How to define my Dirac Delta only on the boundary

Legacy DOLFIN
1

Hello everybody,

I have implemented a Dirac Delta UserExpression on dolfin legacy, however, it proves to be quite a slow implementation. I know that the points that I’ll be applying my Dirac Delta to are located over the boundary of my mesh. Is there a way to define the class Delta so that it only works in the boundary, making my code a little faster?

My code:

  mesh = UnitSquareMesh(100,100)
  
  V = VectorFunctionSpace(mesh, 'Lagrange', degree=1)
  
  class Delta(UserExpression):
      def __init__(self, eps, x0, scale_x, scale_y, **kwargs):
          self.eps = eps
          self.x0 = x0
          self.scale_x = scale_x
          self.scale_y = scale_y
          UserExpression.__init__(self, **kwargs)
  
      def eval(self, values, x):
          eps = self.eps
          dist_squaredx = np.linalg.norm(x[0] - self.x0[0])**2 + eps**2
          dist_squaredy = np.linalg.norm(x[1] - self.x0[1])**2 + eps**2
  
          values[0] = self.scale_x * eps * abs(x[0] - self.x0[0]) / (pi * dist_squaredx)
          values[1] = self.scale_y * eps * abs(x[1] - self.x0[1]) / (pi * dist_squaredy)
  
      def value_shape(self):
          return (2, )
  
  points = [[0,0] , [1,0] , [0.5,0]]
  forces = [[0,-1] , [0,-1], [0,-1]]
  
  
  # Create a list of Delta expressions for each point and force
  deltas = [Delta(eps=1E-4, x0=point, scale_x=force[0]*1000, scale_y=force[1]*1000, degree=5)
            for point, force in zip(points, forces)]

Thanks in advance

2

Hi.
Could you provide some more context for your issue?
For instance, will the point-sources be aligned with the degrees of freedom or mesh vertices?

Secondly, is there a reason for not using the point-source class: Implement point source in the variational formulation - #4 by nate