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25 //
26 // G4RKG3_Stepper implementation
27 //
28 // Created: J.Apostolakis, V.Grichine - 30.01.1997
29 // -------------------------------------------------------------------
30
31 #include "G4RKG3_Stepper.hh"
32 #include "G4LineSection.hh"
33 #include "G4Mag_EqRhs.hh"
34
35 G4RKG3_Stepper::G4RKG3_Stepper(G4Mag_EqRhs* EqRhs)
36 : G4MagIntegratorStepper(EqRhs,6)
37 {
38 }
39
40 G4RKG3_Stepper::~G4RKG3_Stepper() = default;
41
42 void G4RKG3_Stepper::Stepper( const G4double yInput[], // [8]
43 const G4double dydx[], // [6]
44 G4double Step,
45 G4double yOut[], // [8]
46 G4double yErr[] )
47 {
48 G4double B[3];
49 G4int nvar = 6 ;
50 G4double by15 = 1. / 15. ; // was 0.066666666 ;
51
52 G4double yTemp[8], dydxTemp[6], yIn[8];
53
54 // Saving yInput because yInput and yOut can be aliases for same array
55 //
56 for(G4int i=0; i<nvar; ++i)
57 {
58 yIn[i]=yInput[i];
59 }
60 yIn[6] = yInput[6];
61 yIn[7] = yInput[7];
62 G4double h = Step * 0.5;
63 hStep = Step;
64 // Do two half steps
65
66 StepNoErr(yIn, dydx,h, yTemp,B) ;
67
68 // Store Bfld for DistChord Calculation
69 //
70 for(auto i=0; i<3; ++i)
71 {
72 BfldIn[i] = B[i];
73 }
74 // RightHandSide(yTemp,dydxTemp) ;
75
76 GetEquationOfMotion()->EvaluateRhsGivenB(yTemp,B,dydxTemp) ;
77 StepNoErr(yTemp,dydxTemp,h,yOut,B);
78
79 // Store midpoint, chord calculation
80
81 fyMidPoint = G4ThreeVector(yTemp[0], yTemp[1], yTemp[2]);
82
83 // Do a full Step
84 //
85 h *= 2 ;
86 StepNoErr(yIn,dydx,h,yTemp,B);
87 for(G4int i=0; i<nvar; ++i)
88 {
89 yErr[i] = yOut[i] - yTemp[i] ;
90 yOut[i] += yErr[i]*by15 ; // Provides 5th order of accuracy
91 }
92
93 // Store values for DistChord method
94 //
95 fyInitial = G4ThreeVector( yIn[0], yIn[1], yIn[2]);
96 fpInitial = G4ThreeVector( yIn[3], yIn[4], yIn[5]);
97 fyFinal = G4ThreeVector( yOut[0], yOut[1], yOut[2]);
98 }
99
100 // ---------------------------------------------------------------------------
101
102 // Integrator for RK from G3 with evaluation of error in solution and delta
103 // geometry based on naive similarity with the case of uniform magnetic field.
104 // B1[3] is input and is the first magnetic field values
105 // B2[3] is output and is the final magnetic field values.
106 //
107 void G4RKG3_Stepper::StepWithEst( const G4double*,
108 const G4double*,
109 G4double,
110 G4double*,
111 G4double&,
112 G4double&,
113 const G4double*,
114 G4double* )
115
116 {
117 G4Exception("G4RKG3_Stepper::StepWithEst()", "GeomField0001",
118 FatalException, "Method no longer used.");
119 }
120
121 // -----------------------------------------------------------------
122
123 // Integrator RK Stepper from G3 with only two field evaluation per Step.
124 // It is used in propagation initial Step by small substeps after solution
125 // error and delta geometry considerations. B[3] is magnetic field which
126 // is passed from substep to substep.
127 //
128 void G4RKG3_Stepper::StepNoErr(const G4double tIn[8],
129 const G4double dydx[6],
130 G4double Step,
131 G4double tOut[8],
132 G4double B[3] )
133
134 {
135
136 // Copy and edit the routine above, to delete alpha2, beta2, ...
137 //
138 G4double K1[7], K2[7], K3[7], K4[7];
139 G4double tTemp[8]={0.0}, yderiv[6]={0.0};
140
141 // Need Momentum value to give correct values to the coefficients in
142 // equation. Integration on unit velocity, but tIn[3,4,5] is momentum
143
144 G4double mom, inverse_mom;
145 const G4double c1=0.5, c2=0.125, c3=1./6.;
146
147 // Correction for momentum not a velocity
148 // Need the protection !!! must be not zero
149 //
150 mom = std::sqrt(tIn[3]*tIn[3]+tIn[4]*tIn[4]+tIn[5]*tIn[5]);
151 inverse_mom = 1./mom;
152 for(auto i=0; i<3; ++i)
153 {
154 K1[i] = Step * dydx[i+3]*inverse_mom;
155 tTemp[i] = tIn[i] + Step*(c1*tIn[i+3]*inverse_mom + c2*K1[i]) ;
156 tTemp[i+3] = tIn[i+3] + c1*K1[i]*mom ;
157 }
158
159 GetEquationOfMotion()->EvaluateRhsReturnB(tTemp,yderiv,B) ;
160
161 for(auto i=0; i<3; ++i)
162 {
163 K2[i] = Step * yderiv[i+3]*inverse_mom;
164 tTemp[i+3] = tIn[i+3] + c1*K2[i]*mom ;
165 }
166
167 // Given B, calculate yderiv !
168 //
169 GetEquationOfMotion()->EvaluateRhsGivenB(tTemp,B,yderiv) ;
170
171 for(auto i=0; i<3; ++i)
172 {
173 K3[i] = Step * yderiv[i+3]*inverse_mom;
174 tTemp[i] = tIn[i] + Step*(tIn[i+3]*inverse_mom + c1*K3[i]) ;
175 tTemp[i+3] = tIn[i+3] + K3[i]*mom ;
176 }
177
178 // Calculates y-deriv(atives) & returns B too!
179 //
180 GetEquationOfMotion()->EvaluateRhsReturnB(tTemp,yderiv,B) ;
181
182 for(auto i=0; i<3; ++i) // Output trajectory vector
183 {
184 K4[i] = Step * yderiv[i+3]*inverse_mom;
185 tOut[i] = tIn[i] + Step*(tIn[i+3]*inverse_mom+ (K1[i]+K2[i]+K3[i])*c3) ;
186 tOut[i+3] = tIn[i+3] + mom*(K1[i] + 2*K2[i] + 2*K3[i] +K4[i])*c3 ;
187 }
188 tOut[6] = tIn[6];
189 tOut[7] = tIn[7];
190 }
191
192 // ---------------------------------------------------------------------------
193
194 G4double G4RKG3_Stepper::DistChord() const
195 {
196 // Soon: must check whether h/R > 2 pi !!
197 // Method below is good only for < 2 pi
198
199 G4double distChord,distLine;
200
201 if (fyInitial != fyFinal)
202 {
203 distLine = G4LineSection::Distline(fyMidPoint,fyInitial,fyFinal);
204 distChord = distLine;
205 }
206 else
207 {
208 distChord = (fyMidPoint-fyInitial).mag();
209 }
210
211 return distChord;
212 }
213