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12 changes: 0 additions & 12 deletions example/extended-gauss-divergence.F90
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Expand Up @@ -26,25 +26,13 @@ program extended_gauss_divergence
!! where `.SSS.` and `.SS.` are the 1D equivalents of a volume integral over the whole
!! domain and a surface integral over a domain boundary of unit area, respectively.

! PURPOSE: Import derived types (*_t) and abstract interfaces (*_i) from modules (*_m) that
! export the public entities provided by the Formal mimetic abstraction library and
! the Julienne correctness-checking framework. Also import scalar and vector functions
! from a user-defined module: integrand_operands_m.
! KEYWORDS: derived type, use association, abstract interface
! CONTEXT: demonstration of satisfaction of an extended form of the Gauss Divergence Theorem

use julienne_m, only : command_line_t
use formal_m, only : scalar_1D_t, scalar_1D_initializer_i, vector_1D_t, vector_1D_initializer_i
use integrand_operands_m, only : scalar, vector
! END CODE CHUNK

implicit none
! PURPOSE: Define procedure pointers for 1D scalar- and vector-field initialization functions
! KEYWORDS: initial condition, 1D, scalar, vector
! CONTEXT: pass as the first argument in a scalar_1D_t or vector_1D_t constructor function invocation
procedure(scalar_1D_initializer_i), pointer :: scalar_1D_initializer => scalar
procedure(vector_1D_initializer_i), pointer :: vector_1D_initializer => vector
! END CODE CHUNK

type numerical_arguments_t
!! Define default initializations that can be overridden with the command-line arguments
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48 changes: 0 additions & 48 deletions example/vibe-coding/rag-target.F90
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Expand Up @@ -72,12 +72,6 @@
! that need not be in the code that we desire for the retreival augmented generation (RAG)
! process to generate.

! PURPOSE: User-defined module functions for use in initializing scalar and vector fields on
! a one-dimensional (1D) staggered grid. Scalar functions will be sampled at cell
! centers and domian boundaries (domain interval end points in 1D). Vector functions
! will be sampled at cell faces (subinterval end points).
! KEYWORDS: module function, scalar, vector
! CONTEXT:
module rag_integrand_operands_m
implicit none
contains
Expand All @@ -95,75 +89,33 @@ pure function vector(x) result(v)
end function

end module
! END CODE CHUNK

program rag_target

! PURPOSE: Import derived types (*_t) and abstract interfaces (*_i) from modules (*_m) that
! export the public entities provided by the Formal mimetic abstraction library and
! the Julienne correctness-checking framework. Also import scalar and vector functions
! from a user-defined module: rag_integrand_operands_m.
! KEYWORDS: derived type, use association, abstract interface
! CONTEXT: demonstration of satisfaction of an extended form of the Gauss Divergence Theorem

use formal_m, only : scalar_1D_t, scalar_1D_initializer_i, vector_1D_t, vector_1D_initializer_i
use rag_integrand_operands_m, only : scalar, vector
! END CODE CHUNK

implicit none
! PURPOSE: Define procedure pointers for 1D scalar- and vector-field initialization functions
! KEYWORDS: initial condition, 1D, scalar, vector
! CONTEXT: pass as the first argument in a scalar_1D_t or vector_1D_t constructor function invocation
procedure(scalar_1D_initializer_i), pointer :: scalar_1D_initializer => scalar
procedure(vector_1D_initializer_i), pointer :: vector_1D_initializer => vector
! END CODE CHUNK

double precision SSS_v_dot_grad_f_dV, SSS_f_div_v_dV, SS_f_v_dot_dA

! PURPOSE: Construct 1D scalar- and vector-field objects with a specified order of accuracy,
! number of grid cells, and domain boundaries
! KEYWORDS: scalar field, vector field, one-dimensional (1D)
! CONTEXT: construct fields for use as operands in vector-calculus expressions
integrand_factors: &
associate( &
f => scalar_1D_t(scalar_1D_initializer, order=4, cells=200, x_min=0D0, x_max=1D0) &
,v => vector_1D_t(vector_1D_initializer, order=4, cells=200, x_min=0D0, x_max=1D0) &
)
! END CODE CHUNK
differential_volume: &
associate(dV => f%dV())

! PURPOSE: Evaluate a volume integral over the problem domain with an integrand formed
! from the dot product of a vector field v with the gradient of a scalar f
! KEYWORDS: volume integral, dot product, gradient
! CONTEXT: Use to verfiy the extended Gauss divergence theorem.
SSS_v_dot_grad_f_dV = .SSS. (v .dot. .grad. f) * dV
! END CODE CHUNK

