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1 C Work performed under the auspices of the U.S. Department of Energy |
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2 C by Lawrence Livermore National Laboratory under contract number |
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3 C W-7405-Eng-48. |
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4 C |
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5 SUBROUTINE DNEDK(X,Y,YPRIME,NEQ,RES,JACK,PSOL, |
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6 * H,WT,JSTART,IDID,RPAR,IPAR,PHI,GAMMA,SAVR,DELTA,E, |
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7 * WM,IWM,CJ,CJOLD,CJLAST,S,UROUND,EPLI,SQRTN,RSQRTN, |
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8 * EPCON,JCALC,JFLG,KP1,NONNEG,NTYPE,IERNLS) |
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9 C |
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10 C***BEGIN PROLOGUE DNEDK |
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11 C***REFER TO DDASPK |
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12 C***DATE WRITTEN 891219 (YYMMDD) |
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13 C***REVISION DATE 900926 (YYMMDD) |
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14 C***REVISION DATE 940701 (YYMMDD) |
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15 C |
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16 C |
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17 C----------------------------------------------------------------------- |
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18 C***DESCRIPTION |
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19 C |
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20 C DNEDK solves a nonlinear system of |
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21 C algebraic equations of the form |
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22 C G(X,Y,YPRIME) = 0 for the unknown Y. |
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23 C |
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24 C The method used is a matrix-free Newton scheme. |
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25 C |
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26 C The parameters represent |
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27 C X -- Independent variable. |
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28 C Y -- Solution vector at x. |
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29 C YPRIME -- Derivative of solution vector |
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30 C after successful step. |
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31 C NEQ -- Number of equations to be integrated. |
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32 C RES -- External user-supplied subroutine |
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33 C to evaluate the residual. See RES description |
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34 C in DDASPK prologue. |
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35 C JACK -- External user-supplied routine to update |
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36 C the preconditioner. (This is optional). |
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37 C See JAC description for the case |
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38 C INFO(12) = 1 in the DDASPK prologue. |
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39 C PSOL -- External user-supplied routine to solve |
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40 C a linear system using preconditioning. |
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41 C (This is optional). See explanation inside DDASPK. |
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42 C H -- Appropriate step size for this step. |
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43 C WT -- Vector of weights for error criterion. |
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44 C JSTART -- Indicates first call to this routine. |
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45 C If JSTART = 0, then this is the first call, |
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46 C otherwise it is not. |
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47 C IDID -- Completion flag, output by DNEDK. |
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48 C See IDID description in DDASPK prologue. |
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49 C RPAR,IPAR -- Real and integer arrays used for communication |
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50 C between the calling program and external user |
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51 C routines. They are not altered within DASPK. |
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52 C PHI -- Array of divided differences used by |
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53 C DNEDK. The length is NEQ*(K+1), where |
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54 C K is the maximum order. |
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55 C GAMMA -- Array used to predict Y and YPRIME. The length |
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56 C is K+1, where K is the maximum order. |
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57 C SAVR -- Work vector for DNEDK of length NEQ. |
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58 C DELTA -- Work vector for DNEDK of length NEQ. |
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59 C E -- Error accumulation vector for DNEDK of length NEQ. |
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60 C WM,IWM -- Real and integer arrays storing |
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61 C matrix information for linear system |
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62 C solvers, and various other information. |
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63 C CJ -- Parameter always proportional to 1/H. |
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64 C CJOLD -- Saves the value of CJ as of the last call to DITMD. |
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65 C Accounts for changes in CJ needed to |
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66 C decide whether to call DITMD. |
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67 C CJLAST -- Previous value of CJ. |
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68 C S -- A scalar determined by the approximate rate |
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69 C of convergence of the Newton iteration and used |
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70 C in the convergence test for the Newton iteration. |
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71 C |
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72 C If RATE is defined to be an estimate of the |
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73 C rate of convergence of the Newton iteration, |
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74 C then S = RATE/(1.D0-RATE). |
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75 C |
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76 C The closer RATE is to 0., the faster the Newton |
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77 C iteration is converging; the closer RATE is to 1., |
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78 C the slower the Newton iteration is converging. |
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79 C |
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80 C On the first Newton iteration with an up-dated |
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81 C preconditioner S = 100.D0, Thus the initial |
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82 C RATE of convergence is approximately 1. |
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83 C |
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84 C S is preserved from call to call so that the rate |
