Abstract
This study develops an optimized finite difference iterative (OFDI) scheme for the two-dimensional (2D) viscoelastic wave equation. The OFDI scheme is obtained using a proper orthogonal decomposition (POD) method. It has sufficiently high accuracy with very few unknowns for the 2D viscoelastic wave equation. Existence, stability, and convergence of the OFDI solutions are analyzed. Numerical simulations verify efficiency and feasibility of the proposed scheme.
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Project supported by the National Natural Science Foundation of China (No. 11671106) and the Fundamental Research Funds for the Central Universities (No. 2016MS33)
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Xia, H., Luo, Z. Optimized finite difference iterative scheme based on POD technique for 2D viscoelastic wave equation. Appl. Math. Mech.-Engl. Ed. 38, 1721–1732 (2017). https://doi.org/10.1007/s10483-017-2288-8
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DOI: https://doi.org/10.1007/s10483-017-2288-8
Keywords
- optimized finite difference iterative (OFDI) scheme
- viscoelastic wave equation
- proper orthogonal decomposition (POD)
- existence
- stability
- convergence
- numerical simulation