You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
222 lines
7.6 KiB
222 lines
7.6 KiB
2 years ago
|
C Copyright(C) 1999-2020 National Technology & Engineering Solutions
|
||
|
|
C of Sandia, LLC (NTESS). Under the terms of Contract DE-NA0003525 with
|
||
|
|
C NTESS, the U.S. Government retains certain rights in this software.
|
||
|
|
C
|
||
|
|
C See packages/seacas/LICENSE for details
|
||
|
|
|
||
|
|
C========================================================================
|
||
|
|
SUBROUTINE EXTS(IGLND,INVCN,MAXLN,NXGLND,INVLEN,XA,YA,ZA,
|
||
|
|
& CNTRA,SOLEA,SOLENA,ITT,iblk)
|
||
|
|
C
|
||
|
|
C************************************************************************
|
||
|
|
C
|
||
|
|
C Subroutine EXTS sets up the matrix and vectors for a least squares
|
||
|
|
C linear interpolation/extrapolation of element variable data to the
|
||
|
|
C nodes for a 4-node quad element. In the special case of data from
|
||
|
|
C only 3 elements, the result is not least squares fit but a
|
||
|
|
C triangularization.
|
||
|
|
C
|
||
|
|
C Calls subroutines FRGE & BS
|
||
|
|
C
|
||
|
|
C Called by SELTN3
|
||
|
|
C
|
||
|
|
C************************************************************************
|
||
|
|
C
|
||
|
|
C IGLND INT The global node number being processed
|
||
|
|
C INVCN INT Inverse connectivity (1:maxln,1:numnda)
|
||
|
|
C MAXLN INT The maximum number of elements connected to any node
|
||
|
|
C NXGLND INT The local node used to get elements from INVCN
|
||
|
|
C INVLEN INT The number of elements connected to NXGLND
|
||
|
|
C XA,etc REAL Vectors containing nodal coordinates
|
||
|
|
C CNTRA REAL Array containing the coordinates of the element
|
||
|
|
C centroids (1:3)
|
||
|
|
C SOLEA REAL The element variables
|
||
|
|
C SOLENA REAL Element variables at nodes
|
||
|
|
C number with the global mesh node number (1:numnda)
|
||
|
|
C ITT INT truth table
|
||
|
|
C iblk INT element block being processed (not ID)
|
||
|
|
C INTND INT The global node number associated with IGLND
|
||
|
|
C S REAL The coefficient matrix for the least squares fit
|
||
|
|
C L INT Dummy vector - used in FRGE and BS
|
||
|
|
C X REAL The solution vector - used in BS
|
||
|
|
C G REAL Dummy vector - used in FRGE
|
||
|
|
C F REAL The load vector for the least squares fit
|
||
|
|
C
|
||
|
|
C************************************************************************
|
||
|
|
C
|
||
|
|
include 'aexds1.blk'
|
||
|
|
include 'amesh.blk'
|
||
|
|
include 'ebbyeb.blk'
|
||
|
|
include 'tapes.blk'
|
||
|
|
C
|
||
|
|
DIMENSION INVCN(MAXLN,*),XA(*),YA(*),ZA(*)
|
||
|
|
DIMENSION CNTRA(NUMEBA,*),SOLEA(NUMEBA,*)
|
||
|
|
DIMENSION SOLENA(NODESA,NVAREL), ITT(NVAREL,*)
|
||
|
|
DIMENSION IFRST(3), RLENTH(8), XLC(8), YLC(8)
|
||
|
|
C DIMENSION ZLC(8)
|
||
|
|
DOUBLE PRECISION S(3,3),G(3),F(3),X(3)
