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Cloned SEACAS for EXODUS library with extra build files for internal package management.
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EXODUS/packages/seacas/libraries/mapvarlib/flgrad.f

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C Copyright(C) 1999-2021 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=======================================================================
*DECK, FLGRAD
SUBROUTINE FLGRAD(IEL,ICOUNT,IELLST,CNTRA,SHLNRM,SOLEA,SOLGRA,
& ITT,iblk)
C *********************************************************************
C Subroutine FLGRAD performs the actual computation of the gradient
C coefficients using the stuff that was set up in ELGRAD.
C Start by translating into isoparametric coords (very helpful for
C shells and makes some sense for continuum and is very useful for
C subsequent interpolation.
C Then do constrained least squares to f=a0+a1eta+a2ksi+a3phi to
C compute a1, a2, and a3 and stuff results into SOLGRA
C Calls subroutines ERROR
C Called by ELGRAD
C *********************************************************************
C IEL the current element being worked
C ICOUNT the number of elements that share a node with IEL
C IELLST local list of elements that share a node with element
C currently being processed
C CNTRA a list of element centroid coordinates for all elements
C in the current element block (1:ndima,1:numeba)
C SHLNRM normal vector for shell element (1:3)
C SOLEA element variables (1:numeba,1:nvarel)
C SOLGRA element variable gradient (1:ndima,1:numeba,1:nvarel)
C ITT truth table
C iblk element block being processed (not ID)
C IRED reduction in dimensionality of data
C IRED=0 full, IRED=1 colinear, IRED=2 coplanar
C *********************************************************************
include 'aexds1.blk'
include 'amesh.blk'
include 'ebbyeb.blk'
DIMENSION CNTRA(NUMEBA,*), SHLNRM(3), SOLEA(NUMEBA,*)
DIMENSION SOLGRA(NDIMA,NUMEBA,*), IELLST(100), ITT(NVAREL,*)
DOUBLE PRECISION S(3,3), G(3), F(3), X(3)
INTEGER L(3)
C *********************************************************************
IF (ITYPE .EQ. 4 .OR. ITYPE .EQ. 5)THEN
CALL ERROR('FLGRAD','ELEMENT TYPE',' ',ITYPE,
& 'ELEMENT VARIABLE PROCESSING NOT YET IMPLEMENTED',
& 0,' ',' ',1)
END IF
IRED = 0
DO I = 1,3
DO J = 1,3
S(I,J) = 0.0D0
end do
end do
C *********************************************************************
IF (ITYPE .EQ. 13)THEN
C Shell element processing (quasi 2-D)
C If no elements connected, there can be no gradient
IF (ICOUNT .EQ. 0)THEN
DO 110 IVAR = 1, NVAREL
IF (ITT(IVAR,iblk) .EQ. 0)GO TO 110
SOLGRA(1,IEL,IVAR) = 0.
SOLGRA(2,IEL,IVAR) = 0.
SOLGRA(3,IEL,IVAR) = 0.
