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get_matrix_x.f90
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get_matrix_x.f90
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! BSD 2-Clause License
!
! Copyright (c) [2019] [Valeria Barra]
! All rights reserved.
!
! Redistribution and use in source and binary forms, with or without
! modification, are permitted provided that the following conditions are met:
!
! 1. Redistributions of source code must retain the above copyright notice, this
! list of conditions and the following disclaimer.
!
! 2. Redistributions in binary form must reproduce the above copyright notice,
! this list of conditions and the following disclaimer in the documentation
! and/or other materials provided with the distribution.
!
! THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
! ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
! WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
! DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
! ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
! (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
! LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
! ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
! (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
! SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
SUBROUTINE get_matrix_x2(dt,ma_x,ffx,hxxx,hx,ffx0,ffxm,hxxxp&
,hxxx0,hxxxm,hxxxmm,hx0,hxm,hxavem,hxave0,hxavep,fvdwx,fvdwx0&
,fvdwxm, fquadvdwx,fquadvdwx0,fquadvdwxm,fquad,fderquadx0,fderquadxm&
,coeff_one,coeff_three)
USE nrtype
USE domain_time
USE domain_space, ONLY: n, nmmax
USE paras, ONLY: theta,l1,bb,l2
IMPLICIT NONE
!!$ this subroutine assembles all the different contributions in the pentadiagonal matrix
INTERFACE
SUBROUTINE get_matrix_x_c(ffx,ffx0,ffxm,hxxx,hxxxp,hxxx0,hxxxm,hxxxmm,gpp_c,gp_c,g0_c,gm_c,gmm_c)
USE nrtype
USE domain_space, ONLY: n,nmmax
USE paras, ONLY: coef_c,dx4
IMPLICIT NONE
REAL(DP), DIMENSION(nmmax), INTENT(IN) :: ffx,ffx0,ffxm,hxxx,hxxxp,hxxx0,hxxxm,hxxxmm
REAL(DP), DIMENSION(nmmax), INTENT(OUT) :: gpp_c,gp_c,g0_c,gm_c,gmm_c
END SUBROUTINE get_matrix_x_c
SUBROUTINE get_matrix_x_quadterm(fquad,fderquadx0,fderquadxm,hxxx,hxxxp&
,hxxx0,hxxxm,hxxxmm,gpp_quadterm,gp_quadterm,g0_quadterm&
,gm_quadterm,gmm_quadterm)
USE nrtype
USE domain_space, ONLY: n, nmmax
USE paras, ONLY: coef_slip,dx4
IMPLICIT NONE
REAL(DP), DIMENSION(nmmax), INTENT(IN) :: fquad,fderquadx0,fderquadxm,hxxx,hxxxp,hxxx0&
,hxxxm,hxxxmm
REAL(DP), DIMENSION(nmmax), INTENT(OUT) :: gpp_quadterm,gp_quadterm&