! PURPOSE: Evaluate a volume integral over the problem domain with an integrand formed
! from the product of a scalar field f with the divergence of a vector field v
! KEYWORDS: volume integral, divergence
! CONTEXT: Use to verfiy the extended Gauss divergence theorem.
SSS_f_div_v_dV = .SSS. (f * .div. v) * dV
! END CODE CHUNK

end associate differential_volume

differential_area: &
associate(dA => v%dA())
! PURPOSE: Evaluate a boundary surface integral representing the flux of a vector field formed
! from the product of a scalar field f and a vector field v
! KEYWORDS: surface integral, flux
! CONTEXT: Use to verfiy the extended Gauss divergence theorem.
SS_f_v_dot_dA = .SS. (f .x. (v .dot. dA))
! END CODE CHUNK

! PURPOSE: Verify satisfaction of the Extended Gauss Divergence Theorem by computing a residual
! formed from the two volume integrals and one surface integral in the theorem.
! KEYWORDS: Extended Gauss Divergence Theorem, residual
! CONTEXT: A small resudual verifies the satisfaction of the Extended Guass Divergence Theorem
print '(26x,a,g0,a)',"sum = ", SSS_v_dot_grad_f_dV + SSS_f_div_v_dV - SS_f_v_dot_dA, " (residual)"
! END CODE CHUNK
end associate differential_area
end associate integrand_factors

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90 changes: 65 additions & 25 deletions src/formal/divergence_1D_s.F90
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Expand Up @@ -14,6 +14,16 @@

#ifdef __GFORTRAN__

! PURPOSE: Computes the cell-center x-coordinates for a uniform 1D grid given the domain bounds
! and number of cells, returning an array of cell-center locations offset by half a cell
! width from x_min.
! KEYWORDS: grid, cell-center, uniform-mesh, 1D, structured-grid, staggered-grid, utility, gfortran
! CONTEXT: This helper function is only compiled under gfortran and provides cell-center coordinate
! computation needed by the divergence_1D submodule. It constructs a uniform grid with cell
! width dx = (x_max - x_min)/cells and places each cell center at x_min + dx/2 + (cell-1)*dx
! using an implied do loop. Other compilers may provide this functionality through a different
! code path or type-bound procedure. This function is used by divergence_1D_grid to return
! the grid coordinates associated with a divergence_1D_t object.
pure function cell_center_locations(x_min, x_max, cells) result(x)
double precision, intent(in) :: x_min, x_max
integer, intent(in) :: cells
Expand All @@ -24,14 +34,24 @@ pure function cell_center_locations(x_min, x_max, cells) result(x)
x = x_min + dx/2. + [((cell-1)*dx, cell = 1, cells)]
end associate
end function
! END CODE CHUNK

#endif

! PURPOSE: Definition of procedure to compute the product of a scalar and a divergence
! KEYWORDS: scalar multiplication
! CONTEXT: Invoke this function via the binary infix operator "*" with scalar and divergence left- and
! right-hand operands, respectively

! PURPOSE: Computes the element-wise product of a scalar_1D field's interior values with a
! divergence_1D field's cell-centered values, producing a new scalar_x_divergence_1D_t
! object that carries both the multiplied values and the divergence quadrature weights.
! KEYWORDS: scalar-multiplication, divergence, operator-overloading, premultiply, scalar_1D,
! divergence_1D, structured-grid, staggered-grid, quadrature-weights, interior-values
! CONTEXT: This procedure implements the left-multiplication of a scalar_1D_t by a divergence_1D_t
! in the formal library's operator overloading framework. The scalar field has two extra
! boundary values compared to the divergence field's cell-centered values, so the scalar's
! interior slice (index 2 through size-1) is multiplied element-wise with the divergence
! values. The result inherits the scalar field's grid metadata and the divergence field's
! quadrature weights, with a compiler-conditional call to either weights() or
! divergence_1D_weights() to handle gfortran naming differences. Assertions verify that
! the scalar field has exactly two more values than the divergence field and that the
! resulting weights array has the expected size.
module procedure premultiply_scalar_1D
call_julienne_assert(size(scalar_1D%values_) .equalsExpected. size(divergence_1D%values_) + 2)
scalar_x_divergence_1D%tensor_1D_t = &
Expand All @@ -45,41 +65,60 @@ pure function cell_center_locations(x_min, x_max, cells) result(x)
end procedure
! END CODE CHUNK

! PURPOSE: Definition of procedure to compute the product of a divergence and a scalar
! KEYWORDS: scalar multiplication
! CONTEXT: Invoke this function via the binary infix operator "*" with divergence and scalar left- and
! right-hand operands, respectively

