Piecewise-polynomial discretization and Krylov-accelerated multigrid for elliptic interface problems

A new piecewise-polynomial interface method (PIM) for discretizing elliptic problems with complex interfaces between high-contrast materials is derived, analyzed and tested. A Krylov-accelerated interface multigrid approach (IMG) solves the discretization efficiently. Stability and convergence are proved in one dimension, while an extensive array of numerical experiments with complex interfaces and large coefficient transitions demonstrate the accuracy, efficiency and robustness of the method in two dimensions.