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Just extending fourth order PDE in four dimensions, to six dimensions
Desired solution is U(v,w,x,y,z,t), given PDE:
∇4U + 2 ∇2U + 6 U = 0
∂4U(v,w,x,y,z,t)/∂v4 + ∂4U(v,w,x,y,z,t)/∂w4 +
∂4U(v,w,x,y,z,t)/∂x4 + ∂4U(v,w,x,y,z,t)/∂y4 +
∂4U(v,w,x,y,z,t)/∂z4 + ∂4U(v,w,x,y,z,t)/∂t4 +
2 ∂2U(v,w,x,y,z,t)/∂v2 + 2 ∂2U(v,w,x,y,z,t)/∂w2 +
2 ∂2U(v,w,x,y,z,t)/∂x2 + 2 ∂2U(v,w,x,y,z,t)/∂y2 +
2 ∂2U(v,w,x,y,z,t)/∂z2 + 2 ∂2U(v,w,x,y,z,t)/∂t2 +
6 U(v,w,x,y,z,t) = 0
Test a fourth order PDE in six dimensions.
pde46h_eq.adb extended pde44h_eq.adb
pde46h_eq_ada.out verification output
Plotting solution against 6D independent variables
Designed for interactive changing of variables plotted and variables values.
pot6d_gl.c plot program
With a small change, we obtain a nonuniform refinement
Now we use "nuderiv" rather than "rderiv" that can use
nonuniform and different grids in each dimension.
Test a fourth order PDE in six dimensions with nonuniform refinement.
pde46h_nu.adb extended pde46h_eq.adb
pde46h_nu_ada.out verification output
Plotting solution against 6D independent variables
Designed for interactive changing of variables plotted and variables values.
pot6d_gl.c plot program
Least Square Fit 6 independent variables up to sixth power
lsfit.ads Least Square Fit 6D 6P
lsfit.adb Least Square Fit 6D 6P
test_lsfit6.adb test program
test_lsfit6_ada.out test results
Some programs above also need
array3d.ads 3D arrays
array4d.ads 4D arrays
array5d.ads 5D arrays
array6d.ads 6D arrays
real_arrays.ads 2D arrays and operations
real_arrays.adb 2D arrays and operations
integer_arrays.ads 2D arrays and operations
integer_arrays.adb 2D arrays and operations
You won't find many free or commercial 5D and 6D PDE packages
many lesser problems have many opensource and commercial packages
en.wikipedia.org/wiki/list_of_finite_element_software_packages
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