,g0_quadterm,gm_quadterm,gmm_quadterm
END SUBROUTINE get_matrix_x_quadterm
SUBROUTINE get_matrix_x_vdw(fvdwx,fvdwx0,fvdwxm,hx,hx0,hxm,gp_vdw,g0_vdw,gm_vdw)
USE nrtype
USE domain_space, ONLY: n, nmmax
USE paras, ONLY: coef_vdw,dx2
IMPLICIT NONE
REAL(DP), DIMENSION(nmmax), INTENT(IN) :: fvdwx,fvdwx0,fvdwxm,hx,hx0,hxm
REAL(DP), DIMENSION(nmmax), INTENT(OUT) :: gp_vdw,g0_vdw,gm_vdw
END SUBROUTINE get_matrix_x_vdw
SUBROUTINE get_matrix_x_quadvdw(fquadvdwx,fquadvdwx0,fquadvdwxm,hx,hx0,hxm,gp_quadvdw&
,g0_quadvdw,gm_quadvdw)
USE nrtype
USE domain_space, ONLY: n, nmmax
USE paras, ONLY: coef_slip,coef_vdw,dx2
IMPLICIT NONE
REAL(DP), DIMENSION(nmmax), INTENT(IN) :: fquadvdwx,fquadvdwx0,fquadvdwxm,hx,hx0,hxm
REAL(DP), DIMENSION(nmmax), INTENT(OUT) :: gp_quadvdw,g0_quadvdw,gm_quadvdw
END SUBROUTINE get_matrix_x_quadvdw
SUBROUTINE get_matrix_x_hxave(hxavem,hxave0,hxavep,gm_hxave,g0_hxave,gp_hxave)
USE nrtype
USE domain_space, ONLY: n, nmmax
USE paras, ONLY: dx
IMPLICIT NONE
REAL(DP), DIMENSION(nmmax), INTENT(IN) :: hxavem,hxave0,hxavep
REAL(DP), DIMENSION(nmmax), INTENT(OUT) :: gm_hxave,g0_hxave,gp_hxave
END SUBROUTINE get_matrix_x_hxave
END INTERFACE
REAL(DP), INTENT(IN) :: dt
REAL(DP), DIMENSION(nmmax,1:5), INTENT(OUT) :: ma_x
REAL(DP), DIMENSION(nmmax), INTENT(IN) :: ffx,ffx0,ffxm,hxxxp,hxxx0,hxxxm,hxxxmm,hx0,hxm&
,fvdwx,fvdwx0,fvdwxm,fquadvdwx,fquadvdwx0,fquadvdwxm,fquad,fderquadx0,fderquadxm&
,hxxx,hx,coeff_one,coeff_three,hxavem,hxave0,hxavep
REAL(DP) :: gpp_c(nmmax),gp_c(nmmax),g0_c(nmmax),gm_c(nmmax),gmm_c(nmmax)
REAL(DP) :: gpp_quadterm(nmmax), gp_quadterm(nmmax), g0_quadterm(nmmax), gm_quadterm(nmmax)&
,gmm_quadterm(nmmax)
REAL(DP) :: gp_vdw(nmmax),g0_vdw(nmmax),gm_vdw(nmmax)
REAL(DP) :: gp_quadvdw(nmmax),g0_quadvdw(nmmax),gm_quadvdw(nmmax)
REAL(DP) :: gm_hxave(nmmax),g0_hxave(nmmax),gp_hxave(nmmax)
INTEGER(I4B) :: k
CALL get_matrix_x_c(ffx,ffx0,ffxm,hxxx,hxxxp,hxxx0,hxxxm,hxxxmm,gpp_c,gp_c,g0_c,gm_c,gmm_c)
CALL get_matrix_x_quadterm(fquad,fderquadx0,fderquadxm,hxxx,hxxxp,hxxx0,hxxxm,hxxxmm&
,gpp_quadterm,gp_quadterm,g0_quadterm,gm_quadterm,gmm_quadterm)
CALL get_matrix_x_vdw(fvdwx,fvdwx0,fvdwxm,hx,hx0,hxm,gp_vdw,g0_vdw,gm_vdw)
CALL get_matrix_x_quadvdw(fquadvdwx,fquadvdwx0,fquadvdwxm,hx,hx0,hxm&
,gp_quadvdw,g0_quadvdw,gm_quadvdw)
CALL get_matrix_x_hxave(hxavem,hxave0,hxavep,gm_hxave,g0_hxave,gp_hxave)
IF(l2.EQ.0.0d0)THEN ! this IF puts back the code in the original form when l2=0, first order in time equation
DO k=1,n
ma_x(k,1)=(1.0d0-theta)*dt*(gmm_c(k) + bb*gmm_quadterm(k)) + l1*(gmm_c(k))
ma_x(k,2)=(1.0d0-theta)*dt*(gm_c(k)+bb*gm_quadterm(k)+gm_vdw(k)+bb*gm_quadvdw(k))&
