1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
|
*DECK PNDM2E
SUBROUTINE PNDM2E(ITY,NEL,L4,IELEM,ICOL,MAT,VOL,NBMIX,NLF,NVD,
1 NAN,SIGT,SIGTI,XX,YY,KN,QFR,MU,IIMAX,LC,R,V,SYS)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Assembly of system matrices for a mixed-dual formulation of the
* simplified PN method in 2D Cartesian geometry.
*
*Copyright:
* Copyright (C) 2004 Ecole Polytechnique de Montreal
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version
*
*Author(s): A. Hebert
*
*Parameters: input
* ITY type of assembly:
* =0: leakage-removal matrix assembly; =1: cross section matrix
* assembly.
* NEL number of finite elements.
* L4 number of unknowns per energy group and per set of two
* Legendre orders.
* IELEM degree of the Lagrangian finite elements: =1 (linear);
* =2 (parabolic); =3 (cubic); =4 (quartic).
* ICOL type of quadrature: =1 (analytical integration);
* =2 (Gauss-Lobatto); =3 (Gauss-Legendre).
* MAT mixture index assigned to each element.
* VOL volume of each element.
* NBMIX number of mixtures.
* NLF number of Legendre orders for the flux (even number).
* NVD type of void boundary condition if NLF>0 and ICOL=3.
* NAN number of Legendre orders for the cross sections.
* SIGT total minus self-scattering macroscopic cross sections.
* SIGT(:,NAN) generally contains the total cross section only.
* SIGTI inverse macroscopic cross sections ordered by mixture.
* SIGTI(:,NAN) generally contains the inverse total cross
* section only.
* XX X-directed mesh spacings.
* YY Y-directed mesh spacings.
* KN element-ordered unknown list.
* QFR element-ordered boundary conditions.
* MU compressed storage mode indices.
* IIMAX dimension of vector SYS.
* LC order of the unit matrices.
* R unit Cartesian mass matrix.
* V unit nodal coupling matrix.
*
*Parameters: output
* SYS system matrix.
*
*Reference:
* J.J. Lautard, D. Schneider, A.M. Baudron, "Mixed Dual Methods for
* Neutronic Reactor Core Calculations in the CRONOS System,"
* Proc. Int. Conf. on Mathematics and Computation, Reactor
* Physics and Environmental Analysis in Nuclear Applications,
* Madrid, Spain, September 27-30, 1999.
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER ITY,NEL,L4,IELEM,ICOL,MAT(NEL),NBMIX,NLF,NAN,KN(5*NEL),
1 MU(L4),IIMAX,LC
REAL VOL(NEL),SIGT(NBMIX,NAN),SIGTI(NBMIX,NAN),XX(NEL),YY(NEL),
1 QFR(4*NEL),R(LC,LC),V(LC,LC-1),SYS(IIMAX)
*----
* LOCAL VARIABLES
*----
REAL QQ(5,5)
*
IF(ICOL.EQ.3) THEN
IF(NVD.EQ.0) THEN
NZMAR=NLF+1
ELSE IF(NVD.EQ.1) THEN
NZMAR=NLF
ELSE IF(NVD.EQ.2) THEN
NZMAR=65
ENDIF
ELSE
NZMAR=65
ENDIF
DO 12 I0=1,IELEM
DO 11 J0=1,IELEM
QQ(I0,J0)=0.0
DO 10 K0=2,IELEM
QQ(I0,J0)=QQ(I0,J0)+V(K0,I0)*V(K0,J0)/R(K0,K0)
10 CONTINUE
11 CONTINUE
12 CONTINUE
MUMAX=MU(L4)
DO 100 IL=0,NLF-1
ZMARS=0.0
IF(MOD(IL,2).EQ.1) ZMARS=PNMAR2(NZMAR,IL,IL)
FACT=REAL(2*IL+1)
*----
* ASSEMBLY OF THE MAIN COEFFICIENT MATRIX AT ORDER IL.
*----
NUM1=0
NUM2=0
KEY=0
DO 90 K=1,NEL
IBM=MAT(K)
IF(IBM.EQ.0) GO TO 90
VOL0=VOL(K)
GARS=SIGT(IBM,MIN(IL+1,NAN))
IF(MOD(IL,2).EQ.0) THEN
* EVEN PARITY EQUATION.