110 CONTINUE
GO TO 500
C If only one element connected, data is colinear
C If two elements connected, data may be colinear
ELSE IF (ICOUNT .EQ. 1)THEN
IRED = 1
ELSE IF (ICOUNT .EQ. 2)THEN
C Check for colinearity. Create unit vector to 1st connected element
C centroid. Create unit vector to 2nd connected element centroid. Dot
C 1st unit vector with 2nd unit vector. If dot product is greater than
C 0.9, then data is colinear (IRED = 1)
V11 = CNTRA(IELLST(1),1) - CNTRA(IEL,1)
V12 = CNTRA(IELLST(1),2) - CNTRA(IEL,2)
V13 = CNTRA(IELLST(1),3) - CNTRA(IEL,3)
V1MAG = SQRT(V11*V11 + V12*V12 + V13*V13)
V11 = V11 / V1MAG
V12 = V12 / V1MAG
V13 = V13 / V1MAG
V21 = CNTRA(IELLST(2),1) - CNTRA(IEL,1)
V22 = CNTRA(IELLST(2),2) - CNTRA(IEL,2)
V23 = CNTRA(IELLST(2),3) - CNTRA(IEL,3)
V2MAG = SQRT(V21*V21 + V22*V22 + V23*V23)
V21 = V21 / V2MAG
V22 = V22 / V2MAG
V23 = V23 / V2MAG
VDOT = ABS(V11*V21 + V12*V22 + V13*V23)
IF (VDOT .GT. 0.9)THEN
IRED = 1
END IF
END IF
IF (IRED .EQ. 1)THEN
C Colinear data
C rotate into vector
C NOTE: for colinearity, the XD coord is also the magnitude
V11 = CNTRA(IELLST(1),1) - CNTRA(IEL,1)
V12 = CNTRA(IELLST(1),2) - CNTRA(IEL,2)
V13 = CNTRA(IELLST(1),3) - CNTRA(IEL,3)
V1MAG = SQRT(V11*V11 + V12*V12 + V13*V13)
V11 = V11 / V1MAG
V12 = V12 / V1MAG
V13 = V13 / V1MAG
S1 = 0.
DO 120 I = 1, ICOUNT
XORI = CNTRA(IELLST(I),1) - CNTRA(IEL,1)
YORI = CNTRA(IELLST(I),2) - CNTRA(IEL,2)
ZORI = CNTRA(IELLST(I),3) - CNTRA(IEL,3)
XD = XORI*V11 + YORI*V12 +ZORI*V13
S1 = S1 + (XD*XD)
120 CONTINUE
DO 130 IVAR = 1, NVAREL
IF (ITT(IVAR,iblk) .EQ. 0)GO TO 130
F1 = 0.
DO 140 I = 1, ICOUNT
XORI = CNTRA(IELLST(I),1) - CNTRA(IEL,1)
YORI = CNTRA(IELLST(I),2) - CNTRA(IEL,2)
ZORI = CNTRA(IELLST(I),3) - CNTRA(IEL,3)
XD = XORI*V11 + YORI*V12 +ZORI*V13
F1 = SOLEA(IEL,IVAR) * XD
140 CONTINUE
X1D = F1 / S1
SOLGRA(1,IEL,IVAR) = X1D * V11
SOLGRA(2,IEL,IVAR) = X1D * V12
SOLGRA(3,IEL,IVAR) = X1D * V13
130 CONTINUE
ELSE
C Rotate into plane of element and treat as if 2-D
C first unit vector
V11 = CNTRA(IELLST(1),1) - CNTRA(IEL,1)
V12 = CNTRA(IELLST(1),2) - CNTRA(IEL,2)
V13 = CNTRA(IELLST(1),3) - CNTRA(IEL,3)
VMAG = SQRT(V11*V11 + V12*V12 + V13*V13)
V11 = V11 / VMAG
V12 = V12 / VMAG
V13 = V13 / VMAG
C compute 2nd (orthogonal) vector in plane - make it a unit vector
V21 = V12 * SHLNRM(3) - SHLNRM(2) * V13
V22 = SHLNRM(1) * V13 - V11 * SHLNRM(3)
V23 = V11 * SHLNRM(2) - SHLNRM(1) * V12
VMAG2 = SQRT(V21*V21 + V22*V22 + V23*V23)
V21 = V21 / VMAG2
V22 = V22 / VMAG2
V23 = V23 / VMAG2
C Fill up matrix for constrained linear least squares
DO 150 I = 1, ICOUNT
C rotate coords
XORI = CNTRA(IELLST(I),1) - CNTRA(IEL,1)
YORI = CNTRA(IELLST(I),2) - CNTRA(IEL,2)
