mform/m_mform_linalg.F90
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| 1 | !> The m-form linear algebra module | ||
| 2 | !> | ||
| 3 | !> This module provides an inner product, L2 projection, and L2-error computation for the m-form spaces | ||
| 4 | module m_mform_linalg | ||
| 5 | use m_common, only: wp, user_function_3d_interface | ||
| 6 | use m_bspline_basis, only: BSplineFun | ||
| 7 | use m_mform_basis, only: MFormFun, MFormSpace | ||
| 8 | #include "petsc.fi" | ||
| 9 | #include "timer.fi" | ||
| 10 | |||
| 11 | implicit none | ||
| 12 | |||
| 13 | private | ||
| 14 | |||
| 15 | public :: inner_product, l2_error, l2_norm, l2_projection | ||
| 16 | public :: solve_curlA_equals_B | ||
| 17 | |||
| 18 | !> @brief Compute the (L2) inner product of all elements of a m-form space with a user-defined function | ||
| 19 | interface inner_product | ||
| 20 | procedure inner_product_mform_scalar, inner_product_mform_vector | ||
| 21 | end interface | ||
| 22 | |||
| 23 | interface l2_projection | ||
| 24 | procedure l2_projection_mform_scalar, l2_projection_mform_vector | ||
| 25 | end interface | ||
| 26 | |||
| 27 | !> @brief Compute the L2 norm of the difference between an m-form and a user-defined function | ||
| 28 | interface l2_error | ||
| 29 | procedure l2_error_mform_scalar, l2_error_mform_vector | ||
| 30 | end interface | ||
| 31 | |||
| 32 | !> @brief Compute the L2 norm of an m-form | ||
| 33 | interface l2_norm | ||
| 34 | procedure l2_norm_mform | ||
| 35 | end interface | ||
| 36 | |||
| 37 | interface solve_curlA_equals_B | ||
| 38 | module procedure solve_curlA_equals_B_tensorprod | ||
| 39 | end interface | ||
| 40 | |||
| 41 | ! NOTE: a compiler bug in NVHPCSDK requires these variables to be in the module scope | ||
| 42 | ! NOTE: see also: https://forums.developer.nvidia.com/t/compiler-bug-passing-a-procedure-with-a-variable-from-a-local-scope-as-input-to-a-function-leads-to-unexpected-behavior/359876 | ||
| 43 | type(BSplineFun) :: twoform_x_integrated, twoform_y_copy | ||
| 44 | |||
| 45 | contains | ||
| 46 | |||
| 47 | !> @brief Compute the (L2) inner product of all elements of a scalar-valued m-form with a user-defined function | ||
| 48 | !> | ||
| 49 | !> @param[inout] v The resulting m-form containing inner products values | ||
| 50 | !> @param[in] space The m-form space (defines the first argument of the inner product) | ||
| 51 | !> @param[in] userfun The second argument of the inner product is a user-defined function | ||
| 52 | !> @param[in] coord_transform _(optional)_ The coordinate transformation associated with the m-form space | ||
| 53 | !> @param[in] n_quad_extra _(optional)_ The extra number of quadrature points to use for the inner product on top of those needed | ||
| 54 | !> to exactly integrate the B-spline spaces | ||
| 55 | !> @param[in] user_fun_is_physical _(optional)_ Whether the user function is defined in physical coordinates (default: .false.) | ||
| 56 | !> | ||
| 57 | !> @note The resulting m-form `v` is initialized only for the response B-spline indices of the tensor product space (if needed, | ||
| 58 | !> call v%distribute() to distribute the data) | ||
| 59 | 279 | subroutine inner_product_mform_scalar(v, space, userfun, coord_transform, n_quad_extra, user_fun_is_physical) | |
| 60 | use m_tensorprod_linalg, only: inner_product | ||
| 61 | use m_tensorprod_quadrature, only: DEFAULT_EXTRA_QUADRATURE_POINTS | ||
| 62 | use m_coord_transform, only: CoordTransformAbstract, jacobian, transform | ||
| 63 | implicit none | ||
| 64 | |||
| 65 | type(MFormFun), intent(inout) :: v | ||
| 66 | type(MFormSpace), intent(in) :: space | ||
| 67 | procedure(user_function_3d_interface) :: userfun | ||
| 68 | class(CoordTransformAbstract), intent(in), optional :: coord_transform | ||
| 69 | integer, intent(in), optional :: n_quad_extra | ||
| 70 | logical, intent(in), optional :: user_fun_is_physical | ||
| 71 | |||
| 72 | logical :: user_fun_is_physical_ | ||
| 73 | integer :: n_quad_extra_ | ||
| 74 | |||
| 75 | TIMER_DECL(t_total) | ||
| 76 | TIMER_INIT_START(t_total, "MFormFun::inner_product") | ||
| 77 | |||
| 78 |
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279 | if (v%is_initialized()) then |
| 79 | ! NOTE: when the m-form function is already initialized, it is ASSUMED that its space matches with the input space | ||
| 80 | ! TODO: enforce this? we need a cheap yet robust way to check this | ||
| 81 | 32 | call v%reset() | |
| 82 | else | ||
| 83 | 247 | call v%init(space) | |
| 84 | end if | ||
| 85 | |||
| 86 | 279 | user_fun_is_physical_ = .false. | |
| 87 |
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279 | if (present(coord_transform) .and. present(user_fun_is_physical)) then |
| 88 | 4 | user_fun_is_physical_ = user_fun_is_physical | |
| 89 | end if | ||
| 90 | |||
| 91 |
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279 | if (space%m == 1 .or. space%m == 2) then |
| 92 | write (*, '(A,I0,A)') "ERROR in inner_product_mform_scalar: this subroutine is for scalar-valued forms. " & | ||
| 93 | ✗ | //"The provided space is a ", space%m, "-form, which is vector-valued and requires 3 user functions. " | |
| 94 | ✗ | error stop 1 | |
| 95 | end if | ||
| 96 | |||
| 97 |
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279 | if (present(n_quad_extra)) then |
| 98 | 38 | n_quad_extra_ = n_quad_extra | |
| 99 | else | ||
| 100 |
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241 | if (present(coord_transform)) then |
| 101 | 39 | n_quad_extra_ = DEFAULT_EXTRA_QUADRATURE_POINTS | |
| 102 | else | ||
| 103 | 202 | n_quad_extra_ = 0 | |
| 104 | end if | ||
| 105 | end if | ||
| 106 | |||
| 107 | 279 | call inner_product(v%tp_funs(1), space%tp_spaces(1), wrapped_userfun, n_quad_extra=n_quad_extra_) | |
| 108 | |||
| 109 | TIMER_STOP(t_total) | ||
| 110 | contains | ||
| 111 | 23438516 | pure real(wp) function wrapped_userfun(xp, yp, zp) result(ans) | |
| 112 | real(wp), intent(in) :: xp, yp, zp | ||
| 113 | |||
| 114 | real(wp) :: x, y, z | ||
| 115 | |||
| 116 |
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23438516 | if (.not. present(coord_transform)) then |
| 117 | 3831596 | ans = userfun(xp, yp, zp) | |
| 118 | else | ||
| 119 |
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19606920 | if (user_fun_is_physical_) then |
