Enforce the Dirichlet boundary condition by volume constraint in point integral method

Convergence of the Point Integral Method for the Poisson Equation on Manifolds Ii: the Dirichlet Boundary

The Poisson equation on manifolds plays an fundamental role in many applications. Recently, we proposed a novel numerical method called the Point Integral method (PIM) to solve the Poisson equations on manifolds from point clouds. In this paper, we prove the convergence of the point integral method for solving the Poisson equation with the Dirichlet boundary condition.

Analyzing diffraction gratings by a boundary integral equation Neumann-to-Dirichlet map method.

For analyzing diffraction gratings, a new method is developed based on dividing one period of the grating into homogeneous subdomains and computing the Neumann-to-Dirichlet (NtD) maps for these subdomains by boundary integral equations. For a subdomain, the NtD operator maps the normal derivative of the wave field to the wave field on its boundary. The integral operators used in this method are...

The Boundary Integral Equation Method

Mass , Dirichlet Boundary Condition , and the Isotropic Coordinate System

We consider test strings and test branes ending on Dp-branes (p ≤ 6) and NS5-branes in the background, for a heuristic understanding of the dynamics. Whenever some supersymmetry is preserved, a simple BPS bound appears, but the central charge in question is measured by certain isotropic coordinate system, rather than by the actual spacetime geometry. This way, the ground state energy is indepen...

BPS Mass, Dirichlet Boundary Condition, and the Isotropic Coordinate System

We consider test strings and test branes ending on Dp-branes (p ≤ 6) and NS5-branes in the background, for a heuristic understanding of the dynamics. Whenever some supersymmetry is preserved, a simple BPS bound appears, but the central charge in question is measured by certain isotropic coordinate system, rather than by the actual spacetime geometry. This way, the ground state energy is indepen...