Sample Problems > Usage > Implicit_Curves > implicit_curve

{ 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

implicit_curve_boundary