| 120 | 506880 | x = transform(coord_transform, 1, xp, yp, zp) | |
| 121 | 506880 | y = transform(coord_transform, 2, xp, yp, zp) | |
| 122 | 506880 | z = transform(coord_transform, 3, xp, yp, zp) | |
| 123 | 506880 | ans = userfun(x, y, z) | |
| 124 | else | ||
| 125 | 19100040 | ans = userfun(xp, yp, zp) | |
| 126 |
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19100040 | if (v%space%m == 3) then |
| 127 | ! The pushforward transformation for 3-forms yields a factor 1 / jacobian | ||
| 128 | 6942900 | ans = ans / jacobian(coord_transform, xp, yp, zp) | |
| 129 | end if | ||
| 130 | end if | ||
| 131 |
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19606920 | if (v%space%m == 0) then |
| 132 | 12479700 | ans = ans * jacobian(coord_transform, xp, yp, zp) | |
| 133 | end if | ||
| 134 | end if | ||
| 135 | |||
| 136 | 23438516 | end function wrapped_userfun | |
| 137 | end subroutine | ||
| 138 | |||
| 139 | !> @brief Compute the (L2) inner product of all elements of a vector-valued m-form with user-defined functions | ||
| 140 | !> | ||
| 141 | !> @param[inout] v The resulting m-form containing inner products values | ||
| 142 | !> @param[in] space The m-form space (defines the first argument of the inner product) | ||
| 143 | !> @param[in] userfun_x The x-component of the second argument of the inner product | ||
| 144 | !> @param[in] userfun_y The y-component of the second argument of the inner product | ||
| 145 | !> @param[in] userfun_z The z-component of the second argument of the inner product | ||
| 146 | !> @param[in] coord_transform _(optional)_ The coordinate transformation associated with the m-form space | ||
| 147 | !> @param[in] n_quad_extra _(optional)_ The extra number of quadrature points to use for the inner product on top of those needed | ||
| 148 | !> to exactly integrate the B-spline spaces | ||
| 149 | !> @param[in] user_fun_is_physical _(optional)_ Whether the user functions are defined in physical coordinates (default: .false.) | ||
| 150 | !> | ||
| 151 | !> @note The resulting m-form `v` is initialized only for the response B-spline indices of the tensor product space (if needed, | ||
| 152 | !> call v%distribute() to distribute the data) | ||
| 153 | 614 | subroutine inner_product_mform_vector(v, space, userfun_x, userfun_y, userfun_z, coord_transform, n_quad_extra, & | |
| 154 | user_fun_is_physical) | ||
| 155 | use m_tensorprod_linalg, only: inner_product | ||
| 156 | use m_tensorprod_quadrature, only: DEFAULT_EXTRA_QUADRATURE_POINTS | ||
| 157 | use m_coord_transform, only: CoordTransformAbstract, jacobian, jacobian_matrix, jacobian_matrix_inv, transform, G_matrix, & | ||
| 158 | G_matrix_inv | ||
| 159 | implicit none | ||
| 160 | |||
| 161 | type(MFormFun), intent(inout) :: v | ||
| 162 | type(MFormSpace), intent(in) :: space | ||
| 163 | procedure(user_function_3d_interface) :: userfun_x, userfun_y, userfun_z | ||
| 164 | class(CoordTransformAbstract), intent(in), optional :: coord_transform | ||
| 165 | integer, intent(in), optional :: n_quad_extra | ||
| 166 | logical, intent(in), optional :: user_fun_is_physical | ||
| 167 | |||
| 168 | logical :: user_fun_is_physical_, is_diagonal | ||
| 169 | integer :: n_quad_extra_ | ||
| 170 | |||
| 171 | TIMER_DECL(t_total) | ||
| 172 | TIMER_INIT_START(t_total, "MFormFun::inner_product") | ||
| 173 | |||
| 174 |
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614 | if (v%is_initialized()) then |
| 175 | 43 | call v%reset() | |
| 176 | else | ||
| 177 | 571 | call v%init(space) | |
| 178 | end if | ||
| 179 | |||
| 180 | 614 | is_diagonal = .true. | |
| 181 | user_fun_is_physical_ = .false. | ||
| 182 |
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614 | if (present(coord_transform)) then |
| 183 |
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464 | if (present(user_fun_is_physical)) then |
| 184 | 4 | user_fun_is_physical_ = user_fun_is_physical | |
| 185 | end if | ||
| 186 | 464 | is_diagonal = coord_transform%is_orthogonal | |
| 187 | end if | ||
| 188 | |||
| 189 |
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614 | if (space%m == 0 .or. space%m == 3) then |
| 190 | write (*, '(A,I0,A)') "ERROR in inner_product_mform_vector: this subroutine is for vector-valued forms. " & | ||
| 191 | ✗ | //"The provided space is a ", space%m, "-form, which is scalar-valued and requires only 1 user function. " | |
| 192 | ✗ | error stop 1 | |
| 193 | end if | ||
| 194 | |||
| 195 |
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614 | if (present(n_quad_extra)) then |
| 196 | 60 | n_quad_extra_ = n_quad_extra | |
| 197 | else | ||
| 198 |
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554 | if (present(coord_transform)) then |
| 199 | 404 | n_quad_extra_ = DEFAULT_EXTRA_QUADRATURE_POINTS | |
| 200 | else | ||
| 201 | 150 | n_quad_extra_ = 0 | |
| 202 | end if | ||
| 203 | end if | ||
| 204 |
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614 | if (user_fun_is_physical_) then |
| 205 | 2 | call inner_product(v%tp_funs(1), space%tp_spaces(1), wrapped_physical_userfun_xx, n_quad_extra=n_quad_extra_) | |
| 206 | 2 | call inner_product(v%tp_funs(2), space%tp_spaces(2), wrapped_physical_userfun_yy, n_quad_extra=n_quad_extra_) | |
| 207 | 2 | call inner_product(v%tp_funs(3), space%tp_spaces(3), wrapped_physical_userfun_zz, n_quad_extra=n_quad_extra_) | |
| 208 | else | ||
| 209 | 612 | call inner_product(v%tp_funs(1), space%tp_spaces(1), wrapped_userfun_xx, n_quad_extra=n_quad_extra_) | |
| 210 | 612 | call inner_product(v%tp_funs(2), space%tp_spaces(2), wrapped_userfun_yy, n_quad_extra=n_quad_extra_) | |
| 211 | 612 | call inner_product(v%tp_funs(3), space%tp_spaces(3), wrapped_userfun_zz, n_quad_extra=n_quad_extra_) | |
| 212 | end if | ||
| 213 | |||
| 214 | TIMER_STOP(t_total) | ||
| 215 | contains | ||
| 216 | 56023986 | pure real(wp) function wrapped_userfun_xx(xp, yp, zp) result(ans) | |
| 217 | implicit none | ||
| 218 | |||
| 219 | real(wp), intent(in) :: xp, yp, zp | ||
| 220 | |||
| 221 | 56023986 | ans = userfun_x(xp, yp, zp) | |
| 222 |
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56023986 | if (present(coord_transform)) then |
| 223 |
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52525278 | if (space%m == 1) then |
| 224 | ! The pushforward transformation for 1-forms yields | ||
