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Some Movies --- these are animated gifs , you might have to control the frame rate with your software
More Steady Mesh PDE Moving DD method - multiple domains (June 26, 2008)
Below I have included a couple more movies showing the 3 domain solution. I now have this code working for an abitrary number of subdomains. The link on
the left show the individual MMPDE solutions on each domain (top row) and the mesh lines defining the moving subdomains (second row). I have highlighted in black the boundaries of the moving subdomains. The movie on the right glues together the subdomain solves to show convergence to the one domain solution - visible initially in light gray. These movies are from the Jacobi version. The 2 domain movies below are
actually the Gauss Seidel version. I still need to assess the importance of the interpolation of the boundary conditions - currently I just use the 25 output times (in time) to generate the boundary data.
I have also altered the first iteration - initially I fixed the subdomain boundaries (in physical space) but now I allow the interior boundaries to move during the first iteration. I achieved this by basically writing down the MMPDE for the boundary nodes and discretizing back in the domain rather than use centered differences.
Movie I: Domains Solves and Moving Domains
Movie II: Subdomain solutions glued together
Steady Mesh PDE - new moving domain solution (June 19, 2008)
DD is done is computational space resulting in moving domains in physical space. The computations are done with a specified physical solution u so that the solver only solves the mesh pde with DD approach. The bottom plots glues the left and right domain solutions together. In the first couple of iterations you can see the one domain mesh solution x(\xi,t) which is made transperant so that the subdomain solutions show through. The infinity norm error (over all \xi and t) is included in the title of the bottomplot.
The mesh trajectories for the left and right subdomains are shown in the 2nd row of plots. You can see that the subdomains (in physical space) are moving in time, however after the first couple of Schwarz iterations the mesh has essentially converged so the movement of the subdomain boundaries is small.
New 2D Schwarz Runs (June 1, 2008)
2D Mesh and Sols on 3 by 2 Domains
Convergence of the Steady Mesh PDE using DD
Convergence of Steady Mesh PDE using a Schwarz iteration
Mesh Movies --- each frame is a snapshot of the meshes used during each Schwarz iteration
Left to right Jacobi
Left to right Gauss Seidel
Right to left Jacobi
Right to left Gauss Seidel
Two Shock Mesh Jacobi (March 1, 2007)
Solution Movies---each frame shows the solution in all subdomains for each output time during each Schwarz iteration
Jacobi Solution of Two Shock Problem with 32 points per domain(NEW March 1, 2007)
Jacobi Solution of Two Shock Problem with 64 points per domain (NEW March 2, 2007)