Merge branch 'master' into reconnection
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f9b88b7384
@ -381,6 +381,12 @@ module interpolations
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reconstruct_states => reconstruct_ocmp5
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order = 5
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nghosts = max(nghosts, 4)
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case ("ocmp7", "OCMP7")
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name_rec = "7th order Optimized Compact Monotonicity Preserving"
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interfaces => interfaces_dir
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reconstruct_states => reconstruct_ocmp7
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order = 7
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nghosts = max(nghosts, 4)
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case ("gp", "GP")
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write(stmp, '(f16.1)') sgp
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write(name_rec, '("Gaussian Process (",i1,"-point, δ=",a,")")') ngp &
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@ -4489,30 +4495,30 @@ module interpolations
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real(kind=8), dimension(size(fc)) :: r
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real(kind=8), dimension(size(fc)) :: u
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real(kind=8), parameter :: a1 = 5.0163016d-01
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real(kind=8), parameter :: a2 = 2.5394716d-01
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real(kind=8), dimension(3), parameter :: &
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di = [ 5.0163016d-01, 1.0d+00, 2.5394716d-01 ]
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di5 = [ a1, 1.0d+00, a2 ]
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real(kind=8), dimension(5), parameter :: &
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ci5 = [- 3.0d+00 * di(1) - 3.0d+00 * di(3) + 2.0d+00, &
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2.7d+01 * di(1) + 1.7d+01 * di(3) - 1.3d+01, &
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4.7d+01 * di(1) - 4.3d+01 * di(3) + 4.7d+01, &
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- 1.3d+01 * di(1) + 7.7d+01 * di(3) + 2.7d+01, &
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2.0d+00 * di(1) + 1.2d+01 * di(3) - 3.0d+00 ] / 6.0d+01
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ci5 = [- 3.0d+00 * a1 - 3.0d+00 * a2 + 2.0d+00, &
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2.7d+01 * a1 + 1.7d+01 * a2 - 1.3d+01, &
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4.7d+01 * a1 - 4.3d+01 * a2 + 4.7d+01, &
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- 1.3d+01 * a1 + 7.7d+01 * a2 + 2.7d+01, &
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2.0d+00 * a1 + 1.2d+01 * a2 - 3.0d+00 ] / 6.0d+01
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!
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!-------------------------------------------------------------------------------
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!
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n = size(fc)
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! prepare the diagonals of the tridiagonal matrix
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!
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do i = 1, ng
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a(i) = 0.0d+00
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b(i) = 1.0d+00
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c(i) = 0.0d+00
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end do
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do i = ng + 1, n - ng - 1
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a(i) = di(1)
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b(i) = di(2)
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c(i) = di(3)
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a(i) = di5(1)
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b(i) = di5(2)
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c(i) = di5(3)
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end do
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do i = n - ng, n
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a(i) = 0.0d+00
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@ -4522,14 +4528,10 @@ module interpolations
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!! === left-side interpolation ===
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!!
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! prepare the right-hand side of the linear system
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!
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do i = ng, n - ng + 1
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r(i) = sum(ci5(:) * fc(i-2:i+2))
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end do
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! use explicit methods for ghost zones
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!
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r( 1) = sum(ce2(:) * fc( 1: 2))
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r( 2) = sum(ce3(:) * fc( 1: 3))
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do i = 3, ng
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@ -4541,32 +4543,20 @@ module interpolations
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r(n-1) = sum(ce3(:) * fc(n-2: n))
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r(n ) = fc(n )
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! solve the tridiagonal system of equations
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!
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call tridiag(n, a(1:n), b(1:n), c(1:n), r(1:n), u(1:n))
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! apply the monotonicity preserving limiter
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!
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call mp_limiting(fc(:), u(:))
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! return the interpolated values of the left state
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!
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fl(1:n) = u(1:n)
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!! === right-side interpolation ===
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!!
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! invert the cell-centered integrals
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!
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fi(1:n) = fc(n:1:-1)
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! prepare the right-hand side of the linear system
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!
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do i = ng, n - ng + 1
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r(i) = sum(ci5(:) * fi(i-2:i+2))
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end do ! i = ng, n - ng + 1
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! use explicit methods for ghost zones
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!
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r( 1) = sum(ce2(:) * fi( 1: 2))
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r( 2) = sum(ce3(:) * fi( 1: 3))
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do i = 3, ng
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@ -4578,20 +4568,12 @@ module interpolations
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r(n-1) = sum(ce3(:) * fi(n-2: n))
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r(n ) = fi(n )
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! solve the tridiagonal system of equations
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!
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call tridiag(n, a(1:n), b(1:n), c(1:n), r(1:n), u(1:n))
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! apply the monotonicity preserving limiter
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!
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call mp_limiting(fi(:), u(:))
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! return the interpolated values of the right state
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!
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fr(1:n-1) = u(n-1:1:-1)
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! update the extremum points
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!
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i = n - 1
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fl(1) = 0.5d+00 * (fc(1) + fc(2))
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fr(i) = 0.5d+00 * (fc(i) + fc(n))
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@ -4604,6 +4586,147 @@ module interpolations
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!
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!===============================================================================
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!
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! subroutine RECONSTRUCT_OCMP7:
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! -----------------------------
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!
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! Subroutine reconstructs the interface states using the 7th order Optimized
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! Compact Reconstruction Monotonicity Preserving (CRMP) method.