| 225 | 42099750 | ans = ans * G_matrix_inv(coord_transform, 1, 1, xp, yp, zp) | |
| 226 |
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42099750 | if (.not. is_diagonal) then |
| 227 | 3685536 | ans = ans + userfun_y(xp, yp, zp) * G_matrix_inv(coord_transform, 1, 2, xp, yp, zp) | |
| 228 | 3685536 | ans = ans + userfun_z(xp, yp, zp) * G_matrix_inv(coord_transform, 1, 3, xp, yp, zp) | |
| 229 | end if | ||
| 230 | 42099750 | ans = ans * jacobian(coord_transform, xp, yp, zp) | |
| 231 | else | ||
| 232 | ! The pushforward transformation for 2-forms yields | ||
| 233 | 10425528 | ans = ans * G_matrix(coord_transform, 1, 1, xp, yp, zp) | |
| 234 |
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10425528 | if (.not. is_diagonal) then |
| 235 | 1788624 | ans = ans + userfun_y(xp, yp, zp) * G_matrix(coord_transform, 1, 2, xp, yp, zp) | |
| 236 | 1788624 | ans = ans + userfun_z(xp, yp, zp) * G_matrix(coord_transform, 1, 3, xp, yp, zp) | |
| 237 | end if | ||
| 238 | 10425528 | ans = ans / jacobian(coord_transform, xp, yp, zp) | |
| 239 | end if | ||
| 240 | end if | ||
| 241 | |||
| 242 | 56023986 | end function | |
| 243 | |||
| 244 | 489984 | pure real(wp) function wrapped_physical_userfun_xx(xp, yp, zp) result(ans) | |
| 245 | implicit none | ||
| 246 | |||
| 247 | real(wp), intent(in) :: xp, yp, zp | ||
| 248 | |||
| 249 | real(wp) :: x, y, z | ||
| 250 | |||
| 251 | 489984 | x = transform(coord_transform, 1, xp, yp, zp) | |
| 252 | 489984 | y = transform(coord_transform, 2, xp, yp, zp) | |
| 253 | 489984 | z = transform(coord_transform, 3, xp, yp, zp) | |
| 254 | |||
| 255 |
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489984 | if (space%m == 1) then |
| 256 | ! The pushforward transformation for 1-forms yields | ||
| 257 | 268800 | ans = userfun_x(x, y, z) * jacobian_matrix_inv(coord_transform, 1, 1, xp, yp, zp) | |
| 258 | 268800 | ans = ans + userfun_y(x, y, z) * jacobian_matrix_inv(coord_transform, 1, 2, xp, yp, zp) | |
| 259 | 268800 | ans = ans + userfun_z(x, y, z) * jacobian_matrix_inv(coord_transform, 1, 3, xp, yp, zp) | |
| 260 | 268800 | ans = ans * jacobian(coord_transform, xp, yp, zp) | |
| 261 | else | ||
| 262 | ! The pushforward transformation for 2-forms yields | ||
| 263 | 221184 | ans = userfun_x(x, y, z) * jacobian_matrix(coord_transform, 1, 1, xp, yp, zp) | |
| 264 | 221184 | ans = ans + userfun_y(x, y, z) * jacobian_matrix(coord_transform, 2, 1, xp, yp, zp) | |
| 265 | 221184 | ans = ans + userfun_z(x, y, z) * jacobian_matrix(coord_transform, 3, 1, xp, yp, zp) | |
| 266 | end if | ||
| 267 | 489984 | end function | |
| 268 | |||
| 269 | 55974898 | pure real(wp) function wrapped_userfun_yy(xp, yp, zp) result(ans) | |
| 270 | implicit none | ||
| 271 | |||
| 272 | real(wp), intent(in) :: xp, yp, zp | ||
| 273 | |||
| 274 | 55974898 | ans = userfun_y(xp, yp, zp) | |
| 275 |
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55974898 | if (present(coord_transform)) then |
| 276 |
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52459018 | if (space%m == 1) then |
| 277 | ! The pushforward transformation for 1-forms yields | ||
| 278 | 42060616 | ans = ans * G_matrix_inv(coord_transform, 2, 2, xp, yp, zp) | |
| 279 |
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42060616 | if (.not. is_diagonal) then |
| 280 | 3685536 | ans = ans + userfun_x(xp, yp, zp) * G_matrix_inv(coord_transform, 2, 1, xp, yp, zp) | |
| 281 | 3685536 | ans = ans + userfun_z(xp, yp, zp) * G_matrix_inv(coord_transform, 2, 3, xp, yp, zp) | |
| 282 | end if | ||
| 283 | 42060616 | ans = ans * jacobian(coord_transform, xp, yp, zp) | |
| 284 | else | ||
| 285 | ! The pushforward transformation for 2-forms yields | ||
| 286 | 10398402 | ans = ans * G_matrix(coord_transform, 2, 2, xp, yp, zp) | |
| 287 |
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10398402 | if (.not. is_diagonal) then |
| 288 | 1788624 | ans = ans + userfun_x(xp, yp, zp) * G_matrix(coord_transform, 2, 1, xp, yp, zp) | |
| 289 | 1788624 | ans = ans + userfun_z(xp, yp, zp) * G_matrix(coord_transform, 2, 3, xp, yp, zp) | |
| 290 | end if | ||
| 291 | 10398402 | ans = ans / jacobian(coord_transform, xp, yp, zp) | |
| 292 | end if | ||
| 293 | end if | ||
| 294 | |||
| 295 | 55974898 | end function | |
| 296 | |||
| 297 | 491520 | pure real(wp) function wrapped_physical_userfun_yy(xp, yp, zp) result(ans) | |
| 298 | implicit none | ||
| 299 | |||
| 300 | real(wp), intent(in) :: xp, yp, zp | ||
| 301 | |||
| 302 | real(wp) :: x, y, z | ||
| 303 | |||
| 304 | 491520 | x = transform(coord_transform, 1, xp, yp, zp) | |
| 305 | 491520 | y = transform(coord_transform, 2, xp, yp, zp) | |
| 306 | 491520 | z = transform(coord_transform, 3, xp, yp, zp) | |
| 307 | |||
| 308 |
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491520 | if (space%m == 1) then |
| 309 | ! The pushforward transformation for 1-forms yields | ||
| 310 | 276480 | ans = userfun_x(x, y, z) * jacobian_matrix_inv(coord_transform, 2, 1, xp, yp, zp) | |
| 311 | 276480 | ans = ans + userfun_y(x, y, z) * jacobian_matrix_inv(coord_transform, 2, 2, xp, yp, zp) | |
| 312 | 276480 | ans = ans + userfun_z(x, y, z) * jacobian_matrix_inv(coord_transform, 2, 3, xp, yp, zp) | |
| 313 | 276480 | ans = ans * jacobian(coord_transform, xp, yp, zp) | |
| 314 | else | ||
| 315 | ! The pushforward transformation for 2-forms yields | ||
| 316 | 215040 | ans = userfun_x(x, y, z) * jacobian_matrix(coord_transform, 1, 2, xp, yp, zp) | |
| 317 | 215040 | ans = ans + userfun_y(x, y, z) * jacobian_matrix(coord_transform, 2, 2, xp, yp, zp) | |
| 318 | 215040 | ans = ans + userfun_z(x, y, z) * jacobian_matrix(coord_transform, 3, 2, xp, yp, zp) | |
| 319 | end if | ||
| 320 | |||
| 321 | 491520 | end function | |
| 322 | |||
| 323 | 41607443 | pure real(wp) function wrapped_userfun_zz(xp, yp, zp) result(ans) | |
| 324 | implicit none | ||
| 325 | |||
| 326 | real(wp), intent(in) :: xp, yp, zp | ||
| 327 | |||
| 328 | 41607443 | ans = userfun_z(xp, yp, zp) | |
| 329 |
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41607443 | if (present(coord_transform)) then |
| 330 |
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38121489 | if (space%m == 1) then |
| 331 | ! The pushforward transformation for 1-forms yields | ||
| 332 | 22856748 | ans = ans * G_matrix_inv(coord_transform, 3, 3, xp, yp, zp) | |
| 333 |
