  We develop a new finite difference method for the wave equation in second
order form. The finite difference operators satisfy a summation-by-parts (SBP)
property. With boundary conditions and material interface conditions imposed
weakly by the simultaneous-approximation-term (SAT) method, we derive energy
estimates for the semi-discretization. In addition, error estimates are derived
by the normal mode analysis. The proposed method is termed as energy-based
because of its similarity with the energy-based discontinuous Galerkin method.
When imposing the Dirichlet boundary condition and material interface
conditions, the traditional SBP-SAT discretization uses a penalty term with a
mesh-dependent parameter, which is not needed in our method. Furthermore,
numerical dissipation can be added to the discretization through the boundary
and interface conditions. We present numerical experiments that verify
convergence and robustness of the proposed method.