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85 C estimate from a previous step can be applied to |
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86 C the current step. |
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87 C UROUND -- Unit roundoff. |
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88 C EPLI -- convergence test constant. |
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89 C See DDASPK prologue for more details. |
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90 C SQRTN -- Square root of NEQ. |
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91 C RSQRTN -- reciprical of square root of NEQ. |
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92 C EPCON -- Tolerance to test for convergence of the Newton |
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93 C iteration. |
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94 C JCALC -- Flag used to determine when to update |
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95 C the Jacobian matrix. In general: |
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96 C |
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97 C JCALC = -1 ==> Call the DITMD routine to update |
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98 C the Jacobian matrix. |
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99 C JCALC = 0 ==> Jacobian matrix is up-to-date. |
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100 C JCALC = 1 ==> Jacobian matrix is out-dated, |
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101 C but DITMD will not be called unless |
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102 C JCALC is set to -1. |
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103 C JFLG -- Flag showing whether a Jacobian routine is supplied. |
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104 C KP1 -- The current order + 1; updated across calls. |
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105 C NONNEG -- Flag to determine nonnegativity constraints. |
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106 C NTYPE -- Identification code for the DNEDK routine. |
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107 C 1 ==> modified Newton; iterative linear solver. |
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108 C 2 ==> modified Newton; user-supplied linear solver. |
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109 C IERNLS -- Error flag for nonlinear solver. |
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110 C 0 ==> nonlinear solver converged. |
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111 C 1 ==> recoverable error inside non-linear solver. |
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112 C -1 ==> unrecoverable error inside non-linear solver. |
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113 C |
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114 C The following group of variables are passed as arguments to |
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115 C the Newton iteration solver. They are explained in greater detail |
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116 C in DNSK: |
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117 C TOLNEW, MULDEL, MAXIT, IERNEW |
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118 C |
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119 C IERTYP -- Flag which tells whether this subroutine is correct. |
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120 C 0 ==> correct subroutine. |
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121 C 1 ==> incorrect subroutine. |
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122 C |
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123 C----------------------------------------------------------------------- |
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124 C***ROUTINES CALLED |
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125 C RES, JACK, DDWNRM, DNSK |
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126 C |
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127 C***END PROLOGUE DNEDK |
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128 C |
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129 C |
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130 IMPLICIT DOUBLE PRECISION(A-H,O-Z) |
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131 DIMENSION Y(*),YPRIME(*),WT(*) |
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132 DIMENSION PHI(NEQ,*),SAVR(*),DELTA(*),E(*) |
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133 DIMENSION WM(*),IWM(*) |
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134 DIMENSION GAMMA(*),RPAR(*),IPAR(*) |
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135 EXTERNAL RES, JACK, PSOL |
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136 C |
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137 PARAMETER (LNRE=12, LNJE=13, LLOCWP=29, LLCIWP=30) |
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138 C |
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139 SAVE MULDEL, MAXIT, XRATE |
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140 DATA MULDEL/0/, MAXIT/4/, XRATE/0.25D0/ |
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141 C |
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142 C Verify that this is the correct subroutine. |
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143 C |
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144 IERTYP = 0 |
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145 IF (NTYPE .NE. 1) THEN |
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146 IERTYP = 1 |
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147 GO TO 380 |
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148 ENDIF |
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149 C |
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150 C If this is the first step, perform initializations. |
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151 C |
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152 IF (JSTART .EQ. 0) THEN |
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153 CJOLD = CJ |
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154 JCALC = -1 |
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155 S = 100.D0 |
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156 ENDIF |
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157 C |
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158 C Perform all other initializations. |
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159 C |
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160 IERNLS = 0 |
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161 LWP = IWM(LLOCWP) |
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162 LIWP = IWM(LLCIWP) |
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163 C |
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164 C Decide whether to update the preconditioner. |
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165 C |
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166 IF (JFLG .NE. 0) THEN |
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167 TEMP1 = (1.0D0 - XRATE)/(1.0D0 + XRATE) |
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168 TEMP2 = 1.0D0/TEMP1 |
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169 IF (CJ/CJOLD .LT. TEMP1 .OR. CJ/CJOLD .GT. TEMP2) JCALC = -1 |
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170 IF (CJ .NE. CJLAST) S = 100.D0 |
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171 ELSE |
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172 JCALC = 0 |
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173 ENDIF |
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174 C |
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175 C Looping point for updating preconditioner with current stepsize. |
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176 C |
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177 300 CONTINUE |
