The algebraic immersed interface and boundary method for elliptic equations with discontinuous coefficients

A new immersed interface method, the algebraic immersed interface and boundary (AIIB) method, is presented for elliptic equations with immersed interface problems. This method allows accurate discontinuous conditions on immersed boundaries and interfaces to be imposed. The main idea is to create auxiliary unknowns at existing grid locations in order to increase the degrees of freedom of the initial problem. These auxiliary nodes allow to impose...