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22856748 | if (.not. is_diagonal) then |
| 334 | 3685536 | ans = ans + userfun_x(xp, yp, zp) * G_matrix_inv(coord_transform, 3, 1, xp, yp, zp) | |
| 335 | 3685536 | ans = ans + userfun_y(xp, yp, zp) * G_matrix_inv(coord_transform, 3, 2, xp, yp, zp) | |
| 336 | end if | ||
| 337 | 22856748 | ans = ans * jacobian(coord_transform, xp, yp, zp) | |
| 338 | else | ||
| 339 | ! The pushforward transformation for 2-forms yields | ||
| 340 | 15264741 | ans = ans * G_matrix(coord_transform, 3, 3, xp, yp, zp) | |
| 341 |
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15264741 | if (.not. is_diagonal) then |
| 342 | 1788624 | ans = ans + userfun_x(xp, yp, zp) * G_matrix(coord_transform, 3, 1, xp, yp, zp) | |
| 343 | 1788624 | ans = ans + userfun_y(xp, yp, zp) * G_matrix(coord_transform, 3, 2, xp, yp, zp) | |
| 344 | end if | ||
| 345 | 15264741 | ans = ans / jacobian(coord_transform, xp, yp, zp) | |
| 346 | end if | ||
| 347 | end if | ||
| 348 | |||
| 349 | 41607443 | end function | |
| 350 | |||
| 351 | 488448 | pure real(wp) function wrapped_physical_userfun_zz(xp, yp, zp) result(ans) | |
| 352 | implicit none | ||
| 353 | |||
| 354 | real(wp), intent(in) :: xp, yp, zp | ||
| 355 | |||
| 356 | real(wp) :: x, y, z | ||
| 357 | |||
| 358 | 488448 | x = transform(coord_transform, 1, xp, yp, zp) | |
| 359 | 488448 | y = transform(coord_transform, 2, xp, yp, zp) | |
| 360 | 488448 | z = transform(coord_transform, 3, xp, yp, zp) | |
| 361 | |||
| 362 |
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488448 | if (space%m == 1) then |
| 363 | ! The pushforward transformation for 1-forms yields | ||
| 364 | 258048 | ans = userfun_x(x, y, z) * jacobian_matrix_inv(coord_transform, 3, 1, xp, yp, zp) | |
| 365 | 258048 | ans = ans + userfun_y(x, y, z) * jacobian_matrix_inv(coord_transform, 3, 2, xp, yp, zp) | |
| 366 | 258048 | ans = ans + userfun_z(x, y, z) * jacobian_matrix_inv(coord_transform, 3, 3, xp, yp, zp) | |
| 367 | 258048 | ans = ans * jacobian(coord_transform, xp, yp, zp) | |
| 368 | else | ||
| 369 | ! The pushforward transformation for 2-forms yields | ||
| 370 | 230400 | ans = userfun_x(x, y, z) * jacobian_matrix(coord_transform, 1, 3, xp, yp, zp) | |
| 371 | 230400 | ans = ans + userfun_y(x, y, z) * jacobian_matrix(coord_transform, 2, 3, xp, yp, zp) | |
| 372 | 230400 | ans = ans + userfun_z(x, y, z) * jacobian_matrix(coord_transform, 3, 3, xp, yp, zp) | |
| 373 | end if | ||
| 374 | |||
| 375 | 488448 | end function | |
| 376 | |||
| 377 | end subroutine | ||
| 378 | |||
| 379 | !> @brief Compute the L2 projection of a user-defined function onto a scalar-valued m-form space | ||
| 380 | !> | ||
| 381 | !> @param[out] c The resulting m-form containing the L2 projection | ||
| 382 | !> @param[in] space The m-form space onto which the projection is computed | ||
| 383 | !> @param[in] userfun The user-defined function to project onto the m-form space | ||
| 384 | !> @param[in] coord_transform _(optional)_ The coordinate transformation associated with the m-form space | ||
| 385 | !> @param[in] solver _(optional)_ The solver to use for the L2 projection, if not provided, a solver is created internally | ||
| 386 | !> @param[in] n_quad_extra _(optional)_ The extra number of quadrature points to use for the L2 projection on top of those needed | ||
| 387 | !> to exactly integrate the B-spline spaces | ||
| 388 | !> @param[in] user_fun_is_physical _(optional)_ Whether the user function is defined in physical coordinates (default: .false.) | ||
| 389 |
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189 | subroutine l2_projection_mform_scalar(c, space, userfun, coord_transform, solver, n_quad_extra, user_fun_is_physical) |
| 390 | use m_tensorprod_linalg, only: l2_projection | ||
| 391 | use m_mform_solver, only: GenericSolver | ||
| 392 | use m_mform_matrix, only: MassMatrix | ||
| 393 | use m_coord_transform_abstract, only: CoordTransformAbstract | ||
| 394 | implicit none | ||
| 395 | |||
| 396 | type(MFormFun), intent(out) :: c | ||
| 397 | type(MFormSpace), intent(in) :: space | ||
| 398 | procedure(user_function_3d_interface) :: userfun | ||
| 399 | |||
| 400 | class(CoordTransformAbstract), intent(in), optional :: coord_transform | ||
| 401 | type(GenericSolver), intent(in), optional :: solver | ||
| 402 | integer, intent(in), optional :: n_quad_extra | ||
| 403 | logical, intent(in), optional :: user_fun_is_physical | ||
| 404 | |||
| 405 | 189 | type(MFormFun) :: f | |
| 406 | 189 | type(MassMatrix) :: mass | |
| 407 |
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189 | type(GenericSolver) :: solver_ |
| 408 | |||
| 409 | TIMER_DECL(t_total) | ||
| 410 | TIMER_INIT_START(t_total, "MFormFun::l2_projection") | ||
| 411 | |||
| 412 |
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189 | if (space%m == 1 .or. space%m == 2) then |
| 413 | ✗ | error stop "l2_projection for vector-valued forms requires 3 userfunctions" | |
| 414 | end if | ||
| 415 | |||
| 416 | call inner_product(f, space, userfun, n_quad_extra=n_quad_extra, user_fun_is_physical=user_fun_is_physical, & | ||
| 417 | 189 | coord_transform=coord_transform) | |
| 418 | |||
| 419 |
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189 | if (present(solver)) then |
| 420 | 189 | call solver%solve(c, f) | |
| 421 | else | ||
| 422 | ✗ | call mass%init(space, n_quad_extra=n_quad_extra, coord_transform=coord_transform) | |
| 423 | ✗ | call solver_%init(mass, coord_transform=coord_transform) | |
| 424 | ✗ | call solver_%solve(c, f) | |
| 425 | |||
| 426 | ✗ | call mass%destroy() | |
| 427 | ✗ | call solver_%destroy() | |
| 428 | end if | ||
| 429 | |||
| 430 | 189 | call f%destroy() | |
| 431 | TIMER_STOP(t_total) | ||
| 432 |
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|
189 | end subroutine l2_projection_mform_scalar |
| 433 | |||
| 434 | !> @brief Compute the L2 projection of a user-defined function onto a vector-valued m-form space | ||
| 435 | !> | ||
| 436 | !> @param[out] c The resulting m-form containing the L2 projection | ||
| 437 | !> @param[in] space The m-form space onto which the projection is computed | ||
| 438 | !> @param[in] userfun_x The x-component of the user-defined function to project onto the m-form space | ||
| 439 | !> @param[in] userfun_y The y-component of the user-defined function to project onto the m-form space | ||
