Modal analysis of optical waveguides is a basic task in the design advanced waveguide devices and circuits. How to deal with problem electromagnetic heterogeneous interface absorption boundary condition two major difficulties efficient numerical waveguides. Existing high-order accurate finite-difference modal methods have not considered problem, which makes it difficult accurately simulate leak...

We analyze an immersed interface finite element method based on linear polynomials on noninterface triangular elements and piecewise linear polynomials on interface triangular elements. The flux jump condition is weakly enforced on the smooth interface. Optimal error estimates are derived in the broken H1-norm and L2-norm.

We consider the immersed boundary problem in which the boundary separates two very viscous fluids with differing viscosities. The moving elastic boundary may exert a force on the local fluid. The model solution is obtained using the immersed interface method, which computes second-order accurate approximations by incorporating known jumps in the solution or its derivatives into a finite differe...