Sample Problems > Usage > Variable_Types > vector

{ VECTOR_VARIABLES.PDE

This example demonstrates the use of vector-valued variables.

The equations are not intended to represent any real application,

but merely to show some vector constructs.

}

title 'Vector Variables'

variables

U = vector(Ux,Uy) { declares component variables Ux and Uy }

V { a scalar variable to validate Uy }

definitions

u0 = 1-x^2-y^2

u1 = 1+y+x^3

s = vector(4,-6*x)

equations

U: div(grad(U)) +s = 0

V: del2(v) +ycomp(s) = 0

boundaries

Region 1

start(-1,-1)

value(U)=vector(u0,u1)

value(v)=u1

line to (1,-1) to (1,1) to (-1,1) to close

plots

contour(Ux)

contour(Uy,u1)

contour(v,u1)

contour(Ux,Uy)

vector(U)

elevation(u) from(-1,0) to (1,0)

vtk(u,s)

transfer(u,s)

table(u,s)

end

vector_variables