| 440 | !> @param[in] userfun_z The z-component of the user-defined function to project onto the m-form space | ||
| 441 | !> @param[in] coord_transform _(optional)_ The coordinate transformation associated with the m-form space | ||
| 442 | !> @param[in] solver _(optional)_ The solver to use for the L2 projection, if not provided, a solver is created internally | ||
| 443 | !> @param[in] n_quad_extra _(optional)_ The extra number of quadrature points to use for the L2 projection on top of those needed | ||
| 444 | !> to exactly integrate the B-spline spaces | ||
| 445 | !> @param[in] user_fun_is_physical _(optional)_ Whether the user functions are defined in physical coordinates (default: .false.) | ||
| 446 |
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234 | subroutine l2_projection_mform_vector(c, space, userfun_x, userfun_y, userfun_z, coord_transform, solver, n_quad_extra, & |
| 447 | user_fun_is_physical) | ||
| 448 | use m_tensorprod_linalg, only: l2_projection | ||
| 449 | use m_mform_solver, only: GenericSolver | ||
| 450 | use m_mform_matrix, only: MassMatrix | ||
| 451 | use m_coord_transform_abstract, only: CoordTransformAbstract | ||
| 452 | implicit none | ||
| 453 | |||
| 454 | type(MFormFun), intent(out) :: c | ||
| 455 | type(MFormSpace), intent(in) :: space | ||
| 456 | procedure(user_function_3d_interface) :: userfun_x, userfun_y, userfun_z | ||
| 457 | class(CoordTransformAbstract), intent(in), optional :: coord_transform | ||
| 458 | type(GenericSolver), intent(in), optional :: solver | ||
| 459 | integer, intent(in), optional :: n_quad_extra | ||
| 460 | logical, intent(in), optional :: user_fun_is_physical | ||
| 461 | |||
| 462 | 234 | type(MFormFun) :: f | |
| 463 | 234 | type(MassMatrix) :: mass | |
| 464 |
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234 | type(GenericSolver) :: solver_ |
| 465 | |||
| 466 | TIMER_DECL(t_total) | ||
| 467 | TIMER_INIT_START(t_total, "MFormFun::l2_projection") | ||
| 468 | |||
| 469 |
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234 | if (space%m == 0 .or. space%m == 3) then |
| 470 | ✗ | error stop "l2_projection for scalar-valued forms requires 1 userfunction" | |
| 471 | end if | ||
| 472 | |||
| 473 | call inner_product(f, space, userfun_x, userfun_y, userfun_z, n_quad_extra=n_quad_extra, & | ||
| 474 | 234 | & user_fun_is_physical=user_fun_is_physical, coord_transform=coord_transform) | |
| 475 | |||
| 476 |
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234 | if (present(solver)) then |
| 477 | 234 | call solver%solve(c, f) | |
| 478 | else | ||
| 479 | ✗ | call mass%init(space, n_quad_extra=n_quad_extra, coord_transform=coord_transform) | |
| 480 | ✗ | call solver_%init(mass, coord_transform=coord_transform) | |
| 481 | ✗ | call solver_%solve(c, f) | |
| 482 | |||
| 483 | ✗ | call mass%destroy() | |
| 484 | ✗ | call solver_%destroy() | |
| 485 | end if | ||
| 486 | |||
| 487 | 234 | call f%destroy() | |
| 488 | TIMER_STOP(t_total) | ||
| 489 |
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|
234 | end subroutine l2_projection_mform_vector |
| 490 | |||
| 491 | !> @brief Compute the L2 norm of the difference between a scalar-valued m-form and a user-defined function | ||
| 492 | !> | ||
| 493 | !> @param[in] v The m-form to compare with the user-defined function | ||
| 494 | !> @param[in] userfun The user-defined function to compare with the m-form | ||
| 495 | !> @param[in] coord_transform _(optional)_ The coordinate transformation associated with the m-form space | ||
| 496 | !> @param[in] n_quad_extra _(optional)_ The extra number of quadrature points to use for the L2 error on top of those needed | ||
| 497 | !> to exactly integrate the B-spline spaces | ||
| 498 | !> @param[in] user_fun_is_physical _(optional)_ Whether the user function is defined in physical coordinates (default: .false.) | ||
| 499 | !> | ||
| 500 | !> @return The L2 norm of the difference between the m-form and the user-defined function | ||
| 501 | 343 | real(wp) function l2_error_mform_scalar(v, userfun, coord_transform, n_quad_extra, user_fun_is_physical) result(ans) | |
| 502 | use m_tensorprod_basis, only: evaluate | ||
| 503 | use m_tensorprod_linalg, only: integrate | ||
| 504 | use m_coord_transform, only: CoordTransformAbstract, jacobian, transform | ||
| 505 | implicit none | ||
| 506 | |||
| 507 | type(MFormFun), intent(in) :: v | ||
| 508 | procedure(user_function_3d_interface) :: userfun | ||
| 509 | class(CoordTransformAbstract), intent(in), optional :: coord_transform | ||
| 510 | integer, intent(in), optional :: n_quad_extra | ||
| 511 | logical, intent(in), optional :: user_fun_is_physical | ||
| 512 | |||
| 513 | logical :: user_fun_is_physical_ | ||
| 514 | |||
| 515 | TIMER_DECL(t_total) | ||
| 516 | TIMER_INIT_START(t_total, "MFormFun::l2_error") | ||
| 517 | |||
| 518 |
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343 | if (v%space%m == 1 .or. v%space%m == 2) then |
| 519 | ✗ | error stop "l2_error for vector-valued forms requires three userfunctions" | |
| 520 | end if | ||
| 521 | |||
| 522 |
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343 | if (present(coord_transform)) then |
| 523 | 139 | user_fun_is_physical_ = present(user_fun_is_physical) | |
| 524 | else | ||
| 525 | 204 | user_fun_is_physical_ = .false. | |
| 526 | end if | ||
| 527 | |||
| 528 | 343 | ans = sqrt(integrate(v%space%tp_spaces(1), int_function, n_quad_extra=n_quad_extra)) | |
| 529 | |||
| 530 | TIMER_STOP(t_total) | ||
| 531 | contains | ||
| 532 | 48519616 | pure real(wp) function int_function(xp, yp, zp) result(val) | |
| 533 | real(wp), intent(in) :: xp, yp, zp | ||
| 534 | |||
| 535 | real(wp) :: x, y, z, user_val, jac_val | ||
| 536 | |||
| 537 |
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48519616 | if (present(coord_transform)) then |
| 538 | 34861144 | jac_val = jacobian(coord_transform, xp, yp, zp) | |
| 539 | else | ||
| 540 | jac_val = 1.0_wp | ||
| 541 | end if | ||
| 542 | |||
| 543 |
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48519616 | if (.not. user_fun_is_physical_) then |
| 544 | 48519616 | user_val = userfun(xp, yp, zp) | |
| 545 | else | ||
| 546 | ✗ | if (present(coord_transform)) then | |
| 547 | ✗ | x = transform(coord_transform, 1, xp, yp, zp) | |
