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25 //
26 // G4ConstRK4 implementation
27 //
28 // Created: J.Apostolakis, T.Nikitina - 18.09.2008
29 // -------------------------------------------------------------------
30
31 #include "G4ConstRK4.hh"
32 #include "G4ThreeVector.hh"
33 #include "G4LineSection.hh"
34
35 //////////////////////////////////////////////////////////////////
36 //
37 // Constructor sets the number of *State* variables (default = 8)
38 // The number of variables integrated is always 6
39 //
40 G4ConstRK4::G4ConstRK4(G4Mag_EqRhs* EqRhs, G4int numStateVariables)
41 : G4MagErrorStepper(EqRhs, 6, numStateVariables)
42 {
43 // const G4int numberOfVariables= 6;
44 if( numStateVariables < 8 )
45 {
46 std::ostringstream message;
47 message << "The number of State variables at least 8 " << G4endl
48 << "Instead it is - numStateVariables= " << numStateVariables;
49 G4Exception("G4ConstRK4::G4ConstRK4()", "GeomField0002",
50 FatalException, message, "Use another Stepper!");
51 }
52
53 fEq = EqRhs;
54 yMiddle = new G4double[8];
55 dydxMid = new G4double[8];
56 yInitial = new G4double[8];
57 yOneStep = new G4double[8];
58
59 dydxm = new G4double[8];
60 dydxt = new G4double[8];
61 yt = new G4double[8];
62 Field[0]=0.; Field[1]=0.; Field[2]=0.;
63 }
64
65 ////////////////////////////////////////////////////////////////
66 //
67 // Destructor
68
69 G4ConstRK4::~G4ConstRK4()
70 {
71 delete [] yMiddle;
72 delete [] dydxMid;
73 delete [] yInitial;
74 delete [] yOneStep;
75 delete [] dydxm;
76 delete [] dydxt;
77 delete [] yt;
78 }
79
80 //////////////////////////////////////////////////////////////////////
81 //
82 // Given values for the variables y[0,..,n-1] and their derivatives
83 // dydx[0,...,n-1] known at x, use the classical 4th Runge-Kutta
84 // method to advance the solution over an interval h and return the
85 // incremented variables as yout[0,...,n-1], which is not a distinct
86 // array from y. The user supplies the routine RightHandSide(x,y,dydx),
87 // which returns derivatives dydx at x. The source is routine rk4 from
88 // NRC p. 712-713 .
89 //
90 void G4ConstRK4::DumbStepper( const G4double yIn[],
91 const G4double dydx[],
92 G4double h,
93 G4double yOut[])
94 {
95 G4double hh = h*0.5 , h6 = h/6.0 ;
96
97 // 1st Step K1=h*dydx
98 yt[5] = yIn[5] + hh*dydx[5] ;
99 yt[4] = yIn[4] + hh*dydx[4] ;
100 yt[3] = yIn[3] + hh*dydx[3] ;
101 yt[2] = yIn[2] + hh*dydx[2] ;
102 yt[1] = yIn[1] + hh*dydx[1] ;
103 yt[0] = yIn[0] + hh*dydx[0] ;
104 RightHandSideConst(yt,dydxt) ;
105
106 // 2nd Step K2=h*dydxt
107 yt[5] = yIn[5] + hh*dydxt[5] ;
108 yt[4] = yIn[4] + hh*dydxt[4] ;
109 yt[3] = yIn[3] + hh*dydxt[3] ;
110 yt[2] = yIn[2] + hh*dydxt[2] ;
111 yt[1] = yIn[1] + hh*dydxt[1] ;
112 yt[0] = yIn[0] + hh*dydxt[0] ;
113 RightHandSideConst(yt,dydxm) ;
114
115 // 3rd Step K3=h*dydxm
116 // now dydxm=(K2+K3)/h
117 yt[5] = yIn[5] + h*dydxm[5] ;
118 dydxm[5] += dydxt[5] ;
119 yt[4] = yIn[4] + h*dydxm[4] ;
120 dydxm[4] += dydxt[4] ;
121 yt[3] = yIn[3] + h*dydxm[3] ;
122 dydxm[3] += dydxt[3] ;
123 yt[2] = yIn[2] + h*dydxm[2] ;
124 dydxm[2] += dydxt[2] ;
125 yt[1] = yIn[1] + h*dydxm[1] ;
126 dydxm[1] += dydxt[1] ;
127 yt[0] = yIn[0] + h*dydxm[0] ;
128 dydxm[0] += dydxt[0] ;
129 RightHandSideConst(yt,dydxt) ;
130
131 // 4th Step K4=h*dydxt
132 yOut[5] = yIn[5]+h6*(dydx[5]+dydxt[5]+2.0*dydxm[5]);
133 yOut[4] = yIn[4]+h6*(dydx[4]+dydxt[4]+2.0*dydxm[4]);
134 yOut[3] = yIn[3]+h6*(dydx[3]+dydxt[3]+2.0*dydxm[3]);
135 yOut[2] = yIn[2]+h6*(dydx[2]+dydxt[2]+2.0*dydxm[2]);
136 yOut[1] = yIn[1]+h6*(dydx[1]+dydxt[1]+2.0*dydxm[1]);
137 yOut[0] = yIn[0]+h6*(dydx[0]+dydxt[0]+2.0*dydxm[0]);
138
139 } // end of DumbStepper ....................................................
