An Approach For Solving Poisson Equation In Irregular Domains Application To Level-set Methods

We present a Cartesian grid approach for solving Poisson equation on irregular domains. The domain boundary is described by a level-set func-tion. As a key step, we study the second-order accurate methods for com-puting the integrals on arbitrary domain and arbitrary surface. Numerical examples demonstrate that the method can achieve second-order accuracy.