| 548 | ✗ | y = transform(coord_transform, 2, xp, yp, zp) | |
| 549 | ✗ | z = transform(coord_transform, 3, xp, yp, zp) | |
| 550 | ✗ | user_val = userfun(x, y, z) | |
| 551 | |||
| 552 | ✗ | if (v%space%m == 3) then | |
| 553 | ! The pullback transformation for 3-forms yields a factor jacobian | ||
| 554 | ✗ | user_val = user_val * jac_val | |
| 555 | end if | ||
| 556 | end if | ||
| 557 | end if | ||
| 558 | 48519616 | val = (user_val - evaluate(v%tp_funs(1), xp, yp, zp))**2 ! value of the logical m-form | |
| 559 | |||
| 560 |
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48519616 | if (present(coord_transform)) then |
| 561 |
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34861144 | if (v%space%m == 3) then |
| 562 | 6758580 | val = val / jac_val | |
| 563 | else | ||
| 564 | 28102564 | val = val * jac_val | |
| 565 | end if | ||
| 566 | end if | ||
| 567 | 48519616 | end function int_function | |
| 568 | end function | ||
| 569 | |||
| 570 | !> @brief Compute the L2 norm of the difference between a vector-valued m-form and a user-defined function | ||
| 571 | !> | ||
| 572 | !> @param[in] v The m-form to compare with the user-defined function | ||
| 573 | !> @param[in] userfun_x The x-component of the user-defined function to compare with the m-form | ||
| 574 | !> @param[in] userfun_y The y-component of the user-defined function to compare with the m-form | ||
| 575 | !> @param[in] userfun_z The z-component of the user-defined function to compare with the m-form | ||
| 576 | !> @param[in] coord_transform _(optional)_ The coordinate transformation associated with the m-form space | ||
| 577 | !> @param[in] n_quad_extra _(optional)_ The extra number of quadrature points to use for the L2 error on top of those needed | ||
| 578 | !> to exactly integrate the B-spline spaces | ||
| 579 | !> @param[in] user_fun_is_physical _(optional)_ Whether the user functions are defined in physical coordinates (default: .false.) | ||
| 580 | !> | ||
| 581 | !> @return The L2 norm of the difference between the m-form and the user-defined function | ||
| 582 | 337 | real(wp) function l2_error_mform_vector(v, userfun_x, userfun_y, userfun_z, coord_transform & | |
| 583 | , n_quad_extra, user_fun_is_physical) result(ans) | ||
| 584 | use m_mform_basis, only: MFormSpace, get_zero_form_space | ||
| 585 | use m_tensorprod_basis, only: TensorProdSpace, evaluate | ||
| 586 | use m_tensorprod_linalg, only: integrate | ||
| 587 | use m_coord_transform, only: CoordTransformAbstract, jacobian, transform, jacobian_matrix, jacobian_matrix_inv, G_matrix, & | ||
| 588 | G_matrix_inv | ||
| 589 | implicit none | ||
| 590 | |||
| 591 | type(MFormFun), intent(in) :: v | ||
| 592 | procedure(user_function_3d_interface) :: userfun_x, userfun_y, userfun_z | ||
| 593 | class(CoordTransformAbstract), intent(in), optional :: coord_transform | ||
| 594 | integer, intent(in), optional :: n_quad_extra | ||
| 595 | logical, intent(in), optional :: user_fun_is_physical | ||
| 596 | |||
| 597 | logical :: user_fun_is_physical_ | ||
| 598 | type(MFormSpace) :: space0 | ||
| 599 | |||
| 600 | TIMER_DECL(t_total) | ||
| 601 | TIMER_INIT_START(t_total, "MFormFun::l2_error") | ||
| 602 | |||
| 603 |
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|
337 | if (v%space%m == 0 .or. v%space%m == 3) then |
| 604 | ✗ | error stop "l2_error for scalar-valued forms requires one userfunction" | |
| 605 | end if | ||
| 606 | |||
| 607 |
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|
337 | if (present(coord_transform)) then |
| 608 | 110 | user_fun_is_physical_ = present(user_fun_is_physical) | |
| 609 | else | ||
| 610 | 227 | user_fun_is_physical_ = .false. | |
| 611 | end if | ||
| 612 | |||
| 613 | ! TODO: user_fun_is_physical (assumed .false. in current implementation) | ||
| 614 | |||
| 615 | 337 | space0 = get_zero_form_space(v%space) | |
| 616 | |||
| 617 |
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337 | ans = sqrt(integrate(space0%tp_spaces(1), int_function, n_quad_extra=n_quad_extra)) |
| 618 | |||
| 619 | TIMER_STOP(t_total) | ||
| 620 | contains | ||
| 621 | 51742602 | pure real(wp) function int_function(xp, yp, zp) result(val) | |
| 622 | real(wp), intent(in) :: xp, yp, zp | ||
| 623 | |||
| 624 | real(wp) :: x, y, z, jac_val, diff_x, diff_y, diff_z | ||
| 625 | real(wp) :: userfun_xp_val, userfun_yp_val, userfun_zp_val, userfun_x_val, userfun_y_val, userfun_z_val | ||
| 626 | real(wp) :: mat(3, 3) | ||
| 627 | |||
| 628 |
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|
51742602 | if (user_fun_is_physical_) then |
| 629 | ✗ | if (present(coord_transform)) then | |
| 630 | ✗ | x = transform(coord_transform, 1, xp, yp, zp) | |
| 631 | ✗ | y = transform(coord_transform, 2, xp, yp, zp) | |
| 632 | ✗ | z = transform(coord_transform, 3, xp, yp, zp) | |
| 633 | ✗ | userfun_x_val = userfun_x(x, y, z) | |
| 634 | ✗ | userfun_y_val = userfun_y(x, y, z) | |
| 635 | ✗ | userfun_z_val = userfun_z(x, y, z) | |
| 636 | |||
| 637 | ✗ | if (v%space%m == 1) then | |
| 638 | userfun_xp_val = jacobian_matrix(coord_transform, 1, 1, xp, yp, zp) * userfun_x_val + & | ||
| 639 | jacobian_matrix(coord_transform, 2, 1, xp, yp, zp) * userfun_y_val + & | ||
| 640 | ✗ | jacobian_matrix(coord_transform, 3, 1, xp, yp, zp) * userfun_z_val | |
| 641 | userfun_yp_val = jacobian_matrix(coord_transform, 1, 2, xp, yp, zp) * userfun_x_val + & | ||
| 642 | jacobian_matrix(coord_transform, 2, 2, xp, yp, zp) * userfun_y_val + & | ||
| 643 | ✗ | jacobian_matrix(coord_transform, 3, 2, xp, yp, zp) * userfun_z_val | |
| 644 | userfun_zp_val = jacobian_matrix(coord_transform, 1, 3, xp, yp, zp) * userfun_x_val + & | ||
| 645 | jacobian_matrix(coord_transform, 2, 3, xp, yp, zp) * userfun_y_val + & | ||
| 646 | ✗ | jacobian_matrix(coord_transform, 3, 3, xp, yp, zp) * userfun_z_val | |
| 647 | else | ||
| 648 | ✗ | jac_val = jacobian(coord_transform, xp, yp, zp) | |
| 649 | userfun_xp_val = jacobian_matrix_inv(coord_transform, 1, 1, xp, yp, zp) * userfun_x_val + & | ||
| 650 | jacobian_matrix_inv(coord_transform, 1, 2, xp, yp, zp) * userfun_y_val + & | ||
| 651 | ✗ | jacobian_matrix_inv(coord_transform, 1, 3, xp, yp, zp) * userfun_z_val | |
| 652 | userfun_yp_val = jacobian_matrix_inv(coord_transform, 2, 1, xp, yp, zp) * userfun_x_val + & | ||
| 653 | jacobian_matrix_inv(coord_transform, 2, 2, xp, yp, zp) * userfun_y_val + & | ||
