diff options
Diffstat (limited to 'src/GeneralizedPolynomial-Uniform/Hermite/3d.maple')
| -rw-r--r-- | src/GeneralizedPolynomial-Uniform/Hermite/3d.maple | 170 |
1 files changed, 170 insertions, 0 deletions
diff --git a/src/GeneralizedPolynomial-Uniform/Hermite/3d.maple b/src/GeneralizedPolynomial-Uniform/Hermite/3d.maple new file mode 100644 index 0000000..ae52a9f --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Hermite/3d.maple @@ -0,0 +1,170 @@ +# 3d.maple -- compute Hermite interpolation coefficients in 3-D +# $Header$ + +################################################################################ + +# +# 3d, cube, polynomial order=3, derivatives via 3-point order=2 formula +# ==> overall order=2, 4-point molecule +# + +# interpolating polynomial +interp_3d_cube_order2 + := Hermite_polynomial_interpolant(fn_3d_order3, + coeff_set_3d_order3, + [x,y,z], + { + {x} = deriv_3d_dx_3point, + {y} = deriv_3d_dy_3point, + {z} = deriv_3d_dz_3point, + {x,y} = deriv_3d_dxy_3point, + {x,z} = deriv_3d_dxz_3point, + {y,z} = deriv_3d_dyz_3point, + {x,y,z} = deriv_3d_dxyz_3point + }, + {op(posn_list_3d_size2)}, + {op(posn_list_3d_size2)}); + +# I +coeff_as_lc_of_data(%, posn_list_3d_size4); +print_coeff__lc_of_data(%, "coeff_I_", "fp", + "3d.coeffs/3d.cube.order2/coeff-I.compute.c"); + +# d/dx +simplify( diff(interp_3d_cube_order2,x) ); +coeff_as_lc_of_data(%, posn_list_3d_size4); +print_coeff__lc_of_data(%, "coeff_dx_", "fp", + "3d.coeffs/3d.cube.order2/coeff-dx.compute.c"); + +# d/dy +simplify( diff(interp_3d_cube_order2,y) ); +coeff_as_lc_of_data(%, posn_list_3d_size4); +print_coeff__lc_of_data(%, "coeff_dy_", "fp", + "3d.coeffs/3d.cube.order2/coeff-dy.compute.c"); + +# d/dz +simplify( diff(interp_3d_cube_order2,z) ); +coeff_as_lc_of_data(%, posn_list_3d_size4); +print_coeff__lc_of_data(%, "coeff_dz_", "fp", + "3d.coeffs/3d.cube.order2/coeff-dz.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_3d_cube_order2,x,x) ); +coeff_as_lc_of_data(%, posn_list_3d_size4); +print_coeff__lc_of_data(%, "coeff_dxx_", "fp", + "3d.coeffs/3d.cube.order2/coeff-dxx.compute.c"); + +# d^2/dxdy +simplify( diff(interp_3d_cube_order2,x,y) ); +coeff_as_lc_of_data(%, posn_list_3d_size4); +print_coeff__lc_of_data(%, "coeff_dxy_", "fp", + "3d.coeffs/3d.cube.order2/coeff-dxy.compute.c"); + +# d^2/dxdz +simplify( diff(interp_3d_cube_order2,x,z) ); +coeff_as_lc_of_data(%, posn_list_3d_size4); +print_coeff__lc_of_data(%, "coeff_dxz_", "fp", + "3d.coeffs/3d.cube.order2/coeff-dxz.compute.c"); + +# d^2/dy^2 +simplify( diff(interp_3d_cube_order2,y,y) ); +coeff_as_lc_of_data(%, posn_list_3d_size4); +print_coeff__lc_of_data(%, "coeff_dyy_", "fp", + "3d.coeffs/3d.cube.order2/coeff-dyy.compute.c"); + +# d^2/dydz +simplify( diff(interp_3d_cube_order2,y,z) ); +coeff_as_lc_of_data(%, posn_list_3d_size4); +print_coeff__lc_of_data(%, "coeff_dyz_", "fp", + "3d.coeffs/3d.cube.order2/coeff-dyz.compute.c"); + +# d^2/dz^2 +simplify( diff(interp_3d_cube_order2,z,z) ); +coeff_as_lc_of_data(%, posn_list_3d_size4); +print_coeff__lc_of_data(%, "coeff_dzz_", "fp", + "3d.coeffs/3d.cube.order2/coeff-dzz.compute.c"); + +################################################################################ + +# +# 3d, cube, polynomial order=3, derivatives via 5-point order=4 formula +# ==> overall order=3, 6-point molecule +# + +# interpolating polynomial +interp_3d_cube_order3 + := Hermite_polynomial_interpolant(fn_3d_order3, + coeff_set_3d_order3, + [x,y,z], + { + {x} = deriv_3d_dx_5point, + {y} = deriv_3d_dy_5point, + {z} = deriv_3d_dz_5point, + {x,y} = deriv_3d_dxy_5point, + {x,z} = deriv_3d_dxz_5point, + {y,z} = deriv_3d_dyz_5point, + {x,y,z} = deriv_3d_dxyz_5point + }, + {op(posn_list_3d_size2)}, + {op(posn_list_3d_size2)}); + +# I +coeff_as_lc_of_data(%, posn_list_3d_size6); +print_coeff__lc_of_data(%, "coeff_I_", "fp", + "3d.coeffs/3d.cube.order3/coeff-I.compute.c"); + +# d/dx +simplify( diff(interp_3d_cube_order3,x) ); +coeff_as_lc_of_data(%, posn_list_3d_size6); +print_coeff__lc_of_data(%, "coeff_dx_", "fp", + "3d.coeffs/3d.cube.order3/coeff-dx.compute.c"); + +# d/dy +simplify( diff(interp_3d_cube_order3,y) ); +coeff_as_lc_of_data(%, posn_list_3d_size6); +print_coeff__lc_of_data(%, "coeff_dy_", "fp", + "3d.coeffs/3d.cube.order3/coeff-dy.compute.c"); + +# d/dz +simplify( diff(interp_3d_cube_order3,z) ); +coeff_as_lc_of_data(%, posn_list_3d_size6); +print_coeff__lc_of_data(%, "coeff_dz_", "fp", + "3d.coeffs/3d.cube.order3/coeff-dz.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_3d_cube_order3,x,x) ); +coeff_as_lc_of_data(%, posn_list_3d_size6); +print_coeff__lc_of_data(%, "coeff_dxx_", "fp", + "3d.coeffs/3d.cube.order3/coeff-dxx.compute.c"); + +# d^2/dxdy +simplify( diff(interp_3d_cube_order3,x,y) ); +coeff_as_lc_of_data(%, posn_list_3d_size6); +print_coeff__lc_of_data(%, "coeff_dxy_", "fp", + "3d.coeffs/3d.cube.order3/coeff-dxy.compute.c"); + +# d^2/dxdz +simplify( diff(interp_3d_cube_order3,x,z) ); +coeff_as_lc_of_data(%, posn_list_3d_size6); +print_coeff__lc_of_data(%, "coeff_dxz_", "fp", + "3d.coeffs/3d.cube.order3/coeff-dxz.compute.c"); + +# d^2/dy^2 +simplify( diff(interp_3d_cube_order3,y,y) ); +coeff_as_lc_of_data(%, posn_list_3d_size6); +print_coeff__lc_of_data(%, "coeff_dyy_", "fp", + "3d.coeffs/3d.cube.order3/coeff-dyy.compute.c"); + +# d^2/dydz +simplify( diff(interp_3d_cube_order3,y,z) ); +coeff_as_lc_of_data(%, posn_list_3d_size6); +print_coeff__lc_of_data(%, "coeff_dyz_", "fp", + "3d.coeffs/3d.cube.order3/coeff-dyz.compute.c"); + +# d^2/dz^2 +simplify( diff(interp_3d_cube_order3,z,z) ); +coeff_as_lc_of_data(%, posn_list_3d_size6); +print_coeff__lc_of_data(%, "coeff_dzz_", "fp", + "3d.coeffs/3d.cube.order3/coeff-dzz.compute.c"); + +################################################################################ |