ZORI = CNTRA(IELLST(I),3) - CNTRA(IEL,3)
XD = XORI*V11 + YORI*V12 + ZORI*V13
YD = XORI*V21 + YORI*V22 + ZORI*V23
S(1,1) = S(1,1) + DBLE(XD * XD)
S(1,2) = S(1,2) + DBLE(XD * YD)
S(2,2) = S(2,2) + DBLE(YD * YD)
150 CONTINUE
S(2,1) = S(1,2)
S(1,3) = 0.D+00
S(2,3) = 0.D+00
S(3,3) = 1.D+00
S(3,2) = 0.D+00
S(3,1) = 0.D+00
C Forward Gauss
CALL FRGE(3,S,L,G)
C Set up load vectors
DO 160 IVAR = 1, NVAREL
IF (ITT(IVAR,iblk) .EQ. 0)GO TO 160
F(1) = 0.D+00
F(2) = 0.D+00
F(3) = 0.D+00
DO 170 I = 1, ICOUNT
XORI = CNTRA(IELLST(I),1) - CNTRA(IEL,1)
YORI = CNTRA(IELLST(I),2) - CNTRA(IEL,2)
ZORI = CNTRA(IELLST(I),3) - CNTRA(IEL,3)
XD = XORI*V11 + YORI*V12 + ZORI*V13
YD = XORI*V21 + YORI*V22 + ZORI*V23
F(1) = F(1) + DBLE(XD * (SOLEA(IELLST(I),IVAR)
& - SOLEA(IEL,IVAR)))
F(2) = F(2) + DBLE(YD * (SOLEA(IELLST(I),IVAR)
& - SOLEA(IEL,IVAR)))
170 CONTINUE
C Back substitution and load gradient coefficients into SOLGRA
CALL BS(3,S,F,L,X)
C Rotate back and fill up gradient array
SOLGRA(1,IEL,IVAR) = SNGL(X(2))*V11 + SNGL(X(3))*V21
SOLGRA(2,IEL,IVAR) = SNGL(X(2))*V12 + SNGL(X(3))*V22
SOLGRA(3,IEL,IVAR) = SNGL(X(2))*V13 + SNGL(X(3))*V23
160 CONTINUE
END IF
C *********************************************************************
ELSE IF (ITYPE .EQ. 3)THEN
C Quad element processing (2-D)
C If no elements connected, there can be no gradient
IF (ICOUNT .EQ. 0)THEN
DO 210 IVAR = 1, NVAREL
IF (ITT(IVAR,iblk) .EQ. 0)GO TO 210
SOLGRA(1,IEL,IVAR) = 0.
SOLGRA(2,IEL,IVAR) = 0.
210 CONTINUE
GO TO 500
C If only one element connected, data is colinear
C If two elements connected, data may be colinear
ELSE IF (ICOUNT .EQ. 1)THEN
IRED = 1
ELSE IF (ICOUNT .EQ. 2)THEN
C Check for colinearity. Create unit vector to 1st connected element
C centroid. Create unit vector to 2nd connected element centroid. Dot 1st
C unit vector with 2nd unit vector. If mag of dot product is greater than
C 0.9, then data is colinear (IRED = 1)
V11 = CNTRA(IELLST(1),1) - CNTRA(IEL,1)
V12 = CNTRA(IELLST(1),2) - CNTRA(IEL,2)
V1MAG = SQRT(V11*V11 + V12*V12)
V11 = V11 / V1MAG
V12 = V12 / V1MAG
V21 = CNTRA(IELLST(2),1) - CNTRA(IEL,1)
V22 = CNTRA(IELLST(2),2) - CNTRA(IEL,2)
V2MAG = SQRT(V21*V21 + V22*V22)
V21 = V21 / V2MAG
V22 = V22 / V2MAG
VDOT = ABS(V11*V21 + V12*V22)
IF (VDOT .GT. 0.9)THEN
IRED = 1
END IF
END IF
IF(IRED .EQ. 1)THEN
C Colinear data
C Note: constraint at X=0 implies a0 so only 1 equation
C remains to solve for a1
C rotate into vector
C NOTE: for colinearity, the XD coord is also the magnitude
V11 = CNTRA(IELLST(1),1) - CNTRA(IEL,1)
V12 = CNTRA(IELLST(1),2) - CNTRA(IEL,2)
VMAG = SQRT(V11*V11 + V12*V12)
V11 = V11 / VMAG
V12 = V12 / VMAG
S1 = 0.
