We develop a method searching for quasi-conformal maps from point-cloud surfaces
to Euclidean plane. The maps can be got by directly solving Beltrami equation with
proper boundary condition or solving optimization problem of the variational formu-
lation. The point integral methd (PIM) is used for discretization on point clouds.
Numerical experiments suggest that the method converges as the density of points in-
In this paper, we introduce a nonlocal model for linear steady Stokes system with
physical no-slip boundary condition. We use the idea of volume constraint to enforce the no-slip
boundary condition. We prove that the nonlocal model is well-posed and the solution of the nonlocal
system converges to the solution of the original Stokes system when the nonlocality vanishes.
In this paper, we give an integral approximation for the elliptic operators with
anisotropic coecients on smooth manifold. Using the integral approximation, the elliptic equation
is tranformed to an integral equation. The integral approximation preserves the symmetry and
coercivity of the original elliptic operator. Based on these good properties, we prove the convergence
between the solutions of the integral equation and the original elliptic equation.