Enforce the Dirichlet boundary condition by volume constraint in Point Integral method
For researchers working on point cloud-based PDE solvers, this provides a new technique to handle Dirichlet boundaries, though it is an incremental improvement over existing methods.
The paper introduces a volume constraint approach to enforce Dirichlet boundary conditions in the Point Integral method for point cloud discretization, offering an alternative to the Robin boundary approximation.
Recently, Shi and Sun proposed Point Integral method (PIM) to discretize Laplace-Beltrami operator on point cloud. In PIM, Neumann boundary is nature, but Dirichlet boundary needs some special treatment. In our previous work, we use Robin boundary to approximate Dirichlet boundary. In this paper, we introduce another approach to deal with the Dirichlet boundary condition in point integral method using the volume constraint proposed by Du et.al.