Optimized wavelet-Galerkin templates

We compare the Acousmod2d and optimized wavelet-Galerkin methods. These solutions are for the one-dimensional wave equation with periodic boundary conditions on a line size $N=1024$. The wave speed and density are $1$ in the low speed region, and $4$ and $1/4$ in the high speed region, resp. The high speed region extends from grid points $32$ to $198$. The interface conditions are nonreflecting. The source term is a second derivative Ricker wavelet. The grid points per median wavelength range through $12.5$, $10$, $8$, $6$, $4$, $3$, and $2$. The solutions are plotted as the evolve with time. The right moving wave quickly enters and exits the high speed region. Then both waves propagate in the low speed to the right and left. The calculation is continued until the two waves nearly meet.

Figure 64: Wave speed squared model for the comparison of Acousmod2d and D38 optimized wavelet-Galerkin solution.

Figure 65: Comparison of Acousmod2d and D38 optimized wavelet-Galerkin solution with $12.5$ grid points per median wavelength.

Figure 66: Comparison of Acousmod2d and D38 optimized wavelet-Galerkin solution with $12.5$ grid points per median wavelength.

Figure 67: Comparison of Acousmod2d and D38 optimized wavelet-Galerkin solution with $12.5$ grid points per median wavelength.

Figure 68: Comparison of Acousmod2d and D38 optimized wavelet-Galerkin solution with $12.5$ grid points per median wavelength.

Figure 69: Comparison of Acousmod2d and D38 optimized wavelet-Galerkin solution with $12.5$ grid points per median wavelength.

Figure 70: Comparison of Acousmod2d and D38 optimized wavelet-Galerkin solution with $10$ grid points per median wavelength.

Figure 71: Comparison of Acousmod2d and D38 optimized wavelet-Galerkin solution with $10$ grid points per median wavelength.

Figure 72: Comparison of Acousmod2d and D38 optimized wavelet-Galerkin solution with $10$ grid points per median wavelength.

Figure 73: Comparison of Acousmod2d and D38 optimized wavelet-Galerkin solution with $8$ grid points per median wavelength.

Figure 74: Comparison of Acousmod2d and D38 optimized wavelet-Galerkin solution with $8$ grid points per median wavelength.

Figure 75: Comparison of Acousmod2d and D38 optimized wavelet-Galerkin solution with $6$ grid points per median wavelength.

Figure 76: Comparison of Acousmod2d and D38 optimized wavelet-Galerkin solution with $6$ grid points per median wavelength.

Figure 77: Comparison of Acousmod2d and D38 optimized wavelet-Galerkin solution with $6$ grid points per median wavelength.

Figure 78: D38 optimized wavelet-Galerkin solution with $4$ grid points per median wavelength.

Figure 79: D38 optimized wavelet-Galerkin solution with $4$ grid points per median wavelength.

Figure 80: D38 optimized wavelet-Galerkin solution with $3$ grid points per median wavelength.

Figure 81: D38 optimized wavelet-Galerkin solution with $3$ grid points per median wavelength.

Figure 82: D38 optimized wavelet-Galerkin solution with $2$ grid points per median wavelength.