|
||
|
|
INTEGER L(3)
|
||
|
|
C
|
||
|
|
C************************************************************************
|
||
|
|
C
|
||
|
|
C Zero matrix
|
||
|
|
C
|
||
|
|
DO I = 1,3
|
||
|
|
IFRST(I) = I
|
||
|
|
DO J = 1,3
|
||
|
|
S(I,J) = 0.D+00
|
||
|
|
end do
|
||
|
|
end do
|
||
|
|
c
|
||
|
|
c find distance from interpolation point to element centroids
|
||
|
|
c
|
||
|
|
DO I = 1, INVLEN
|
||
|
|
A = XA(IGLND) - CNTRA(INVCN(I,NXGLND),1)
|
||
|
|
B = YA(IGLND) - CNTRA(INVCN(I,NXGLND),2)
|
||
|
|
C = ZA(IGLND) - CNTRA(INVCN(I,NXGLND),3)
|
||
|
|
RLENTH(I) = SQRT(A*A + B*B + C*C)
|
||
|
|
end do
|
||
|
|
C
|
||
|
|
C find the three closest element centroids
|
||
|
|
C
|
||
|
|
IF (INVLEN .EQ. 3) THEN
|
||
|
|
DO I = 1, 2
|
||
|
|
IF (RLENTH(I) .GT. RLENTH(I+1))THEN
|
||
|
|
ITEMP = IFRST(I)
|
||
|
|
IFRST(I) = IFRST(I+1)
|
||
|
|
IFRST(I+1) = ITEMP
|
||
|
|
END IF
|
||
|
|
end do
|
||
|
|
IF (RLENTH(1) .GT. RLENTH(2))THEN
|
||
|
|
ITEMP = IFRST(1)
|
||
|
|
IFRST(1) = IFRST(2)
|
||
|
|
IFRST(2) = ITEMP
|
||
|
|
END IF
|
||
|
|
C
|
||
|
|
ELSE
|
||
|
|
DO I = 2, INVLEN
|
||
|
|
IF (RLENTH(I) .LT. RLENTH(IFRST(1))) IFRST(1) = I
|
||
|
|
end do
|
||
|
|
IFRST(2) = 1
|
||
|
|
IF (IFRST(1) .EQ. 1) IFRST(2) = 2
|
||
|
|
DO I = IFRST(2), INVLEN
|
||
|
|
IF (I .EQ. IFRST(1))GO TO 50
|
||
|
|
IF (RLENTH(I) .LT. RLENTH(IFRST(2)))IFRST(2) = I
|
||
|
|
50 CONTINUE
|
||
|
|
end do
|
||
|
|
IFRST(3) = 1
|
||
|
|
IF (IFRST(1) .EQ. 1 .OR. IFRST(2) .EQ. 1) IFRST(3)=2
|
||
|
|
IF (IFRST(1) .EQ. IFRST(3) .OR. IFRST(2) .EQ. IFRST(3))
|
||
|
|
& IFRST(3)=3
|
||
|
|
DO I = IFRST(3), INVLEN
|
||
|
|
IF (I .EQ. IFRST(1))GO TO 60
|
||
|
|
IF (I .EQ. IFRST(2))GO TO 60
|
||
|
|
IF (RLENTH(I) .LT. RLENTH(IFRST(3))) IFRST(3) = I
|
||
|
|
60 CONTINUE
|
||
|
|
end do
|
||
|
|
END IF
|
||
|
|
C
|
||
|
|
C use three closest element centroids to define a plane
|
||
|
|
C establish coordinate system on this plane centered on
|
||
|
|
C interpolation point
|
||
|
|
C
|
||
|
|
A11 = CNTRA(INVCN(IFRST(2),NXGLND),1) -
|
||
|
|
& CNTRA(INVCN(IFRST(1),NXGLND),1)
|
||
|
|
A12 = CNTRA(INVCN(IFRST(2),NXGLND),2) -
|
||
|
|
& CNTRA(INVCN(IFRST(1),NXGLND),2)
|
||
|
|
A13 = CNTRA(INVCN(IFRST(2),NXGLND),3) -
|
||
|
|
& CNTRA(INVCN(IFRST(1),NXGLND),3)
|
||
|
|
RLN = SQRT(A11*A11 + A12*A12 + A13*A13)
|
||
|
|
A11 = A11/RLN
|
||
|
|
A12 = A12/RLN
|
||
|
|
A13 = A13/RLN
|
||
|
|
C
|
||
|
|
A31 = (CNTRA(INVCN(IFRST(2),NXGLND),2) -
|
||
|
|
& CNTRA(INVCN(IFRST(1),NXGLND),2))
|
||
|
|
& * (CNTRA(INVCN(IFRST(3),NXGLND),3) -
|
||
|
|
& CNTRA(INVCN(IFRST(1),NXGLND),3))
|
||
|
|
& - (CNTRA(INVCN(IFRST(2),NXGLND),3) -
|
||
|
|
& CNTRA(INVCN(IFRST(1),NXGLND),3))
|
||
|
|
& * (CNTRA(INVCN(IFRST(3),NXGLND),2) -
|
||
|
|
& CNTRA(INVCN(IFRST(1),NXGLND),2))
|
||
|
|
A32 = (CNTRA(INVCN(IFRST(2),NXGLND),3) -
|
||
|
|
