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25 // 25 //
26 // class G4HelixMixedStepper 26 // class G4HelixMixedStepper
27 // 27 //
28 // Class description: 28 // Class description:
29 // 29 //
30 // G4HelixMixedStepper split the Method used f 30 // G4HelixMixedStepper split the Method used for Integration in two:
31 // 31 //
32 // If Stepping Angle ( h / R_curve) < pi/3 << 32 // If Stepping Angle ( h / R_curve) < pi/3 use Classical RK4Stepper
33 // use Stepper for small step(Classical <<
34 // Else use HelixExplicitEuler Stepper 33 // Else use HelixExplicitEuler Stepper
35 // 34 //
36 // Created: T.Nikitina, CERN - 18.05.2007, der << 35 // History:
>> 36 // Derived from ExactHelicalStepper 18/05/07
>> 37 //
37 // ------------------------------------------- 38 // -------------------------------------------------------------------------
38 39
39 #include "G4HelixMixedStepper.hh" 40 #include "G4HelixMixedStepper.hh"
40 #include "G4PhysicalConstants.hh" <<
41 #include "G4ClassicalRK4.hh" 41 #include "G4ClassicalRK4.hh"
42 #include "G4CashKarpRKF45.hh" <<
43 #include "G4SimpleRunge.hh" <<
44 #include "G4HelixImplicitEuler.hh" <<
45 #include "G4HelixExplicitEuler.hh" <<
46 #include "G4HelixSimpleRunge.hh" <<
47 #include "G4ExactHelixStepper.hh" <<
48 #include "G4ExplicitEuler.hh" <<
49 #include "G4ImplicitEuler.hh" <<
50 #include "G4SimpleHeum.hh" <<
51 #include "G4RKG3_Stepper.hh" <<
52 #include "G4NystromRK4.hh" <<
53 <<
54 // Additional potential steppers <<
55 #include "G4DormandPrince745.hh" <<
56 #include "G4BogackiShampine23.hh" <<
57 #include "G4BogackiShampine45.hh" <<
58 #include "G4TsitourasRK45.hh" <<
59 <<
60 #include "G4ThreeVector.hh" 42 #include "G4ThreeVector.hh"
61 #include "G4LineSection.hh" << 43 G4HelixMixedStepper::G4HelixMixedStepper(G4Mag_EqRhs *EqRhs)
62 <<
63 // ------------------------------------------- <<
64 G4HelixMixedStepper:: <<
65 G4HelixMixedStepper(G4Mag_EqRhs* EqRhs, <<
66 G4int stepperNumber <<
67 G4double angleThreshol <<
68 : G4MagHelicalStepper(EqRhs) 44 : G4MagHelicalStepper(EqRhs)
>> 45
69 { 46 {
70 if( angleThreshold < 0.0 ) << 47
71 { << 48 fRK4Stepper= new G4ClassicalRK4(EqRhs);
72 fAngle_threshold = (1.0/3.0)*pi; <<
73 } <<
74 else <<
75 { <<
76 fAngle_threshold = angleThreshold; <<
77 } <<
78 <<
79 if(stepperNumber<0) <<
80 { <<
81 // stepperNumber = 4; // Default is RK4 <<
82 stepperNumber = 745; // Default is Dorm <<
83 // stepperNumber = 8; // Default is Cash <<
84 } <<
85 <<
86 fStepperNumber = stepperNumber; // Store th <<
87 fRK4Stepper = SetupStepper(EqRhs, fStepper <<
88 } 49 }
89 50
90 // ------------------------------------------- << 51 G4HelixMixedStepper::~G4HelixMixedStepper() {
91 G4HelixMixedStepper::~G4HelixMixedStepper() << 52 delete(fRK4Stepper);
92 { << 53 }
93 delete fRK4Stepper; << 54 void G4HelixMixedStepper::Stepper( const G4double yInput[7],
94 if (fVerbose>0) { PrintCalls(); } << 55 const G4double dydx[7],