140
141 ////////////////////////////////////////////////////////////////
142 //
143 // Stepper
144
145 void
146 G4ConstRK4::Stepper( const G4double yInput[],
147 const G4double dydx[],
148 G4double hstep,
149 G4double yOutput[],
150 G4double yError [] )
151 {
152 const G4int nvar = 6; // number of variables integrated
153 const G4int maxvar = GetNumberOfStateVariables();
154
155 // Correction for Richardson extrapolation
156 G4double correction = 1. / ( (1 << IntegratorOrder()) -1 );
157
158 G4int i;
159
160 // Saving yInput because yInput and yOutput can be aliases for same array
161 for (i=0; i<maxvar; ++i) { yInitial[i]= yInput[i]; }
162
163 // Must copy the part of the state *not* integrated to the output
164 for (i=nvar; i<maxvar; ++i) { yOutput[i]= yInput[i]; }
165
166 // yInitial[7]= yInput[7]; // The time is typically needed
167 yMiddle[7] = yInput[7]; // Copy the time from initial value
168 yOneStep[7] = yInput[7]; // As it contributes to final value of yOutput ?
169 // yOutput[7] = yInput[7]; // -> dumb stepper does it too for RK4
170 yError[7] = 0.0;
171
172 G4double halfStep = hstep * 0.5;
173
174 // Do two half steps
175 //
176 GetConstField(yInitial,Field);
177 DumbStepper (yInitial, dydx, halfStep, yMiddle);
178 RightHandSideConst(yMiddle, dydxMid);
179 DumbStepper (yMiddle, dydxMid, halfStep, yOutput);
180
181 // Store midpoint, chord calculation
182 //
183 fMidPoint = G4ThreeVector( yMiddle[0], yMiddle[1], yMiddle[2]);
184
185 // Do a full Step
186 //
187 DumbStepper(yInitial, dydx, hstep, yOneStep);
188 for(i=0; i<nvar; ++i)
189 {
190 yError [i] = yOutput[i] - yOneStep[i] ;
191 yOutput[i] += yError[i]*correction ;
192 // Provides accuracy increased by 1 order via the
193 // Richardson extrapolation
194 }
195
196 fInitialPoint = G4ThreeVector( yInitial[0], yInitial[1], yInitial[2]);
197 fFinalPoint = G4ThreeVector( yOutput[0], yOutput[1], yOutput[2]);
198
199 return;
200 }
201
202 ////////////////////////////////////////////////////////////////
203 //
204 // Estimate the maximum distance from the curve to the chord
205 //
206 // We estimate this using the distance of the midpoint to chord.
207 // The method below is good only for angle deviations < 2 pi;
208 // this restriction should not be a problem for the Runge Kutta methods,
209 // which generally cannot integrate accurately for large angle deviations
210 //
211 G4double G4ConstRK4::DistChord() const
212 {
213 G4double distLine, distChord;
214
215 if (fInitialPoint != fFinalPoint)
216 {
217 distLine= G4LineSection::Distline( fMidPoint, fInitialPoint, fFinalPoint );
218 // This is a class method that gives distance of Mid
219 // from the Chord between the Initial and Final points
220 distChord = distLine;
221 }
222 else
223 {
224 distChord = (fMidPoint-fInitialPoint).mag();
225 }
226 return distChord;
227 }
228