DO 220 I = 1, ICOUNT
XORI = CNTRA(IELLST(I),1) - CNTRA(IEL,1)
YORI = CNTRA(IELLST(I),2) - CNTRA(IEL,2)
XD = XORI*V11 + YORI*V12
S1 = S1 + (XD*XD)
220 CONTINUE
DO 230 IVAR = 1, NVAREL
IF (ITT(IVAR,iblk) .EQ. 0)GO TO 230
F1 = 0.
DO 240 I = 1, ICOUNT
XORI = CNTRA(IELLST(I),1) - CNTRA(IEL,1)
YORI = CNTRA(IELLST(I),2) - CNTRA(IEL,2)
XD = XORI*V11 + YORI*V12
F1 = SOLEA(IEL,IVAR) * XD
240 CONTINUE
X1D = F1 / S1
SOLGRA(1,IEL,IVAR) = X1D * V11
SOLGRA(2,IEL,IVAR) = X1D * V12
230 CONTINUE
ELSE IF(IRED .EQ. 0)THEN
C Full 2-D data
C Fill up matrix for constrained linear least squares
DO 250 I = 1, ICOUNT
XD = (CNTRA(IELLST(I),1) - CNTRA(IEL,1))
YD = (CNTRA(IELLST(I),2) - CNTRA(IEL,2))
S(1,1) = S(1,1) + DBLE(XD * XD)
S(1,2) = S(1,2) + DBLE(XD * YD)
S(2,2) = S(2,2) + DBLE(YD * YD)
250 CONTINUE
S(2,1) = S(1,2)
S(1,3) = 0.D+00
S(2,3) = 0.D+00
S(3,3) = 1.D+00
S(3,2) = 0.D+00
S(3,1) = 0.D+00
C Forward Gauss
CALL FRGE(3,S,L,G)
C Set up load vectors
DO 260 IVAR = 1, NVAREL
IF (ITT(IVAR,iblk) .EQ. 0)GO TO 260
F(1) = 0.D+00
F(2) = 0.D+00
F(3) = 0.D+00
DO 270 I = 1, ICOUNT
XD = (CNTRA(IELLST(I),1) - CNTRA(IEL,1))
YD = (CNTRA(IELLST(I),2) - CNTRA(IEL,2))
F(1) = F(1) + DBLE(XD * (SOLEA(IELLST(I),IVAR)
& - SOLEA(IEL,IVAR)))
F(2) = F(2) + DBLE(YD * (SOLEA(IELLST(I),IVAR)
& - SOLEA(IEL,IVAR)))
270 CONTINUE
C Back substitution and load gradient coefficients into SOLGRA
CALL BS(3,S,F,L,X)
C Fill up gradient array
SOLGRA(1,IEL,IVAR) = SNGL(X(1))
SOLGRA(2,IEL,IVAR) = SNGL(X(2))
260 CONTINUE
END IF
C *********************************************************************
ELSE IF (ITYPE .EQ. 10 .OR. ITYPE .EQ. 6)THEN
C Hex element processing (3-D)
C If no elements connected, there can be no gradient
IF (ICOUNT .EQ. 0)THEN
DO 310 IVAR = 1, NVAREL
IF (ITT(IVAR,iblk) .EQ. 0)GO TO 310
SOLGRA(1,IEL,IVAR) = 0.
SOLGRA(2,IEL,IVAR) = 0.
SOLGRA(3,IEL,IVAR) = 0.