95 } << 56 G4double Step,
>> 57 G4double yOut[7],
>> 58 G4double yErr[])
96 59
97 // ------------------------------------------- <<
98 void G4HelixMixedStepper::Stepper( const G4do <<
99 const G4do <<
100 G4do <<
101 G4do <<
102 G4do <<
103 { 60 {
104 // Estimation of the Stepping Angle << 61
105 // << 62 //Estimation of the Stepping Angle
>> 63
106 G4ThreeVector Bfld; 64 G4ThreeVector Bfld;
107 MagFieldEvaluate(yInput, Bfld); << 65 MagFieldEvaluate(yInput, Bfld);
108 << 66
109 G4double Bmag = Bfld.mag(); 67 G4double Bmag = Bfld.mag();
110 const G4double* pIn = yInput+3; << 68 const G4double *pIn = yInput+3;
111 G4ThreeVector initVelocity = G4ThreeVector( << 69 G4ThreeVector initVelocity= G4ThreeVector( pIn[0], pIn[1], pIn[2]);
112 G4double velocityVal = initVelocity.mag(); << 70 G4double velocityVal = initVelocity.mag();
113 << 71 G4double R_1;
114 const G4double R_1 = std::abs(GetInverseCurv << 72 G4double Ang_curve;
115 // curv = inverse Radius << 73
116 G4double Ang_curve = R_1 * Step; << 74 R_1=std::abs(GetInverseCurve(velocityVal,Bmag));
117 // SetAngCurve(Ang_curve); << 75 Ang_curve=R_1*Step;
118 // SetCurve(std::abs(1/R_1)); << 76 SetAngCurve(Ang_curve);
119 << 77 fLastStepSize=Step;
120 if(Ang_curve < fAngle_threshold) <<
121 { <<
122 ++fNumCallsRK4; <<
123 fRK4Stepper->Stepper(yInput,dydx,Step,yOut <<
124 } <<
125 else <<
126 { <<
127 constexpr G4int nvar = 6 ; <<
128 constexpr G4int nvarMax = 8 ; <<
129 G4double yTemp[nvarMax], yIn[nvarMax] <<
130 G4ThreeVector Bfld_midpoint; <<
131 <<
132 SetAngCurve(Ang_curve); <<
133 SetCurve(std::abs(1.0/R_1)); <<
134 ++fNumCallsHelix; <<
135 <<
136 // Saving yInput because yInput and yOut c <<
137 // <<
138 for(G4int i=0; i<nvar; ++i) <<
139 { <<
140 yIn[i]=yInput[i]; <<
141 } <<
142 <<
143 G4double halfS = Step * 0.5; <<
144 78
145 // 1. Do first half step and full step << 79 if(Ang_curve<0.33*pi){
146 // <<
147 AdvanceHelix(yIn, Bfld, halfS, yTemp, yTem <<
148 <<
149 MagFieldEvaluate(yTemp, Bfld_midpoint) ; <<
150 <<
151 // 2. Do second half step - with revised f <<
152 // NOTE: Could avoid this call if 'Bfld_m <<
153 // or diff 'almost' zero <<
154 // <<
155 AdvanceHelix(yTemp, Bfld_midpoint, halfS, <<
156 // Not requesting y at s=2*h (halfS) <<
157 80
158 // 3. Estimate the integration error << 81 fRK4Stepper->Stepper(yInput,dydx,Step,yOut,yErr);
159 // should be (nearly) zero if Bfield= c << 82
160 // << 83 }
161 for(G4int i=0; i<nvar; ++i) << 84 else{
162 { << 85 const G4int nvar = 6 ;
163 yErr[i] = yOut[i] - yTemp2[i]; << 86 G4int i;
>> 87 G4double yTemp[7], yIn[7] ;
>> 88 G4ThreeVector Bfld_midpoint;
>> 89 // Saving yInput because yInput and yOut can be aliases for same array
>> 90 for(i=0;i<nvar;i++) yIn[i]=yInput[i];
>> 91
>> 92 G4double h = Step * 0.5;
>> 93
>> 94 // Do two half steps
>> 95 AdvanceHelix(yIn, Bfld, h, yTemp);
>> 96 MagFieldEvaluate(yTemp, Bfld_midpoint) ;
>> 97 AdvanceHelix(yTemp, Bfld_midpoint, h, yOut);
>> 98 // Do a full step