& CNTRA(INVCN(IFRST(1),NXGLND),3))
|
||
|
|
& * (CNTRA(INVCN(IFRST(3),NXGLND),1) -
|
||
|
|
& CNTRA(INVCN(IFRST(1),NXGLND),1))
|
||
|
|
& - (CNTRA(INVCN(IFRST(2),NXGLND),1) -
|
||
|
|
& CNTRA(INVCN(IFRST(1),NXGLND),1))
|
||
|
|
& * (CNTRA(INVCN(IFRST(3),NXGLND),3) -
|
||
|
|
& CNTRA(INVCN(IFRST(1),NXGLND),3))
|
||
|
|
A33 = (CNTRA(INVCN(IFRST(2),NXGLND),1) -
|
||
|
|
& CNTRA(INVCN(IFRST(1),NXGLND),1))
|
||
|
|
& * (CNTRA(INVCN(IFRST(3),NXGLND),2) -
|
||
|
|
& CNTRA(INVCN(IFRST(1),NXGLND),2))
|
||
|
|
& - (CNTRA(INVCN(IFRST(2),NXGLND),2) -
|
||
|
|
& CNTRA(INVCN(IFRST(1),NXGLND),2))
|
||
|
|
& * (CNTRA(INVCN(IFRST(3),NXGLND),1) -
|
||
|
|
& CNTRA(INVCN(IFRST(1),NXGLND),1))
|
||
|
|
RLN = SQRT(A31*A31 + A32*A32 + A33*A33)
|
||
|
|
A31 = A31/RLN
|
||
|
|
A32 = A32/RLN
|
||
|
|
A33 = A33/RLN
|
||
|
|
C
|
||
|
|
A21 = A32*A13 - A33*A12
|
||
|
|
A22 = A11*A33 - A31*A13
|
||
|
|
A23 = A31*A12 - A11*A32
|
||
|
|
C
|
||
|
|
DO I = 1, INVLEN
|
||
|
|
XLC(I) = A11 * (CNTRA(INVCN(I,NXGLND),1) - XA(IGLND))
|
||
|
|
& + A12 * (CNTRA(INVCN(I,NXGLND),2) - YA(IGLND))
|
||
|
|
& + A13 * (CNTRA(INVCN(I,NXGLND),3) - ZA(IGLND))
|
||
|
|
YLC(I) = A21 * (CNTRA(INVCN(I,NXGLND),1) - XA(IGLND))
|
||
|
|
& + A22 * (CNTRA(INVCN(I,NXGLND),2) - YA(IGLND))
|
||
|
|
& + A23 * (CNTRA(INVCN(I,NXGLND),3) - ZA(IGLND))
|
||
|
|
end do
|
||
|
|
C
|
||
|
|
C
|
||
|
|
C Set up matrix for linear fit
|
||
|
|
C
|
||
|
|
S(1,1) = INVLEN
|
||
|
|
DO I = 1, INVLEN
|
||
|
|
S(1,2) = S(1,2) + DBLE(XLC(I))
|
||
|
|
S(1,3) = S(1,3) + DBLE(YLC(I))
|
||
|
|
S(2,2) = S(2,2) + DBLE(XLC(I) * XLC(I))
|
||
|
|
S(2,3) = S(2,3) + DBLE(YLC(I) * XLC(I))
|
||
|
|
S(3,3) = S(3,3) + DBLE(YLC(I) * YLC(I))
|
||
|
|
end do
|
||
|
|
S(2,1) = S(1,2)
|
||
|
|
S(3,1) = S(1,3)
|
||
|
|
S(3,2) = S(2,3)
|
||
|
|
C
|
||
|
|
C Forward Gauss elimination (Kincaid pg. 220) (double precision)
|
||
|
|
C
|
||
|
|
CALL FRGE(3,S,L,G)
|
||
|
|
C
|
||
|
|
C Set up load vectors - number of element variables
|
||
|
|
C
|
||
|
|
DO IVAR = 1, NVAREL
|
||
|
|
IF (ITT(IVAR,iblk) .EQ. 0)GO TO 90
|
||
|
|
F(1) = 0.D+00
|
||
|
|
F(2) = 0.D+00
|
||
|
|
F(3) = 0.D+00
|
||
|
|
DO I = 1, INVLEN
|
||
|
|
F(1) = F(1) + DBLE(SOLEA(INVCN(I,NXGLND),IVAR))
|
||
|
|
F(2) = F(2) + DBLE(SOLEA(INVCN(I,NXGLND),IVAR) * XLC(I))
|
||
|
|
F(3) = F(3) + DBLE(SOLEA(INVCN(I,NXGLND),IVAR) * YLC(I))
|
||
|
|
end do
|
||
|
|
C
|
||
|
|
C Back substitution (Kincaid pg. 223) (double precision)
|
||
|
|
C
|
||
|
|
CALL BS(3,S,F,L,X)
|
||
|
|
C
|
||
|
|
C Fill in nodal element value array (SOLENA)
|
||
|
|
C Note: X and Y distances in S and F are centered on node being
|
||
|
|
C interpolated, thus X and Y are zero in the eq.
|
||
|
|
C Value = X(1) + X(2) * X + X(3) * Y
|
||
|
|
C
|
||
|
|
SOLENA(IGLND,IVAR) = SNGL(X(1))
|
||
|
|
90 CONTINUE
|
||
|
|
end do
|
||
|
|
RETURN
|
||
|
|
END
|