! PURPOSE: Delegates right-multiplication of a divergence_1D field by a scalar_1D field to the
! premultiply_scalar_1D procedure, ensuring commutativity of scalar-divergence
! multiplication.
! KEYWORDS: scalar-multiplication, divergence, operator-overloading, postmultiply, commutativity,
! scalar_1D, divergence_1D, delegation
! CONTEXT: This procedure implements the right-multiplication form (divergence * scalar) by
! delegating to premultiply_scalar_1D (scalar * divergence) in the formal library's
! operator overloading framework. Since scalar-divergence multiplication is commutative,
! this thin wrapper avoids duplicating the multiplication logic and ensures both operator
! orderings produce identical results.
module procedure postmultiply_scalar_1D
scalar_x_divergence_1D = premultiply_scalar_1D(scalar_1D, divergence_1D)
end procedure
! END CODE CHUNK

! PURPOSE: Definition of procedure to provide the cell-centered values of divergences.
! KEYWORDS: staggered grid, divergence
! CONTEXT: Invoke this function via the "values" generic binding to produce discrete divergence values.

! PURPOSE: Returns the cell-centered divergence values stored in a divergence_1D_t object.
! KEYWORDS: divergence, accessor, cell-centered-values, divergence_1D, getter
! CONTEXT: This procedure is a simple accessor that exposes the internally stored cell-centered
! divergence values from a divergence_1D_t object. It is used by test functions and other
! operators in the formal library to retrieve computed divergence data for comparison
! against analytical expectations or for use in compound operator expressions.
module procedure divergence_1D_values
cell_centered_values = self%values_
end procedure
! END CODE CHUNK

! PURPOSE: Definition of procedure to provide staggered-grid locations at which divergence values are stored: cell centers.
! KEYWORDS: cell centers, staggered grid, divergence
! CONTEXT: Invoke this function via the "grid" generic binding to produce discrete gradient-vector locations for
! initialization-function sampling, printing, or plotting.

! PURPOSE: Returns the cell-center x-coordinates of the 1D grid associated with a divergence_1D_t
! object by delegating to the cell_center_locations helper function.
! KEYWORDS: grid, cell-center, accessor, divergence_1D, structured-grid, staggered-grid, getter
! CONTEXT: This procedure provides access to the grid coordinates associated with a divergence_1D_t
! object in the formal library. It delegates to the cell_center_locations function, passing
! the stored domain bounds and cell count. Test functions use this accessor to retrieve
! grid coordinates for constructing spatially-varying expected values when verifying
! divergence operator results.
module procedure divergence_1D_grid
cell_centers = cell_center_locations(self%x_min_, self%x_max_, self%cells_)
end procedure
! END CODE CHUNK

! PURPOSE: Definition of procedure to compute the quadrature weights for use in the mimetic inner products of a scalar
! and the divergence of a vector.
! KEYWORDS: quadrature, numerical integration, coefficients, weights
! CONTEXT: Invoke this function via the "weights" generic binding to produce the quadrature weights
! associated with mimetic approximations to divergences.

! PURPOSE: Computes the mimetic quadrature weights for a divergence_1D_t object, returning an
! array of m+2 weights where m is the number of cells, with boundary skin weights that
! ensure discrete conservation properties and interior weights of 1.0.
! KEYWORDS: quadrature-weights, mimetic, divergence, boundary-weights, Corbino-Castillo,
! structured-grid, staggered-grid, 2nd-order, 4th-order, conservation, summation-by-parts
! CONTEXT: This procedure computes the quadrature weights used for discrete integration involving
! divergence fields in the formal library's mimetic finite-difference framework. The
! weights follow the formulation of Corbino & Castillo (2020) Eqs. 14-15 and 19, where
! boundary "skin" weights deviate from unity to maintain discrete conservation and
! summation-by-parts properties. For 2nd-order discretizations the skin is empty (all
! weights are 1.0), while for 4th-order discretizations an 8-element skin array provides
! the boundary corrections. The skin is mirrored symmetrically at both domain boundaries.
! Assertions verify that the grid has sufficient cells to accommodate the skin depth on
! both sides and that the resulting weights array has the expected size of cells+2.
! Unsupported orders trigger an error stop.
module procedure divergence_1D_weights
integer c

Expand All @@ -102,4 +141,5 @@ pure function cell_center_locations(x_min, x_max, cells) result(x)
call_julienne_assert(size(weights) .equalsExpected. self%cells_+2)
end procedure
! END CODE CHUNK

end submodule divergence_1D_s
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