implicit_curve_boundary

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implicit_curve_boundary

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{ IMPLICIT_CURVE_BOUNDARY.PDE

 

 This example creates a polynomial boundary segment using the

 implicit ADAPT CURVE descriptor. With ADAPT, FlexPDE finds the

 solution to the given expression that goes through the current

 point and tracks the curve in the direction specified (+Y).

}

Title 'Implicit Curve Boundary'

Coordinates cartesian2

Variables u

 

Definitions

    k = 1

    u0 = 1-x^2-y^2

    s = 2*3/4+5*2/4

 

Initial Values u = 1

 

Equations

 U: div(K*grad(u)) + s = 0

 

Boundaries

region 1

  start(-0.1, 0.004) value(u)=u0  

  line to (0.1,0.004)

  { create a boundary segment that follows the expression

     (x^2+y^2)^2 - 3*x^2*y - y^3 = A, where A is calculated using

     the current point, and start moving in the +Y direction. }

  adapt curve ((x^2+y^2)^2 - 3*x^2*y - y^3) by (+y) to close

 

Plots

contour(u)

surface(u)

 

End