Korostyshevskaya, Oksana; Minkoff, Susan E. A matrix analysis of operator-based upscaling for the wave equation. (English) Zbl 1116.35076 SIAM J. Numer. Anal. 44, No. 2, 586-612 (2006). In this paper, the authors converted the second-order acoustic wave equation into a system of two first-order equations which involve solving for pressure and its gradient. The algorithm is based conceptually on the mixed finite element method. However the pressure equation is solved via finite difference due to an equivalence between these two methods. Theory is developed and numerical experiments are performed for illustration. Reviewer: Prabhat Kumar Mahanti (Saint John) Cited in 9 Documents MSC: 35L05 Wave equation 74Q15 Effective constitutive equations in solid mechanics 86A15 Seismology (including tsunami modeling), earthquakes 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs Keywords:upscaling; acoustic wave propagation; multiscale method; wave propagation; acoustic gradient operator; second-order acoustic wave equation PDFBibTeX XMLCite \textit{O. Korostyshevskaya} and \textit{S. E. Minkoff}, SIAM J. Numer. Anal. 44, No. 2, 586--612 (2006; Zbl 1116.35076) Full Text: DOI Link