Immersed Interface CIP for One Dimensional Hyperbolic Equations

Numerical schemes for a system of one-dimensional hyperbolic equations

In this paper modern numerical methods for one-dimensional hyperbolic equations are reviewed. Several results of advanced numerical simulations for complex systems are presented. These results prove that the numerical codes, based on the Godunov–type methods cope very well with all numerically induced problems.

Quasilinear Hyperbolic{parabolic Equations of One{dimensional Viscoelasticity

We study the global existence of solutions of initial-boundary-value problems for a quasilinear hyperbolic-parabolic equation describing the longitudinal motion of a one-dimensional viscoelastic rod. We treat a variety of nonhomogeneous boundary conditions, requiring separate analyses, because they lead to distinctive physical eeects. We employ a constitutive equation giving the stress as a gen...

An Immersed Interface Method for Incompressible Navier-Stokes Equations

Interface States and Interface-Bulk Correspondence of One-dimensional Hyperbolic Metamaterials

We investigate the interface state on one-dimensional hyperbolic metamaterial (1DHMM). Initially, we analyze the plasmonic band structure of binary 1DHMM and analytically determine its band crossing condition. Then, we scrutinize the existence of an interface state in the plasmonic band gap of 1DHMM on three types of interfaces: dielectric/1DHMM, metal/1DHMM, and 1DHMM/1DHMM. We find that the b...

A new high-order immersed interface method for solving elliptic equations with imbedded interface of discontinuity

This paper presents a new high-order immersed interface method for elliptic equations with imbedded interface of discontinuity. Compared with the original second-order immersed interface method of [R.J. LeVeque, Z. Li. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 31 (1994) 1001–25], the new method achieves arbitr...