310 CONTINUE
GO TO 500
C If only one element connected, data is colinear
C If two elements connected, data may be colinear
ELSE IF (ICOUNT .EQ. 1)THEN
IRED = 1
ELSE IF (ICOUNT .EQ. 2)THEN
C Check for colinearity. Create unit vector to 1st connected element
C centroid. Create unit vector to 2nd connected element centroid. Dot 1st
C unit vector with 2nd unit vector. If mag of dot product is greater than
C 0.9, then data is colinear (IRED = 1)
V11 = CNTRA(IELLST(1),1) - CNTRA(IEL,1)
V12 = CNTRA(IELLST(1),2) - CNTRA(IEL,2)
V13 = CNTRA(IELLST(1),3) - CNTRA(IEL,3)
V1MAG = SQRT(V11*V11 + V12*V12 + V13*V13)
V11 = V11 / V1MAG
V12 = V12 / V1MAG
V13 = V13 / V1MAG
V21 = CNTRA(IELLST(2),1) - CNTRA(IEL,1)
V22 = CNTRA(IELLST(2),2) - CNTRA(IEL,2)
V23 = CNTRA(IELLST(2),3) - CNTRA(IEL,3)
V2MAG = SQRT(V21*V21 + V22*V22 + V23*V23)
V21 = V21 / V2MAG
V22 = V22 / V2MAG
V23 = V23 / V2MAG
VDOT = ABS(V11*V21 + V12*V22 + V13*V23)
IF (VDOT .GT. 0.9)THEN
IRED = 1
ELSE
IRED = 2
C X-product vector-1 with vector-2 to get normal to plane defined
C by the two vectors; then make it a unit vector
VN1 = V12*V23 - V22*V13
VN2 = V13*V21 - V11*V23
VN3 = V11*V22 - V21*V12
VNMAG = SQRT(VN1*VN1 + VN2*VN2 + VN3*VN3)
END IF
ELSE IF (ICOUNT .GT. 2 .AND. ICOUNT .LT. 11)THEN
C Check for coplanarity
C vector to 1st connected element
V11 = CNTRA(IELLST(1),1) - CNTRA(IEL,1)
V12 = CNTRA(IELLST(1),2) - CNTRA(IEL,2)
V13 = CNTRA(IELLST(1),3) - CNTRA(IEL,3)
C Construct a vector to second connected element
ICK = 2
311 CONTINUE
V21 = CNTRA(IELLST(ICK),1) - CNTRA(IEL,1)
V22 = CNTRA(IELLST(ICK),2) - CNTRA(IEL,2)
V23 = CNTRA(IELLST(ICK),3) - CNTRA(IEL,3)
C X-product vector-1 with vector-2 to get normal to plane defined
C by the two vectors; then make it a unit vector
VN1 = V12*V23 - V22*V13
VN2 = V13*V21 - V11*V23
VN3 = V11*V22 - V21*V12
VNMAG = SQRT(VN1*VN1 + VN2*VN2 + VN3*VN3)
C check for colinearity of elements
C if colinear, get new element and try again
IF (VNMAG .LT. 1.E-13)THEN
ICK = 3
GO TO 311
END IF
VN1 = VN1 / VNMAG
VN2 = VN2 / VNMAG
VN3 = VN3 / VNMAG
C Dot product of normal vector with unit vectors
C to the remaining element centroids. If dot product
C is too small, set IRED=2 and try the next vector.
C If dot product is more than 0.1, data is not coplanar
C set IRED = 0 and get on with it.
DO 320 I = 3, ICOUNT
V1 = CNTRA(IELLST(I),1) - CNTRA(IEL,1)
V2 = CNTRA(IELLST(I),2) - CNTRA(IEL,2)
V3 = CNTRA(IELLST(I),3) - CNTRA(IEL,3)
VIMAG = SQRT(V1*V1 + V2*V2 + V3*V3)
V1 = V1 / VIMAG
V2 = V2 / VIMAG
V3 = V3 / VIMAG
VDOT = ABS(VN1*V1 + VN2*V2 + VN3*V3)
IF (VDOT .LT. 0.1)THEN
IRED = 2
ELSE
IRED = 0
GO TO 330
END IF
320 CONTINUE
330 CONTINUE
END IF
IF (IRED .EQ. 1)THEN
C Colinear data
C rotate into vector
C NOTE: for colinearity, the XD coord is also the magnitude
V11 = CNTRA(IELLST(1),1) - CNTRA(IEL,1)
V12 = CNTRA(IELLST(1),2) - CNTRA(IEL,2)
V13 = CNTRA(IELLST(1),3) - CNTRA(IEL,3)
V1MAG = SQRT(V11*V11 + V12*V12 + V13*V13)
V11 = V11 / V1MAG
V12 = V12 / V1MAG
V13 = V13 / V1MAG
S1 = 0.
