The Immersed Interface Method is a computational technique used in numerical simulations for solving partial differential equations on complex geometries. It was developed by Professor George Em Karniadakis and Professor Steven J. Ruuth in 1992. The method involves embedding an interface into a Cartesian grid, allowing for simulations on irregular boundaries or geometries without the need for complex mesh generation or resolution techniques. Immersed Interface Method is widely used in fluid dynamics, heat transfer, and other fields where complex geometry plays a significant role in the simulation. Overall, the Immersed Interface Method provides a flexible and efficient way to handle complex geometries in numerical simulations, making it a valuable tool for researchers and engineers in various fields.