| 654 | ✗ | jacobian_matrix_inv(coord_transform, 2, 3, xp, yp, zp) * userfun_z_val | |
| 655 | userfun_zp_val = jacobian_matrix_inv(coord_transform, 3, 1, xp, yp, zp) * userfun_x_val + & | ||
| 656 | jacobian_matrix_inv(coord_transform, 3, 2, xp, yp, zp) * userfun_y_val + & | ||
| 657 | ✗ | jacobian_matrix_inv(coord_transform, 3, 3, xp, yp, zp) * userfun_z_val | |
| 658 | ✗ | userfun_xp_val = userfun_xp_val * jac_val | |
| 659 | ✗ | userfun_yp_val = userfun_yp_val * jac_val | |
| 660 | ✗ | userfun_zp_val = userfun_zp_val * jac_val | |
| 661 | end if | ||
| 662 | end if | ||
| 663 | else | ||
| 664 | 51742602 | userfun_xp_val = userfun_x(xp, yp, zp) | |
| 665 | 51742602 | userfun_yp_val = userfun_y(xp, yp, zp) | |
| 666 | 51742602 | userfun_zp_val = userfun_z(xp, yp, zp) | |
| 667 | end if | ||
| 668 | 51742602 | diff_x = userfun_xp_val - evaluate(v%tp_funs(1), xp, yp, zp) | |
| 669 | 51742602 | diff_y = userfun_yp_val - evaluate(v%tp_funs(2), xp, yp, zp) | |
| 670 | 51742602 | diff_z = userfun_zp_val - evaluate(v%tp_funs(3), xp, yp, zp) | |
| 671 | |||
| 672 |
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|
51742602 | if (.not. present(coord_transform)) then |
| 673 | 24910050 | val = diff_x**2 + diff_y**2 + diff_z**2 | |
| 674 | else | ||
| 675 | 26832552 | jac_val = jacobian(coord_transform, xp, yp, zp) | |
| 676 |
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|
26832552 | if (v%space%m == 1) then |
| 677 | 11834580 | mat(1, 1) = G_matrix_inv(coord_transform, 1, 1, xp, yp, zp) * jac_val | |
| 678 | 11834580 | mat(2, 2) = G_matrix_inv(coord_transform, 2, 2, xp, yp, zp) * jac_val | |
| 679 | 11834580 | mat(3, 3) = G_matrix_inv(coord_transform, 3, 3, xp, yp, zp) * jac_val | |
| 680 |
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|
11834580 | if (.not. coord_transform%is_orthogonal) then |
| 681 | 2644416 | mat(1, 2) = G_matrix_inv(coord_transform, 1, 2, xp, yp, zp) * jac_val | |
| 682 | 2644416 | mat(1, 3) = G_matrix_inv(coord_transform, 1, 3, xp, yp, zp) * jac_val | |
| 683 | 2644416 | mat(2, 3) = G_matrix_inv(coord_transform, 2, 3, xp, yp, zp) * jac_val | |
| 684 | end if | ||
| 685 | else ! if (v%space%m == 2) then | ||
| 686 | 14997972 | mat(1, 1) = G_matrix(coord_transform, 1, 1, xp, yp, zp) / jac_val | |
| 687 | 14997972 | mat(2, 2) = G_matrix(coord_transform, 2, 2, xp, yp, zp) / jac_val | |
| 688 | 14997972 | mat(3, 3) = G_matrix(coord_transform, 3, 3, xp, yp, zp) / jac_val | |
| 689 |
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|
14997972 | if (.not. coord_transform%is_orthogonal) then |
| 690 | 2644416 | mat(1, 2) = G_matrix(coord_transform, 1, 2, xp, yp, zp) / jac_val | |
| 691 | 2644416 | mat(1, 3) = G_matrix(coord_transform, 1, 3, xp, yp, zp) / jac_val | |
| 692 | 2644416 | mat(2, 3) = G_matrix(coord_transform, 2, 3, xp, yp, zp) / jac_val | |
| 693 | end if | ||
| 694 | end if | ||
| 695 | 26832552 | val = diff_x**2 * mat(1, 1) + diff_y**2 * mat(2, 2) + diff_z**2 * mat(3, 3) | |
| 696 |
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|
26832552 | if (.not. coord_transform%is_orthogonal) then |
| 697 | 5288832 | val = val + 2.0_wp * (diff_x * diff_y * mat(1, 2) + diff_x * diff_z * mat(1, 3) + diff_y * diff_z * mat(2, 3)) | |
| 698 | end if | ||
| 699 | end if | ||
| 700 | |||
| 701 | 51742602 | end function int_function | |
| 702 | |||
| 703 | end function | ||
| 704 | |||
| 705 | !> @brief Compute the L2 norm of an m-form | ||
| 706 | !> | ||
| 707 | !> @param[in] v The m-form | ||
| 708 | !> @param[in] coord_transform _(optional)_ The coordinate transformation associated with the m-form space | ||
| 709 | !> | ||
| 710 | !> @return The L2 norm of the m-form | ||
| 711 | 39 | real(wp) function l2_norm_mform(v, coord_transform) result(ans) | |
| 712 | use m_common, only: zero_function | ||
| 713 | use m_coord_transform, only: CoordTransformAbstract | ||
| 714 | implicit none | ||
| 715 | |||
| 716 | type(MFormFun), intent(in) :: v | ||
| 717 | class(CoordTransformAbstract), intent(in), optional :: coord_transform | ||
| 718 | |||
| 719 | TIMER_DECL(t_total) | ||
| 720 | TIMER_INIT_START(t_total, "MFormFun::l2_norm") | ||
| 721 | |||
| 722 |
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|
39 | if (v%space%m == 1 .or. v%space%m == 2) then |
| 723 | 37 | ans = l2_error(v, zero_function, zero_function, zero_function, coord_transform=coord_transform) | |
| 724 | else | ||
| 725 | 2 | ans = l2_error(v, zero_function, coord_transform=coord_transform) | |
| 726 | end if | ||
| 727 | TIMER_STOP(t_total) | ||
| 728 | 39 | end function | |
| 729 | |||
| 730 | !> @brief Find the weakly divergence-free one-form whose curl is the given two-form (in 2D, assuming homogeneous BC) | ||
| 731 | !> | ||
| 732 | !> @param[out] oneform The resulting one-form whose curl is the given two-form | ||
| 733 | !> @param[in] twoform_x The x-component of the two-form whose curl 'inverse' is to be computed | ||
| 734 | !> @param[in] twoform_y The y-component of the two-form whose curl 'inverse' is to be computed | ||
| 735 | !> @param[in] twoform_space The space of the provided two-form components | ||
| 736 | !> @param[in] cylinder_transform The coordinate transformation associated with the m-form space | ||
| 737 | !> @param[inout] zeroform_solver _(optional)_ The divgrad solver, if not provided, a solver is created internally | ||
| 738 | !> @param[in] constraint _(optional)_ The constraint to be applied to both solvers (besides the boundary conditions) | ||
| 739 |
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|
249 | subroutine solve_curlA_equals_B_tensorprod(oneform, twoform_x, twoform_y, twoform_space, cylinder_transform, zeroform_solver, & |
| 740 | constraint) | ||
| 741 | use m_common, only: zero_function, user_function_3d_interface, cumsum | ||
| 742 | use m_bspline_basis, only: BSplineFun | ||
| 743 | use m_mform_solver, only: GenericSolver | ||
| 744 | use m_mform_matrix, only: MassMatrix, DiffDiffMatrix | ||
| 745 | use m_mform_basis, only: MFormFun, gradient, gradient_adjoint, curl_adjoint, previous | ||
| 746 | use m_mform_constraint_abstract, only: MFormConstraintLocal | ||
| 747 | use m_mform_constraint_boundary, only: MFormDirichlet, MFormNeumann | ||
| 748 | use m_coord_transform, only: CylinderTransform | ||
| 749 | implicit none | ||
| 750 | |||