DO 340 I = 1, ICOUNT
XORI = CNTRA(IELLST(I),1) - CNTRA(IEL,1)
YORI = CNTRA(IELLST(I),2) - CNTRA(IEL,2)
ZORI = CNTRA(IELLST(I),3) - CNTRA(IEL,3)
XD = XORI*V11 + YORI*V12 +ZORI*V13
S1 = S1 + (XD*XD)
340 CONTINUE
DO 350 IVAR = 1, NVAREL
IF (ITT(IVAR,iblk) .EQ. 0)GO TO 350
F1 = 0.
DO 360 I = 1, ICOUNT
XORI = CNTRA(IELLST(I),1) - CNTRA(IEL,1)
YORI = CNTRA(IELLST(I),2) - CNTRA(IEL,2)
ZORI = CNTRA(IELLST(I),3) - CNTRA(IEL,3)
XD = XORI*V11 + YORI*V12 +ZORI*V13
F1 = SOLEA(IEL,IVAR) * XD
360 CONTINUE
X1D = F1 / S1
SOLGRA(1,IEL,IVAR) = X1D * V11
SOLGRA(2,IEL,IVAR) = X1D * V12
SOLGRA(3,IEL,IVAR) = X1D * V13
350 CONTINUE
ELSE IF (IRED .EQ. 2)THEN
C Coplanar data
C first unit vector
V11 = CNTRA(IELLST(1),1) - CNTRA(IEL,1)
V12 = CNTRA(IELLST(1),2) - CNTRA(IEL,2)
V13 = CNTRA(IELLST(1),3) - CNTRA(IEL,3)
V1MAG = SQRT(V11*V11 + V12*V12 + V13*V13)
V11 = V11 / V1MAG
V12 = V12 / V1MAG
V13 = V13 / V1MAG
C compute 2nd (orthogonal) vector in plane - make it a unit vector
V21 = V12 * VN3 - VN2 * V13
V22 = VN1 * V13 - V11 * VN3
V23 = V11 * VN2 - VN1 * V12
V2MAG = SQRT(V21*V21 + V22*V22 + V23*V23)
V21 = V21 / V2MAG
V22 = V22 / V2MAG
V23 = V23 / V2MAG
C Fill up matrix for constrained linear least squares
DO 370 I = 1, ICOUNT
C rotate coords
XORI = CNTRA(IELLST(I),1) - CNTRA(IEL,1)
YORI = CNTRA(IELLST(I),2) - CNTRA(IEL,2)
ZORI = CNTRA(IELLST(I),3) - CNTRA(IEL,3)
XD = XORI*V11 + YORI*V12 + ZORI*V13
YD = XORI*V21 + YORI*V22 + ZORI*V23
S(1,1) = S(1,1) + DBLE(XD * XD)
S(1,2) = S(1,2) + DBLE(XD * YD)
S(2,2) = S(2,2) + DBLE(YD * YD)
370 CONTINUE
S(2,1) = S(1,2)
S(1,3) = 0.D+00
S(2,3) = 0.D+00
S(3,3) = 1.D+00
S(3,2) = 0.D+00
S(3,1) = 0.D+00
C Forward Gauss
CALL FRGE(3,S,L,G)
C Set up load vectors
DO 380 IVAR = 1, NVAREL
IF (ITT(IVAR,iblk) .EQ. 0)GO TO 380
F(1) = 0.D+00
F(2) = 0.D+00
F(3) = 0.D+00
DO 390 I = 1, ICOUNT
XORI = CNTRA(IELLST(I),1) - CNTRA(IEL,1)
YORI = CNTRA(IELLST(I),2) - CNTRA(IEL,2)
ZORI = CNTRA(IELLST(I),3) - CNTRA(IEL,3)
XD = XORI*V11 + YORI*V12 + ZORI*V13
YD = XORI*V21 + YORI*V22 + ZORI*V23
