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25 //
26 // G4RK547FEq3 implementation
27 //
28 // The Butcher table of the Higham & Hall 5(4)7 method is:
29 //
30 // 0 |
31 // 11/45 | 11/45
32 // 11/30 | 11/120 11/40
33 // 55/56 | 106865/87808 -408375/87808 193875/43904
34 // 9/10 | 79503/121000 -1053/440 147753/56870 27048/710875
35 // 1 | 89303/78045 -2025/473 994650/244541 -2547216/28122215 475/2967
36 // 1 | 1247/10890 0 57375/108053 -1229312/1962015 125/207 43/114
37 //---------------------------------------------------------------------------------------------------------------------
38 // 1247/10890 0 57375/108053 -1229312/1962015 125/207 43/114 0
39 // 21487/185130 0 963225/1836901 -39864832/33354255 2575/3519 4472/4845 -1/10
40 //
41 // Author: Dmitry Sorokin, Google Summer of Code 2017
42 // Supervision: John Apostolakis, CERN
43 // --------------------------------------------------------------------
44
45 #include "G4RK547FEq3.hh"
46 #include "G4LineSection.hh"
47 #include "G4FieldUtils.hh"
48
49 using namespace field_utils;
50
51 G4RK547FEq3::G4RK547FEq3(G4EquationOfMotion* EqRhs, G4int integrationVariables)
52 : G4MagIntegratorStepper(EqRhs, integrationVariables)
53 {
54 }
55
56 void G4RK547FEq3::makeStep( const G4double yInput[],
57 const G4double dydx[],
58 const G4double hstep,
59 G4double yOutput[],
60 G4double* dydxOutput,
61 G4double* yError ) const
62 {
63 G4double yTemp[G4FieldTrack::ncompSVEC];
64 for (G4int i=GetNumberOfVariables(); i<GetNumberOfStateVariables(); ++i)
65 {
66 yOutput[i] = yTemp[i] = yInput[i];
67 }
68
69 G4double ak2[G4FieldTrack::ncompSVEC],
70 ak3[G4FieldTrack::ncompSVEC],
71 ak4[G4FieldTrack::ncompSVEC],
72 ak5[G4FieldTrack::ncompSVEC],
73 ak6[G4FieldTrack::ncompSVEC];
74
75 const G4double b21 = 11./45.,
76 b31 = 11./120., b32 = 11./40.,
77 b41 = 106865./87808., b42 = -408375./87808.,
78 b43 = 193875./43904.,
79 b51 = 79503./121000., b52 = -1053./440.,
80 b53 = 147753./56870., b54 = 27048./710875.,
81 b61 = 89303./78045., b62 = -2025./473.,
82 b63 = 994650./244541., b64 = -2547216./28122215.,
83 b65 = 475./2967.,
84 b71 = 1247./10890., b72 = 0., b73 = 57375./108053.,
85 b74 = -1229312./1962015., b75 = 125./207.,
86 b76 = 43./114.;
87
88 const G4double dc1 = b71 - 21487./185130.,
89 dc2 = b72 - 0.,
90 dc3 = b73 - 963225./1836901.,
91 dc4 = b74 + 39864832./33354255.,
92 dc5 = b75 - 2575./3519.,
93 dc6 = b76 - 4472./4845.,
94 dc7 = 0. + 1./10.;
95
96 // RightHandSide(yInput, dydx);
97 for(G4int i = 0; i < GetNumberOfVariables(); ++i)
98 {
99 yTemp[i] = yInput[i] + hstep * b21 * dydx[i];
100 }
101
102 RightHandSide(yTemp, ak2);
103 for(G4int i = 0; i < GetNumberOfVariables(); ++i)
104 {
105 yTemp[i] = yInput[i] + hstep * (b31 * dydx[i] + b32 * ak2[i]);
106 }
107
108 RightHandSide(yTemp, ak3);
109 for(G4int i = 0;i < GetNumberOfVariables(); ++i)
110 {
111 yTemp[i] = yInput[i] + hstep * (b41 * dydx[i] + b42 * ak2[i] +
112 b43 * ak3[i]);
113 }
114
115 RightHandSide(yTemp, ak4);
116 for(G4int i = 0; i < GetNumberOfVariables(); ++i)
117 {
118 yTemp[i] = yInput[i] + hstep * (b51 * dydx[i] + b52 * ak2[i] +
119 b53 * ak3[i] + b54 * ak4[i]);
120 }
121
122 RightHandSide(yTemp, ak5);
123 for(G4int i = 0; i < GetNumberOfVariables(); ++i)
124 {
125 yTemp[i] = yInput[i] + hstep * (b61 * dydx[i] + b62 * ak2[i] +
126 b63 * ak3[i] + b64 * ak4[i] +
127 b65 * ak5[i]);
128 }
129
130 RightHandSide(yTemp, ak6);
131 for(G4int i = 0; i < GetNumberOfVariables(); ++i)
132 {
133 yOutput[i] = yInput[i] + hstep * (b71 * dydx[i] + b72 * ak2[i] +
134 b73 * ak3[i] + b74 * ak4[i] +
135 b75 * ak5[i] + b76 * ak6[i]);
136 }
137 if ((dydxOutput != nullptr) && (yError != nullptr))
138 {
139 RightHandSide(yOutput, dydxOutput);
140 for(G4int i = 0; i < GetNumberOfVariables(); ++i)
141 {
142 yError[i] = hstep * (dc1 * dydx[i] + dc2 * ak2[i] + dc3 * ak3[i] +
143 dc4 * ak4[i] + dc5 * ak5[i] + dc6 * ak6[i] +
144 dc7 * dydxOutput[i]);
145 }
146 }
147 }
148
149 void G4RK547FEq3::Stepper( const G4double yInput[],
150 const G4double dydx[],
151 G4double hstep,
152 G4double yOutput[],
153 G4double yError[] )
154 {
155 copy(fyIn, yInput);
156 copy(fdydx, dydx);
157 fhstep = hstep;
158
159 makeStep(fyIn, fdydx, fhstep, fyOut, fdydxOut, yError);
160
161 copy(yOutput, fyOut);
162 }
163
164 void G4RK547FEq3::Stepper( const G4double yInput[],
165 const G4double dydx[],
166 G4double hstep,
167 G4double yOutput[],
168 G4double yError[],
169 G4double dydxOutput[] )
170 {
171 copy(fyIn, yInput);
172 copy(fdydx, dydx);
173 fhstep = hstep;
174
175 makeStep(fyIn, fdydx, fhstep, fyOut, fdydxOut, yError);
176
177 copy(yOutput, fyOut);
178 copy(dydxOutput, fdydxOut);
179 }
180
181 G4double G4RK547FEq3::DistChord() const
182 {
183 G4double yMid[G4FieldTrack::ncompSVEC];
184 makeStep(fyIn, fdydx, fhstep / 2., yMid);
185
186 const G4ThreeVector begin = makeVector(fyIn, Value3D::Position);
187 const G4ThreeVector mid = makeVector(yMid, Value3D::Position);
188 const G4ThreeVector end = makeVector(fyOut, Value3D::Position);
189
190 return G4LineSection::Distline(mid, begin, end);
191 }
192