Heat equation with Delta Dirac function as boundary condition

[janduigamer13]

Sorry for being unclear. My Right hand side in this problem, is not associated with Delta Dirac Function. I’ll try to explain in a better way. I have the heat equation and what I’m trying to do is use different Dirichlet boundary conditions in this equation. Specifically, I’m trying to set the corners of the square with a heat source stated by me as this u_d expression in this domain, and in a circle of radius 0.25 centered at this square domain, an impulse represented by the Delta Dirac function. Basically, what I tried with this b, is based on the topic:

Point Sources (Redux)

Following my post above, with a minor adaptations, a point source can be implemented as follows: # Create a point source for Poisson problem # Author: Jørgen S. Dokken # SPDX-License-Identifier: MIT from mpi4py import MPI from petsc4py import PETSc import dolfinx import dolfinx.fem.petsc import numpy as np import ufl def compute_cell_contributions(V, points): # Determine what process owns a point and what cells it lies within mesh = V.mesh _, _, owning_points, cells = dolfinx.cp…

But I’m trying to change this of acting in a point to act on this circular subdomain. And, sorry, I have noticed now that my formulation is not correct, it is supposed to be a function f at the right hand side of Heat Equation:

The function f is actually:

f = Constant(beta - 2 - 2*alpha)