Explicit 2D 4th order space

[eusoubrasileiro]

What steps will reproduce the problem?

1. Running WaveFd.Exp2DWave following the required convergence criteria.

What is the expected output? What do you see instead? To find the wave progressing through time and fading according its time length, for example, a wavelet of 50 ms should vanish from its original position after 60ms, for example. Being found somewhere else ahead.

Look after other implementations (Leo) and also post in stack exchange scicomp.

[eusoubrasileiro]

I am not seeing the wave progressing.

[eusoubrasileiro]

• Leo implemented using same mexhat ricker punctual 4th order space
• D. Hale used Ricker but over a 3x3 square around (sufdmod2.c) with an exponential decrease smooth exp(-dx2-dz2) from the source location.
• R. M. Alford and K. R. Kelly Accuracy of finite-difference modeling of the acoustic wave equation (1974 Geophysics) uses the actual analytic solution of wave equation just in a small region around the source position; Using a the first derivative of the Gaussian function. (Like a Ricker 90 rotated, 0 at 0) (though don't know specific details of implementation)
• Z. Alterman and F. C. Karal - Propagation of elastic waves in layered media by finite difference methods B. Seismological Society of America 1968 - used a custom source polynomial and the exact analytic solution inside a circled area around the source (some advanced adaptions were made more complex than Alford).

I tried Leo's and Hale's solution booth didn't work so far with many exponential decreasing options. Should go for the exact solution using Fourier Transform.

[eusoubrasileiro]

Rev47 ahead! Solved!FUCKING PROBLEM AND STUPID!!!! 1) Python error pointer manipulation Ufuture point to same class as Ucurrent 2) Source wrong implemented.

Everything documented and answered also question in scicomp http://scicomp.stackexchange.com/questions/7256/explicit-4th-order-space-wave-equation-not-stable-implementation

• Using the alford analytic solution around a square make possible solution prettier (smoother more realistic), dimension of square 2.

Discovered by trying to implement a finite difference based on madagascar recipe. http://www.ahay.org/RSF/book/rsf/manual/manual_html/node7.html An example: Finite-Difference modeling

Rev 55 fix a normalization issue found also documented in Explicit2D_details.tex