How to apply a load on a single point or a node

[RR_rr]

Thank you, Dokken. It works.

[RR_rr]

@dokken

delta = Delta(eps=1E-4, x0=np.array([1, 1]), degree=5)

Hi, Dokken. Sorry to bother you again. The value at the source point will increase as the value of eps decreases. Theoretically, the value at the source point is infinite, so the eps should be very very small. So maybe it is better to use eps=1E-9 or smaller? or eps=1E-4 is enough?

[dokken]

This depends on the quadrature degree and mesh resolution, and is best left for each individual problem.

[RR_rr]

@dokken

class Delta(UserExpression):
    def __init__(self, eps, x0, **kwargs):
        self.eps = eps
        self.x0 = x0
        UserExpression.__init__(self, **kwargs)
    def eval(self, values, x):
        eps = self.eps
        values[0] = eps/pi/(np.linalg.norm(x-self.x0)**2 + eps**2)
        values[1] = 0

    def value_shape(self): return (2, )

delta = Delta(eps=1E-4, x0=np.array([1, 1]), degree=5)

Hi, Dokken. When I use the Delta function, the computation cost is very large. Is there any way to decrease the computation cost? Thank you very much in advance.

[dokken]

Use the point source that is not a delta function (but a sharp eval), or reduce the domain your are integrating delta over to an area that is close to covering the point source, rather than the whole domain.

[RR_rr]

Thank you. I am going to try it.

[RR_rr]

Hi, Dokken. I reduced the domain where I intergrate the delta function from the whole domain to a subdomain that includes the point source. The results are good and the computation cost drops a lot. Thank you very much for your advice.