Multiresolution-Based Adaptive Simulation of Wave Equation
Hassan Yousefi, Asadollah Noorzad, Jamshid Farjoodi, Mehdi Vahidi · 2012
A modified wavelet-based adaptive-grid scheme is proposed for simulating elastic wave propagation in media with sharp transition of physical properties. The solution grid is adapted by interpolation wavelet; the wavelet transform is used as a tool to detect high-gradient zones. The cubic smoothing spline is employed as a postprocessor to remove spurious oscillations developed in the numerical solution of second order hyperbolic systems. The filtering procedure is directly done in the non-uniform grid, an ill-posed problem. Smoothing splines are indeed a kind of Tikhonov regulization method; hence the smoothing results are stable and reliable. This smoothing method works satisfactory in irregular grid points. Finally some 2D wave propagation problems are simulated to demonstrate the efficiency of the proposed method.