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178 C |
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179 C Initialize all error flags to zero. |
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180 C |
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181 IERPJ = 0 |
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182 IRES = 0 |
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183 IERSL = 0 |
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184 IERNEW = 0 |
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185 C |
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186 C Predict the solution and derivative and compute the tolerance |
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187 C for the Newton iteration. |
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188 C |
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189 DO 310 I=1,NEQ |
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190 Y(I)=PHI(I,1) |
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191 310 YPRIME(I)=0.0D0 |
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192 DO 330 J=2,KP1 |
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193 DO 320 I=1,NEQ |
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194 Y(I)=Y(I)+PHI(I,J) |
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195 320 YPRIME(I)=YPRIME(I)+GAMMA(J)*PHI(I,J) |
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196 330 CONTINUE |
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197 EPLIN = EPLI*EPCON |
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198 TOLNEW = EPLIN |
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199 C |
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200 C Call RES to initialize DELTA. |
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201 C |
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202 IWM(LNRE)=IWM(LNRE)+1 |
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203 CALL RES(X,Y,YPRIME,CJ,DELTA,IRES,RPAR,IPAR) |
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204 IF (IRES .LT. 0) GO TO 380 |
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205 C |
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206 C |
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207 C If indicated, update the preconditioner. |
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208 C Set JCALC to 0 as an indicator that this has been done. |
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209 C |
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210 IF(JCALC .EQ. -1)THEN |
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211 IWM(LNJE) = IWM(LNJE) + 1 |
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212 JCALC=0 |
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213 CALL JACK (RES, IRES, NEQ, X, Y, YPRIME, WT, DELTA, E, H, CJ, |
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214 * WM(LWP), IWM(LIWP), IERPJ, RPAR, IPAR) |
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215 CJOLD=CJ |
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216 S = 100.D0 |
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217 IF (IRES .LT. 0) GO TO 380 |
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218 IF (IERPJ .NE. 0) GO TO 380 |
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219 ENDIF |
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220 C |
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221 C Call the nonlinear Newton solver. |
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222 C |
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223 CALL DNSK(X,Y,YPRIME,NEQ,RES,PSOL,WT,RPAR,IPAR,SAVR, |
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224 * DELTA,E,WM,IWM,CJ,SQRTN,RSQRTN,EPLIN,EPCON, |
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225 * S,TEMP1,TOLNEW,MULDEL,MAXIT,IRES,IERSL,IERNEW) |
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226 C |
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227 IF (IERNEW .GT. 0 .AND. JCALC .NE. 0) THEN |
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228 C |
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229 C The Newton iteration had a recoverable failure with an old |
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230 C preconditioner. Retry the step with a new preconditioner. |
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231 C |
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232 JCALC = -1 |
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233 GO TO 300 |
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234 ENDIF |
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235 C |
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236 IF (IERNEW .NE. 0) GO TO 380 |
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237 C |
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238 C The Newton iteration has converged. If nonnegativity of |
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239 C solution is required, set the solution nonnegative, if the |
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240 C perturbation to do it is small enough. If the change is too |
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241 C large, then consider the corrector iteration to have failed. |
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242 C |
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243 IF(NONNEG .EQ. 0) GO TO 390 |
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244 DO 360 I = 1,NEQ |
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245 360 DELTA(I) = MIN(Y(I),0.0D0) |
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246 DELNRM = DDWNRM(NEQ,DELTA,WT,RPAR,IPAR) |
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247 IF(DELNRM .GT. EPCON) GO TO 380 |
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248 DO 370 I = 1,NEQ |
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249 370 E(I) = E(I) - DELTA(I) |
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250 GO TO 390 |
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251 C |
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252 C |
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253 C Exits from nonlinear solver. |
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254 C No convergence with current preconditioner. |
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255 C Compute IERNLS and IDID accordingly. |
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256 C |
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257 380 CONTINUE |
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258 IF (IRES .LE. -2 .OR. IERSL .LT. 0 .OR. IERTYP .NE. 0) THEN |
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259 IERNLS = -1 |
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260 IF (IRES .LE. -2) IDID = -11 |
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261 IF (IERSL .LT. 0) IDID = -13 |
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262 IF (IERTYP .NE. 0) IDID = -15 |
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263 ELSE |
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264 IERNLS = 1 |
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265 IF (IRES .EQ. -1) IDID = -10 |
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266 IF (IERPJ .NE. 0) IDID = -5 |
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267 IF (IERSL .GT. 0) IDID = -14 |
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268 ENDIF |
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269 C |
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270 C |
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271 390 JCALC = 1 |
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272 RETURN |
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273 C |
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274 C------END OF SUBROUTINE DNEDK------------------------------------------ |
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275 END |