F(1) = F(1) + DBLE(XD * (SOLEA(IELLST(I),IVAR)
& - SOLEA(IEL,IVAR)))
F(2) = F(2) + DBLE(YD * (SOLEA(IELLST(I),IVAR)
& - SOLEA(IEL,IVAR)))
390 CONTINUE
C Back substitution and load gradient coefficients into SOLGRA
CALL BS(3,S,F,L,X)
C Rotate back and fill up gradient array
SOLGRA(1,IEL,IVAR) = SNGL(X(1))*V11 + SNGL(X(2))*V21
SOLGRA(2,IEL,IVAR) = SNGL(X(1))*V12 + SNGL(X(2))*V22
SOLGRA(3,IEL,IVAR) = SNGL(X(1))*V13 + SNGL(X(2))*V23
380 CONTINUE
ELSE
C Fully 3-D data (IRED=0)
C Zero the matrix
C Note: constraint at X=Y=Z=0 implies a0 so only 3 equations
C remain to solve for a1, a2, and a3
DO I = 1, 3
DO J = 1, 3
S(I,J) = 0.D+00
end do
end do
C Fill up matrix for constrained linear least squares
DO 410 I = 1, ICOUNT
XD = CNTRA(IELLST(I),1) - CNTRA(IEL,1)
YD = CNTRA(IELLST(I),2) - CNTRA(IEL,2)
ZD = CNTRA(IELLST(I),3) - CNTRA(IEL,3)
S(1,1) = S(1,1) + DBLE(XD * XD)
S(1,2) = S(1,2) + DBLE(XD * YD)
S(1,3) = S(1,3) + DBLE(XD * ZD)
S(2,2) = S(2,2) + DBLE(YD * YD)
S(2,3) = S(2,3) + DBLE(YD * ZD)
S(3,3) = S(3,3) + DBLE(ZD * ZD)
410 CONTINUE
S(2,1) = S(1,2)
S(3,1) = S(1,3)
S(3,2) = S(2,3)
C Forward Gauss
CALL FRGE(3,S,L,G)
C Set up load vectors
DO 420 IVAR = 1, NVAREL
IF (ITT(IVAR,iblk) .EQ. 0)GO TO 420
F(1) = 0.D+00
F(2) = 0.D+00
F(3) = 0.D+00
DO 430 I = 1, ICOUNT
XD = CNTRA(IELLST(I),1) - CNTRA(IEL,1)
YD = CNTRA(IELLST(I),2) - CNTRA(IEL,2)
ZD = CNTRA(IELLST(I),3) - CNTRA(IEL,3)
F(1) = F(1) + DBLE(XD * (SOLEA(IELLST(I),IVAR)
& - SOLEA(IEL,IVAR)))
F(2) = F(2) + DBLE(YD * (SOLEA(IELLST(I),IVAR)
& - SOLEA(IEL,IVAR)))
F(3) = F(3) + DBLE(ZD * (SOLEA(IELLST(I),IVAR)
& - SOLEA(IEL,IVAR)))
430 CONTINUE
C Back substitution and load gradient coefficients into SOLGRA
CALL BS(3,S,F,L,X)
C Fill up gradient array
SOLGRA(1,IEL,IVAR) = SNGL(X(1))
SOLGRA(2,IEL,IVAR) = SNGL(X(2))
SOLGRA(3,IEL,IVAR) = SNGL(X(3))
420 CONTINUE
END IF
ELSE
CALL ERROR ('MAPVAR','INCORRECT ELEMENT TYPE',
& 'ELEMENT TYPE =',ITYPE,
& 'NOT YET IMPLEMENTED',0,' ',' ',1)
END IF
500 CONTINUE
RETURN
END