The second example considered consists of a linear plane strain wave of sufficiently small strength crossing an interface between two materials with density ratio of 2. The material constants are $\gamma 1=\gamma 2=1.4,\u2009p\u221e,1=p\u221e,2=1,\u2009\mu 1=\mu 2=0,\u2009\rho 0,1=0.5$, and *ρ*_{0,2} = 1. The reference scales used here for nondimensionalization are $p\u2217=p\u221e,1\u2217=p\u221e,2\u2217$, and $\rho \u2217=\rho 0,2\u2217$. A slab of material 2 between *x* = 0.5 and 0.9 is surrounded by material 1, and the domain in *x* ∈ [0, 1] is periodic. Each material interface is described by volume fractions varying from *α*_{min} = 10^{−6} to 1 − *α*_{min} with error function profiles of thickness 0.001. A compression wave is initialized at *x* = 0.35 with normal stress profile $\sigma 11=\u221210\u22124\u2009exp[\u2212((x\u2212cL,1t\u22120.35)/0.035)2]$ where $cL,i=(\lambda L,i+2\mu L,i)/\rho 0,i$ is the linear longitudinal wave speed in material *i* and *μ*_{L}_{,}_{i} = *μ*_{i} and *λ*_{L}_{,}_{i} = *γ*_{i}p_{∞}_{,}_{i} − 2*μ*_{i}/3 are the equivalent Lamé coefficients (see, e.g., Ref. [26]). Other components of stress, deformations, densities, and velocities are initialized so as to obtain a linear plane strain wave propagating to the right.