DO 25 I0=1,IELEM
DO 20 J0=1,IELEM
JND1=KN(NUM1+1)+(I0-1)*IELEM+J0-1
KEY=(IL/2)*MUMAX+MU(JND1)
SYS(KEY)=SYS(KEY)+FACT*VOL0*GARS
20 CONTINUE
25 CONTINUE
ELSE
GARSI=SIGTI(IBM,MIN(IL+1,NAN))
DO 80 I0=1,IELEM
* PARTIAL INVERSION OF THE ODD PARITY EQUATION. MODIFICATION OF
* THE EVEN PARITY EQUATION.
DO 45 J0=1,IELEM
JND1=KN(NUM1+1)+(I0-1)*IELEM+J0-1
DO 30 K0=1,J0
IF(QQ(J0,K0).EQ.0.0) GO TO 30
KND1=KN(NUM1+1)+(I0-1)*IELEM+K0-1
KEY=(IL/2)*MUMAX+MU(JND1)-JND1+KND1
SYS(KEY)=SYS(KEY)+(REAL(IL)**2)*VOL0*QQ(J0,K0)*GARSI/(FACT*
1 XX(K)*XX(K))
IF(IL.LE.NLF-3) THEN
KEY=((IL+2)/2)*MUMAX+MU(JND1)-JND1+KND1
SYS(KEY)=SYS(KEY)+(REAL(IL+1)**2)*VOL0*QQ(J0,K0)*GARSI/
1 (FACT*XX(K)*XX(K))
ENDIF
30 CONTINUE
JND1=KN(NUM1+1)+(J0-1)*IELEM+I0-1
DO 40 K0=1,J0
IF(QQ(J0,K0).EQ.0.0) GO TO 40
KND1=KN(NUM1+1)+(K0-1)*IELEM+I0-1
KEY=(IL/2)*MUMAX+MU(JND1)-JND1+KND1
SYS(KEY)=SYS(KEY)+(REAL(IL)**2)*VOL0*QQ(J0,K0)*GARSI/(FACT*
1 YY(K)*YY(K))
IF(IL.LE.NLF-3) THEN
KEY=((IL+2)/2)*MUMAX+MU(JND1)-JND1+KND1
SYS(KEY)=SYS(KEY)+(REAL(IL+1)**2)*VOL0*QQ(J0,K0)*GARSI/
1 (FACT*YY(K)*YY(K))
ENDIF
40 CONTINUE
45 CONTINUE
*
* ODD PARITY EQUATION.
DO 55 IC=1,2
IIC=1
IF(IC.EQ.2) IIC=IELEM+1
IND1=ABS(KN(NUM1+1+IC))+I0-1
S1=REAL(SIGN(1,KN(NUM1+1+IC)))
DO 50 JC=1,2
JJC=1
IF(JC.EQ.2) JJC=IELEM+1
IND2=ABS(KN(NUM1+1+JC))+I0-1
IF((KN(NUM1+1+IC).NE.0).AND.(KN(NUM1+1+JC).NE.0).AND.
1 (IND1.GE.IND2)) THEN
S2=REAL(SIGN(1,KN(NUM1+1+JC)))
KEY=(IL/2)*MUMAX+MU(IND1)-IND1+IND2
SYS(KEY)=SYS(KEY)-S1*S2*FACT*R(IIC,JJC)*VOL0*GARS
ENDIF
50 CONTINUE
55 CONTINUE
DO 65 IC=3,4
IIC=1
IF(IC.EQ.4) IIC=IELEM+1
IND1=ABS(KN(NUM1+1+IC))+I0-1
S1=REAL(SIGN(1,KN(NUM1+1+IC)))
DO 60 JC=3,4
JJC=1
IF(JC.EQ.4) JJC=IELEM+1
IND2=ABS(KN(NUM1+1+JC))+I0-1
IF((KN(NUM1+1+IC).NE.0).AND.(KN(NUM1+1+JC).NE.0).AND.
