Wave propagation has a wide range of applications in, e.g., seismology, CO2 storage, and medical imaging. Simulating the wave propagation phenomena on computers is the cornerstone of many research areas and industrial processes. Due to their purely hyperbolic nature, wave equations have little tolerance to defects in the numerical discretizations and are prone to instability issues, which tend to develop when different discretizations are combined. In this talk, we will explore a family of hybrid discretization techniques for wave equations that preserve the energy conserving property of the continuous wave systems and hence prevent the development of instability in simulations. The synergy between the presented techniques and high-performance computing will be highlighted.

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