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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 DNSD(X,Y,YPRIME,NEQ,RES,PDUM,WT,RPAR,IPAR, |
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6 * DUMSVR,DELTA,E,WM,IWM,CJ,DUMS,DUMR,DUME,EPCON, |
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7 * S,CONFAC,TOLNEW,MULDEL,MAXIT,IRES,IDUM,IERNEW) |
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8 C |
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9 C***BEGIN PROLOGUE DNSD |
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10 C***REFER TO DDASPK |
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11 C***DATE WRITTEN 891219 (YYMMDD) |
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12 C***REVISION DATE 900926 (YYMMDD) |
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13 C***REVISION DATE 950126 (YYMMDD) |
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14 C |
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15 C |
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16 C----------------------------------------------------------------------- |
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17 C***DESCRIPTION |
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18 C |
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19 C DNSD solves a nonlinear system of |
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20 C algebraic equations of the form |
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21 C G(X,Y,YPRIME) = 0 for the unknown Y. |
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22 C |
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23 C The method used is a modified Newton scheme. |
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24 C |
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25 C The parameters represent |
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26 C |
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27 C X -- Independent variable. |
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28 C Y -- Solution vector. |
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29 C YPRIME -- Derivative of solution vector. |
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30 C NEQ -- Number of unknowns. |
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31 C RES -- External user-supplied subroutine |
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32 C to evaluate the residual. See RES description |
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33 C in DDASPK prologue. |
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34 C PDUM -- Dummy argument. |
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35 C WT -- Vector of weights for error criterion. |
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36 C RPAR,IPAR -- Real and integer arrays used for communication |
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37 C between the calling program and external user |
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38 C routines. They are not altered within DASPK. |
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39 C DUMSVR -- Dummy argument. |
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40 C DELTA -- Work vector for DNSD of length NEQ. |
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41 C E -- Error accumulation vector for DNSD of length NEQ. |
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42 C WM,IWM -- Real and integer arrays storing |
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43 C matrix information such as the matrix |
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44 C of partial derivatives, permutation |
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45 C vector, and various other information. |
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46 C CJ -- Parameter always proportional to 1/H (step size). |
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47 C DUMS -- Dummy argument. |
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48 C DUMR -- Dummy argument. |
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49 C DUME -- Dummy argument. |
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50 C EPCON -- Tolerance to test for convergence of the Newton |
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51 C iteration. |
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52 C S -- Used for error convergence tests. |
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53 C In the Newton iteration: S = RATE/(1 - RATE), |
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54 C where RATE is the estimated rate of convergence |
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55 C of the Newton iteration. |
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56 C The calling routine passes the initial value |
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57 C of S to the Newton iteration. |
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58 C CONFAC -- A residual scale factor to improve convergence. |
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59 C TOLNEW -- Tolerance on the norm of Newton correction in |
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60 C alternative Newton convergence test. |
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61 C MULDEL -- A flag indicating whether or not to multiply |
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62 C DELTA by CONFAC. |
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63 C 0 ==> do not scale DELTA by CONFAC. |
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64 C 1 ==> scale DELTA by CONFAC. |
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65 C MAXIT -- Maximum allowed number of Newton iterations. |
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66 C IRES -- Error flag returned from RES. See RES description |
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67 C in DDASPK prologue. If IRES = -1, then IERNEW |
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68 C will be set to 1. |
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69 C If IRES < -1, then IERNEW will be set to -1. |
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70 C IDUM -- Dummy argument. |
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71 C IERNEW -- Error flag for Newton iteration. |
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72 C 0 ==> Newton iteration converged. |
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73 C 1 ==> recoverable error inside Newton iteration. |
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74 C -1 ==> unrecoverable error inside Newton iteration. |
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75 C |
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76 C All arguments with "DUM" in their names are dummy arguments |
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77 C which are not used in this routine. |
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78 C----------------------------------------------------------------------- |
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79 C |
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80 C***ROUTINES CALLED |
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81 C DSLVD, DDWNRM, RES |
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82 C |
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83 C***END PROLOGUE DNSD |
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84 C |
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85 C |
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86 IMPLICIT DOUBLE PRECISION(A-H,O-Z) |
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87 DIMENSION Y(*),YPRIME(*),WT(*),DELTA(*),E(*) |
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88 DIMENSION WM(*),IWM(*), RPAR(*),IPAR(*) |
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89 EXTERNAL RES |
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90 C |
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91 PARAMETER (LNRE=12, LNNI=19) |
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92 C |
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93 C Initialize Newton counter M and accumulation vector E. |
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94 C |
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95 M = 0 |
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96 DO 100 I=1,NEQ |
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97 100 E(I)=0.0D0 |
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98 C |
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99 C Corrector loop. |
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100 C |
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101 300 CONTINUE |
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102 IWM(LNNI) = IWM(LNNI) + 1 |
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103 C |
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104 C If necessary, multiply residual by convergence factor. |
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105 C |
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106 IF (MULDEL .EQ. 1) THEN |
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107 DO 320 I = 1,NEQ |
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108 320 DELTA(I) = DELTA(I) * CONFAC |
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109 ENDIF |
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110 C |
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111 C Compute a new iterate (back-substitution). |
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112 C Store the correction in DELTA. |
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113 C |
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114 CALL DSLVD(NEQ,DELTA,WM,IWM) |
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115 C |
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116 C Update Y, E, and YPRIME. |
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117 C |
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118 DO 340 I=1,NEQ |
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119 Y(I)=Y(I)-DELTA(I) |
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120 E(I)=E(I)-DELTA(I) |
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121 340 YPRIME(I)=YPRIME(I)-CJ*DELTA(I) |
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122 C |
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123 C Test for convergence of the iteration. |
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124 C |
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125 DELNRM=DDWNRM(NEQ,DELTA,WT,RPAR,IPAR) |
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126 IF (DELNRM .LE. TOLNEW) GO TO 370 |
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127 IF (M .EQ. 0) THEN |
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128 OLDNRM = DELNRM |
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129 ELSE |
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130 RATE = (DELNRM/OLDNRM)**(1.0D0/M) |
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131 IF (RATE .GT. 0.9D0) GO TO 380 |
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132 S = RATE/(1.0D0 - RATE) |
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133 ENDIF |
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134 IF (S*DELNRM .LE. EPCON) GO TO 370 |
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135 C |
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136 C The corrector has not yet converged. |
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137 C Update M and test whether the |
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138 C maximum number of iterations have |
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139 C been tried. |
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140 C |
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141 M=M+1 |
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142 IF(M.GE.MAXIT) GO TO 380 |
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143 C |
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144 C Evaluate the residual, |
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145 C and go back to do another iteration. |
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146 C |
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147 IWM(LNRE)=IWM(LNRE)+1 |
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148 CALL RES(X,Y,YPRIME,CJ,DELTA,IRES,RPAR,IPAR) |
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149 IF (IRES .LT. 0) GO TO 380 |
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150 GO TO 300 |
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151 C |
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152 C The iteration has converged. |
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153 C |
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154 370 RETURN |
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155 C |
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156 C The iteration has not converged. Set IERNEW appropriately. |
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157 C |
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158 380 CONTINUE |
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159 IF (IRES .LE. -2 ) THEN |
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160 IERNEW = -1 |
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161 ELSE |
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162 IERNEW = 1 |
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163 ENDIF |
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164 RETURN |
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165 C |
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166 C |
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167 C------END OF SUBROUTINE DNSD------------------------------------------- |
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168 END |