| 751 | type(MFormFun), intent(out) :: oneform | ||
| 752 | type(BSplineFun), intent(in) :: twoform_x, twoform_y | ||
| 753 | type(MFormSpace), intent(in) :: twoform_space | ||
| 754 | type(GenericSolver), intent(inout), target, optional :: zeroform_solver | ||
| 755 | class(MFormConstraintLocal), intent(in), optional :: constraint | ||
| 756 | type(CylinderTransform), intent(in), optional :: cylinder_transform | ||
| 757 | 249 | type(GenericSolver), target :: zeroform_solver_ | |
| 758 | type(GenericSolver), pointer :: zeroform_solver_p | ||
| 759 | 249 | type(DiffDiffMatrix) :: divgrad | |
| 760 |
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|
249 | type(MFormFun) :: f, df, zeroform, grad, oneform_tmp |
| 761 | type(MFormSpace) :: oneform_space | ||
| 762 | class(MFormConstraintLocal), allocatable :: constraint_local | ||
| 763 | integer :: twoform_m, i, j, k | ||
| 764 | character(len=100) :: err_msg | ||
| 765 | |||
| 766 | TIMER_DECL(t_total) | ||
| 767 | TIMER_INIT_START(t_total, "MFormFun::solve_curlA_equals_B") | ||
| 768 | |||
| 769 | ! TODO calling previous() multiple times (for each twoform) is not efficient | ||
| 770 | 249 | oneform_space = previous(twoform_space) | |
| 771 | 249 | twoform_m = twoform_space%m | |
| 772 | |||
| 773 |
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|
249 | if (twoform_m /= 2) then |
| 774 | ✗ | write (err_msg, '(A,I0,A)') "ERROR in solve_curlA_equals_B_ori: the provided space is a ", twoform_m, & | |
| 775 | ✗ | "-form, but a 2-form is required." | |
| 776 | ✗ | error stop err_msg | |
| 777 | end if | ||
| 778 |
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|
249 | if (twoform_space%dimensionality == 3) then |
| 779 | ✗ | error stop "ERROR in solve_curlA_equals_B_ori: the provided space is not 2D, but a 2D space is required." | |
| 780 | end if | ||
| 781 | |||
| 782 |
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|
249 | if (present(zeroform_solver)) then |
| 783 | zeroform_solver_p => zeroform_solver | ||
| 784 | else | ||
| 785 |
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35 | call divgrad%init(previous(oneform_space), coord_transform=cylinder_transform) |
| 786 |
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|
35 | call zeroform_solver_%init(divgrad, constraint1=MFormNeumann(), constraint2=constraint, coord_transform=cylinder_transform) |
| 787 | zeroform_solver_p => zeroform_solver_ | ||
| 788 | end if | ||
| 789 | |||
| 790 | ! Step one: find a one-form such that curl oneform = twoform | ||
| 791 | ! This can be done analytically since the two-form is given as a product of 1D B-splines | ||
| 792 | 249 | call twoform_x_integrated%init(oneform_space%tp_spaces(2)%spaces(1)) | |
| 793 | 249 | call cumsum(twoform_x_integrated%data, twoform_x%data) | |
| 794 | 249 | call twoform_y_copy%init(twoform_y%bspline) | |
| 795 |
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|
8105 | twoform_y_copy%data = twoform_y%data |
| 796 | 249 | call oneform_tmp%init(oneform_space) | |
| 797 |
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|
498 | do k = oneform_space%tp_spaces(2)%rank_resp_bspline%k0, oneform_space%tp_spaces(2)%rank_resp_bspline%k1 |
| 798 |
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|
7374 | do j = oneform_space%tp_spaces(2)%rank_resp_bspline%j0, oneform_space%tp_spaces(2)%rank_resp_bspline%j1 |
| 799 |
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|
170513 | do i = oneform_space%tp_spaces(2)%rank_resp_bspline%i0, oneform_space%tp_spaces(2)%rank_resp_bspline%i1 |
| 800 | 170264 | oneform_tmp%tp_funs(2)%data(i, j, k) = twoform_x_integrated%data(i) * twoform_y%data(j) | |
| 801 | end do | ||
| 802 | end do | ||
| 803 | end do | ||
| 804 | |||
| 805 | 249 | call oneform_tmp%distribute() | |
| 806 | |||
| 807 | ! Step two: project the one-form onto the weakly divergence-free space | ||
| 808 | 249 | call inner_product(f, oneform_space, zero_function, wrapped_oneform_y, zero_function, cylinder_transform) | |
| 809 | |||
| 810 | 249 | call gradient_adjoint(df, f) | |
| 811 | 249 | call zeroform_solver_p%solve(zeroform, df) | |
| 812 | 249 | call gradient(grad, zeroform) | |
| 813 | 249 | call oneform_tmp%axpy(-1.0_wp, grad) | |
| 814 | |||
| 815 |
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249 | if (present(constraint)) then |
| 816 |
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|
35 | allocate (constraint_local, source=constraint) |
| 817 | 35 | call constraint_local%init(oneform_space, cylinder_transform) | |
| 818 | 35 | call constraint_local%apply(oneform, oneform_tmp) | |
| 819 | 35 | call constraint_local%destroy() | |
| 820 |
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|
70 | deallocate (constraint_local) |
| 821 | else | ||
| 822 | ! NOTE: this is a deep copy using the overloaded assignment(=) operator | ||
| 823 | 214 | oneform = oneform_tmp | |
| 824 | end if | ||
| 825 | |||
| 826 | 249 | call f%destroy() | |
| 827 | 249 | call df%destroy() | |
| 828 | 249 | call grad%destroy() | |
| 829 | 249 | call zeroform%destroy() | |
| 830 | 249 | call oneform_tmp%destroy() | |
| 831 | 249 | call twoform_x_integrated%destroy() | |
| 832 | |||
| 833 |
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|
284 | if (.not. present(zeroform_solver)) then |
| 834 | 35 | call divgrad%destroy() | |
| 835 | 35 | call zeroform_solver_%destroy() | |
| 836 | end if | ||
| 837 | TIMER_STOP(t_total) | ||
| 838 | contains | ||
| 839 | ! pure real(wp) function wrapped_oneform_x(xp, yp, zp) result(ans) | ||
| 840 | ! implicit none | ||
| 841 | |||
| 842 | ! real(wp), intent(in) :: xp, yp, zp | ||
| 843 | |||
| 844 | ! ans = evaluate(oneform_tmp, 1, xp, yp, zp, eval_logical_form=.true.) | ||
| 845 | ! end function wrapped_oneform_x | ||
| 846 | |||
| 847 | 17569824 | pure real(wp) function wrapped_oneform_y(xp, yp, zp) result(ans) | |
| 848 | use m_bspline_basis, only: evaluate | ||
| 849 | implicit none | ||
| 850 | |||
| 851 | real(wp), intent(in) :: xp, yp, zp | ||
| 852 | |||
| 853 | ! ans = evaluate(oneform_tmp, 2, xp, yp, zp, eval_logical_form=.true.) | ||
| 854 | 17569824 | ans = evaluate(twoform_x_integrated, xp) * evaluate(twoform_y_copy, yp) | |
| 855 | 17569824 | end function wrapped_oneform_y | |
| 856 | end subroutine solve_curlA_equals_B_tensorprod | ||
| 857 | |||
| 858 | end module m_mform_linalg | ||
| 859 |