'

 

Variables u

 

Definitions

  wide=1

  w = wide/2

 

  ! Define a Gaussian on the outer boundary, centered at half the perimeter

  ! (this depends on the boundary being defined in a single path!)

  gausl = exp( -(edge_distance("outer")-4*wide)^2 / w^2 )

 

  ! form the integral of the Gaussian over the boundary

  lint = surf_integral(gausl,"outer")

 

Equations

  div(grad(u)) = 0

 

Boundaries

  Region 1

  start "outer" (-wide,-wide)

  line to(wide,-wide) to(wide,wide) to(-wide,wide) to close

 

Plots

  grid(x,y)

 

  ! display the Gaussian and compare the explicit integral to the automatic plot integral

  elevation(gausl) on "outer" report lint

 

end