  Numerical simulation of wave propagation in elastic media faces the
challenges arising from increasing demand of high resolution in modern 3-D
imaging applications, which requires a balance between efficiency and accuracy
in addition to being friendly to the distributed high-performance computing
environment. In this paper, we propose a distributed local spline simulator
(LOSS) for solving the wave equation. LOSS uses patched cubic B-splines to
represent the wavefields and attains an accurate evaluation of spatial
derivatives with linear complexity. In order to link the adjacent patches, a
perfectly matched boundary condition is introduced to give a closure of local
spline coefficients. Owing to the rapid decay property of the local wavelets in
dual space, it can recover the global spline as accurately as possible only at
the cost of local communications among adjacent neighbors. Several typical
numerical examples, including 2-D acoustic wave equation and P- and S- wave
propagation in 3-D homogenous or heterogenous media, are provided to validate
its convergence, accuracy and parallel scalability.
