Galerkin FEM for elliptic PDEs
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sphere.sh 1.3KB

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  1. #!/usr/bin/env bash
  2. gmsh -3 -format vtk -o sphere.vtk sphere.geo
  3. gmsh -2 -format stl -o sphereBox.stl sphereBox.geo
  4. //paraview --state=boundarySphere.pvsm
  5. ../ResampleWithDataset sphere.vtk sphereBox.stl MergedSphere.vtu
  6. ../VTKEdgeGsphere MergedSphere.vtu 2.25 gravity sphereGrav.vtu
  7. ../FEM4EllipticPDE_bhmag sphereGrav.vtu sphereGrav.vtu sphereOutGrav.vtu
  8. paraview --state=sliceGravSphere3.pvsm
  9. #IMPORTANT!
  10. # Select ResampleWithDataset1
  11. # -->File -> SaveData -> MergedSphere.vtu
  12. # Set up problem
  13. # Gravity problem
  14. #../VTKEdgeGsphere MergedSphere.vtu 2.25 gravity sphereGrav.vtu
  15. #../FEM4EllipticPDE_bhmag sphereGrav.vtu sphereGrav.vtu sphereOutGrav.vtu
  16. #paraview --state=sliceSphere.pvsm
  17. # --data=sphereOut.vtu
  18. # even finer meshing
  19. # radius = 4, u = \pm .9 analytic = \pm 1.33
  20. # Finer meshing
  21. # radius = 5, u = \pm 1.65 analytic = \pm 1.67
  22. # radius = 4, u = \pm 1.09 analytic = \pm 1.33
  23. # radius = 5, u = \pm 2.5 analytic = \pm 1.67
  24. # radius = 4, u = \pm 1.66 analytic = \pm 1.33
  25. # radius = 3, u= \pm .926 -.985 analytic = \pm 1
  26. # radius = 2, u = \pm.42 analytic = \pm .667
  27. # for radius=1, u = \pm .111 analytic = \pm .333
  28. # for radius=.5, u = \pm .0477 -.0462 analytic = \pm .167