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!
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! Arguments are described in subroutine reconstruct().
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!
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! References:
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!
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! [1] Myeong-Hwan Ahn, Duck-Joo Lee,
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! "Modified Monotonicity Preserving Constraints for High-Resolution
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! Optimized Compact Scheme",
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! Journal of Scientific Computing,
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! 2020, vol. 83, p. 34
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! https://doi.org/10.1007/s10915-020-01221-0
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!
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!===============================================================================
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!
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subroutine reconstruct_ocmp7(h, fc, fl, fr)
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use algebra, only : pentadiag
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implicit none
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real(kind=8) , intent(in) :: h
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real(kind=8), dimension(:), intent(in) :: fc
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real(kind=8), dimension(:), intent(out) :: fl, fr
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integer :: n, i
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real(kind=8), dimension(size(fc)) :: fi
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real(kind=8), dimension(size(fc)) :: e, c, d, a, b
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real(kind=8), dimension(size(fc)) :: r
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real(kind=8), dimension(size(fc)) :: u
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real(kind=8), parameter :: a1 = 6.6850691831375709863684029643567d-01
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real(kind=8), parameter :: a2 = 3.3644225201902153852210572056440d-01
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real(kind=8), dimension(5), parameter :: &
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di7 = [ (3.0d+00 * a1 + 2.0d+00 * a2 - 2.0d+00) / 8.0d+00, &
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a1, 1.0d+00, a2, &
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( a1 + 6.0d+00 * a2 - 2.0d+00) / 4.0d+01 ]
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real(kind=8), dimension(5), parameter :: &
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ci7 = [ 1.80d+01 * a1 + 1.80d+01 * a2 - 1.60d+01, &
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5.43d+02 * a1 + 2.68d+02 * a2 - 2.91d+02, &
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3.43d+02 * a1 - 3.32d+02 * a2 + 5.09d+02, &
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-1.07d+02 * a1 + 5.68d+02 * a2 + 3.09d+02, &
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4.30d+01 * a1 + 3.18d+02 * a2 - 9.10d+01 ] / 6.0d+02
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!
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!-------------------------------------------------------------------------------
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!
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n = size(fc)
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! prepare the diagonals of the tridiagonal matrix
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!
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do i = 1, ng
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e(i) = 0.0d+00
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c(i) = 0.0d+00
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d(i) = 1.0d+00
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a(i) = 0.0d+00
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b(i) = 0.0d+00
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end do
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do i = ng + 1, n - ng - 1
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e(i) = di7(1)
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c(i) = di7(2)
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d(i) = di7(3)
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a(i) = di7(4)
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b(i) = di7(5)
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end do
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do i = n - ng, n
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e(i) = 0.0d+00
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c(i) = 0.0d+00
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d(i) = 1.0d+00
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a(i) = 0.0d+00
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b(i) = 0.0d+00
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end do
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!! === left-side interpolation ===
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!!
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do i = ng, n - ng + 1
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r(i) = sum(ci7(:) * fc(i-2:i+2))
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end do
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r( 1) = sum(ce2(:) * fc( 1: 2))
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r( 2) = sum(ce3(:) * fc( 1: 3))
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r( 3) = sum(ce5(:) * fc( 1: 5))
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do i = 4, ng
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r(i) = sum(ce7(:) * fc(i-3:i+3))
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end do
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do i = n - ng, n - 3
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r(i) = sum(ce7(:) * fc(i-3:i+3))
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end do
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r(n-2) = sum(ce5(:) * fc(n-4: n))
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r(n-1) = sum(ce3(:) * fc(n-2: n))
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r(n ) = fc(n )
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call pentadiag(n, e(:), c(:), d(:), a(:), b(:), r(:), u(:))
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call mp_limiting(fc(:), u(:))
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fl(1:n) = u(1:n)
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!! === right-side interpolation ===
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!!
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fi(1:n) = fc(n:1:-1)
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do i = ng, n - ng + 1
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r(i) = sum(ci7(:) * fi(i-2:i+2))
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end do ! i = ng, n - ng + 1
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r( 1) = sum(ce2(:) * fi( 1: 2))
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r( 2) = sum(ce3(:) * fi( 1: 3))
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r( 3) = sum(ce5(:) * fi( 1: 5))
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do i = 4, ng
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r(i) = sum(ce7(:) * fi(i-3:i+3))
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end do
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do i = n - ng, n - 3
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r(i) = sum(ce7(:) * fi(i-3:i+3))
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end do
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r(n-2) = sum(ce5(:) * fi(n-4: n))
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r(n-1) = sum(ce3(:) * fi(n-2: n))
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r(n ) = fi(n )
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call pentadiag(n, e(:), c(:), d(:), a(:), b(:), r(:), u(:))
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call mp_limiting(fi(:), u(:))
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fr(1:n-1) = u(n-1:1:-1)
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i = n - 1
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fl(1) = 0.5d+00 * (fc(1) + fc(2))
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fr(i) = 0.5d+00 * (fc(i) + fc(n))
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fl(n) = fc(n)
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fr(n) = fc(n)
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!-------------------------------------------------------------------------------
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!
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end subroutine reconstruct_ocmp7
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!
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!===============================================================================
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!
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! subroutine PREPARE_GP:
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! ---------------------
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!
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