1 (IND1.GE.IND2)) THEN
S2=REAL(SIGN(1,KN(NUM1+1+JC)))
KEY=(IL/2)*MUMAX+MU(IND1)-IND1+IND2
SYS(KEY)=SYS(KEY)-S1*S2*FACT*R(IIC,JJC)*VOL0*GARS
ENDIF
60 CONTINUE
65 CONTINUE
IF(ITY.EQ.1) GO TO 80
*
IND1=ABS(KN(NUM1+2))+I0-1
IND2=ABS(KN(NUM1+3))+I0-1
IND3=ABS(KN(NUM1+4))+I0-1
IND4=ABS(KN(NUM1+5))+I0-1
IF((QFR(NUM2+1).NE.0.0).AND.(KN(NUM1+2).NE.0)) THEN
KEY=(IL/2)*MUMAX+MU(IND1)
SYS(KEY)=SYS(KEY)-0.5*FACT*QFR(NUM2+1)*ZMARS
ENDIF
IF((QFR(NUM2+2).NE.0.0).AND.(KN(NUM1+3).NE.0)) THEN
KEY=(IL/2)*MUMAX+MU(IND2)
SYS(KEY)=SYS(KEY)-0.5*FACT*QFR(NUM2+2)*ZMARS
ENDIF
IF((QFR(NUM2+3).NE.0.0).AND.(KN(NUM1+4).NE.0)) THEN
KEY=(IL/2)*MUMAX+MU(IND3)
SYS(KEY)=SYS(KEY)-0.5*FACT*QFR(NUM2+3)*ZMARS
ENDIF
IF((QFR(NUM2+4).NE.0.0).AND.(KN(NUM1+5).NE.0)) THEN
KEY=(IL/2)*MUMAX+MU(IND4)
SYS(KEY)=SYS(KEY)-0.5*FACT*QFR(NUM2+4)*ZMARS
ENDIF
*
DO 70 J0=1,IELEM
JND1=KN(NUM1+1)+(I0-1)*IELEM+J0-1
IF(KN(NUM1+2).NE.0) THEN
S1=REAL(SIGN(1,KN(NUM1+2)))
IF(JND1.GT.IND1) KEY=(IL/2)*MUMAX+MU(JND1)-JND1+IND1
IF(JND1.LT.IND1) KEY=(IL/2)*MUMAX+MU(IND1)-IND1+JND1
SYS(KEY)=SYS(KEY)+S1*REAL(IL)*VOL0*V(1,J0)/XX(K)
ENDIF
IF(KN(NUM1+3).NE.0) THEN
S2=REAL(SIGN(1,KN(NUM1+3)))
IF(JND1.GT.IND2) KEY=(IL/2)*MUMAX+MU(JND1)-JND1+IND2
IF(JND1.LT.IND2) KEY=(IL/2)*MUMAX+MU(IND2)-IND2+JND1
SYS(KEY)=SYS(KEY)+S2*REAL(IL)*VOL0*V(IELEM+1,J0)/XX(K)
ENDIF
JND1=KN(NUM1+1)+(J0-1)*IELEM+I0-1
IF(KN(NUM1+4).NE.0) THEN
S3=REAL(SIGN(1,KN(NUM1+4)))
IF(JND1.GT.IND3) KEY=(IL/2)*MUMAX+MU(JND1)-JND1+IND3
IF(JND1.LT.IND3) KEY=(IL/2)*MUMAX+MU(IND3)-IND3+JND1
SYS(KEY)=SYS(KEY)+S3*REAL(IL)*VOL0*V(1,J0)/YY(K)
ENDIF
IF(KN(NUM1+5).NE.0) THEN
S4=REAL(SIGN(1,KN(NUM1+5)))
IF(JND1.GT.IND4) KEY=(IL/2)*MUMAX+MU(JND1)-JND1+IND4
IF(JND1.LT.IND4) KEY=(IL/2)*MUMAX+MU(IND4)-IND4+JND1
SYS(KEY)=SYS(KEY)+S4*REAL(IL)*VOL0*V(IELEM+1,J0)/YY(K)
ENDIF
70 CONTINUE
80 CONTINUE
ENDIF
NUM1=NUM1+5
NUM2=NUM2+4
90 CONTINUE
100 CONTINUE
RETURN
END
|
