examples.levelSet.distanceFunction.interior

Here we solve the level set equation in two dimension for an interior region. The equation is given by:

$$\begin{array}{rl}\text{abs}\mathrm{\nabla }\varphi & =1\\ \varphi & =0\text{at}\{\begin{array}{l}x=(d,L-d)\text{ for }d\le y\le L-d\\ y=(d,L-d)\text{ for }d\le x\le L-d\end{array}\end{array}$$

Do the tests:

>>> var.calcDistanceFunction(order=1) 

>>> dX = dx / 2.
>>> dY = dy / 2.
>>> mm = dX * dY / numerix.sqrt(dX**2 + dY**2)
>>> def evalCell(phix, phiy, dx, dy):
...     aa = dy**2 + dx**2
...     bb = -2 * ( phix * dy**2 + phiy * dx**2)
...     cc = dy**2 * phix**2 + dx**2 * phiy**2 - dx**2 * dy**2
...     sqr = numerix.sqrt(bb**2 - 4. * aa * cc)
...     return ((-bb - sqr) / 2. / aa,  (-bb + sqr) / 2. / aa)
>>> v1 = evalCell(dY, dX, dx, dy)[1]
>>> v2 = max(-dY*3, -dX*3)
>>> values = numerix.array((  v1,   dY,   dY,  dY,  v1,
...                           dX,  -mm,   -dY,  -mm,   dX,
...                           dX,  -dX,   -v1,  -dX,   dX,
...                           dX,  -mm,   -dY,  -mm,   dX,
...                           v1,   dY,   dY,  dY,  v1  ))
>>> print(var.allclose(values, atol = 1e-10)) 
1

Last updated on Feb 14, 2025. Created using Sphinx 7.1.2.