+l1*(gm_c(k) + gm_vdw(k)) + coeff_three(k)*gm_hxave(k)
ma_x(k,3)=coeff_one(k)+(1.0d0-theta)*dt*(g0_c(k)+bb*g0_quadterm(k)+g0_vdw(k)&
+bb*g0_quadvdw(k)) + coeff_three(k)*g0_hxave(k) + l1*(g0_c(k) + g0_vdw(k))
ma_x(k,4)=(1.0d0-theta)*dt*(gp_c(k)+bb*gp_quadterm(k)+gp_vdw(k)+bb*gp_quadvdw(k))&
+l1*(gp_c(k) + gp_vdw(k)) + coeff_three(k)*gp_hxave(k)
ma_x(k,5)=(1.0d0-theta)*dt*(gpp_c(k) + bb*gpp_quadterm(k)) + l1*(gpp_c(k))
END DO
ELSE ! this is the latest version of the code, for l2 NOT zero, second order in time equation
IF(t.EQ.t0)THEN ! This creates a slightly different matrix only for the first time step, n=0, accounting for the initial h^(-1)=h^1
DO k=1,n
ma_x(k,1)=(1.0d0-theta)*(dt**2)*(gmm_c(k) + bb*gmm_quadterm(k))&
+l1*dt*(gmm_c(k)) + l2*dt*bb*(gmm_quadterm(k))
ma_x(k,2)=(1.0d0-theta)*(dt**2)*(gm_c(k)+bb*gm_quadterm(k)+gm_vdw(k)+bb*gm_quadvdw(k))&
+l1*dt*(gm_c(k) + gm_vdw(k))+l2*dt*bb*(gm_quadvdw(k) + gm_quadterm(k))&
+ dt*coeff_three(k)*gm_hxave(k)
ma_x(k,3)=2.0d0*l2 + dt*coeff_one(k) + (1.0d0-theta)*(dt**2)*(g0_c(k)+bb*g0_quadterm(k)+g0_vdw(k)&
+bb*g0_quadvdw(k)) + dt*coeff_three(k)*g0_hxave(k) + l1*dt*(g0_c(k) + g0_vdw(k))&
+l2*dt*bb*(g0_quadvdw(k) + g0_quadterm(k))
ma_x(k,4)=(1.0d0-theta)*(dt**2)*(gp_c(k)+bb*gp_quadterm(k)+gp_vdw(k)+bb*gp_quadvdw(k))&
+l1*dt*(gp_c(k) + gp_vdw(k))+l2*dt*bb*(gp_quadvdw(k) + gp_quadterm(k))&
+ dt*coeff_three(k)*gp_hxave(k)
ma_x(k,5)=(1.0d0-theta)*(dt**2)*(gpp_c(k) + bb*gpp_quadterm(k))&
+l1*dt*(gpp_c(k)) + l2*dt*bb*(gpp_quadterm(k))
END DO
ELSE ! this is the general case, for any time step n>=1, the difference is that there is only l2 in the main diagonal, instead of 2*l2
DO k=1,n
ma_x(k,1)=(1.0d0-theta)*(dt**2)*(gmm_c(k) + bb*gmm_quadterm(k))&
+l1*dt*(gmm_c(k)) + l2*dt*bb*(gmm_quadterm(k))
ma_x(k,2)=(1.0d0-theta)*(dt**2)*(gm_c(k)+bb*gm_quadterm(k)+gm_vdw(k)+bb*gm_quadvdw(k))&
+l1*dt*(gm_c(k) + gm_vdw(k))+l2*dt*bb*(gm_quadvdw(k) + gm_quadterm(k))&
+ dt*coeff_three(k)*gm_hxave(k)
ma_x(k,3)= l2 + dt*coeff_one(k) + (1.0d0-theta)*(dt**2)*(g0_c(k)+bb*g0_quadterm(k)+g0_vdw(k)&
+bb*g0_quadvdw(k)) + dt*coeff_three(k)*g0_hxave(k) + l1*dt*(g0_c(k) + g0_vdw(k))&
+l2*dt*bb*(g0_quadvdw(k) + g0_quadterm(k))
ma_x(k,4)=(1.0d0-theta)*(dt**2)*(gp_c(k)+bb*gp_quadterm(k)+gp_vdw(k)+bb*gp_quadvdw(k))&
+l1*dt*(gp_c(k) + gp_vdw(k))+l2*dt*bb*(gp_quadvdw(k) + gp_quadterm(k))&
+ dt*coeff_three(k)*gp_hxave(k)
ma_x(k,5)=(1.0d0-theta)*(dt**2)*(gpp_c(k) + bb*gpp_quadterm(k))&
+l1*dt*(gpp_c(k)) + l2*dt*bb*(gpp_quadterm(k))
END DO
END IF
END IF
RETURN
END SUBROUTINE get_matrix_x2