>> 99 h = Step ;
>> 100 AdvanceHelix(yIn, Bfld, h, yTemp);
>> 101 // Error estimation
>> 102 for(i=0;i<nvar;i++) {
>> 103 yErr[i] = yOut[i] - yTemp[i] ;
>> 104 }
164 } 105 }
165 } << 106
>> 107
>> 108
>> 109
166 } 110 }
167 111
168 // ------------------------------------------- << 112 void
169 void G4HelixMixedStepper::DumbStepper( const G << 113 G4HelixMixedStepper::DumbStepper( const G4double yIn[],
170 G << 114 G4ThreeVector Bfld,
171 G << 115 G4double h,
172 G << 116 G4double yOut[])
173 { 117 {
174 AdvanceHelix(yIn, Bfld, h, yOut); << 118
175 } << 119
>> 120 AdvanceHelix(yIn, Bfld, h, yOut);
176 121
>> 122
>> 123
>> 124 }
177 // ------------------------------------------- 125 // ---------------------------------------------------------------------------
178 G4double G4HelixMixedStepper::DistChord() cons << 126
>> 127 G4double G4HelixMixedStepper::DistChord() const
179 { 128 {
180 // Implementation : must check whether h/R > 129 // Implementation : must check whether h/R > 2 pi !!
181 // If( h/R < pi) use G4LineSection::DistL 130 // If( h/R < pi) use G4LineSection::DistLine
182 // Else DistChord=R_helix 131 // Else DistChord=R_helix
183 // 132 //
184 G4double distChord; 133 G4double distChord;
>> 134 G4double H_helix;
>> 135 H_helix=fLastStepSize;
185 G4double Ang_curve=GetAngCurve(); 136 G4double Ang_curve=GetAngCurve();
186 137
187 if(Ang_curve<=pi) << 138 if(Ang_curve<pi){
188 { << 139
189 distChord=GetRadHelix()*(1-std::cos(0.5*An << 140 distChord=0.5*H_helix*std::tan(0.25*Ang_curve);
190 } <<
191 else <<
192 { <<
193 if(Ang_curve<twopi) <<
194 { <<
195 distChord=GetRadHelix()*(1+std::cos(0.5* <<
196 } <<
197 else <<
198 { <<
199 distChord=2.*GetRadHelix(); <<
200 } <<
201 } <<
202 <<
203 return distChord; <<
204 } <<
205 <<
206 // ------------------------------------------- <<
207 void G4HelixMixedStepper::PrintCalls() <<
208 { <<
209 G4cout << "In HelixMixedStepper::Number of c <<
210 << fNumCallsRK4 <<
211 << " and Number of calls to Helix = <<
212 } <<
213 141
214 // ------------------------------------------- <<
215 G4MagIntegratorStepper* <<
216 G4HelixMixedStepper::SetupStepper(G4Mag_EqRhs* <<
217 { <<
218 G4MagIntegratorStepper* pStepper; <<
219 if (fVerbose>0) { G4cout << " G4HelixMixedSt <<
220 } <<
221 switch ( StepperNumber ) <<
222 { <<
223 // Robust, classic method <<
224 case 4: <<
225 pStepper = new G4ClassicalRK4( pE ); <<
226 if (fVerbose>0) { G4cout << "G4Classic <<
227 break; <<
228 <<
229 // Steppers with embedded estimation of <<
230 case 8: <<
231 pStepper = new G4CashKarpRKF45( pE ); <<
232 if (fVerbose>0) { G4cout << "G4CashKar <<
233 break; <<
234 case 13: <<
235 pStepper = new G4NystromRK4( pE ); <<
236 if (fVerbose>0) { G4cout << "G4Nystrom <<
237 break; <<
238 <<
239 // Lowest order RK Stepper - experimenta <<
240 case 1: <<
241 pStepper = new G4ImplicitEuler( pE ); <<
242 if (fVerbose>0) { G4cout << "G4Implici <<
243 break; <<
244 <<
245 // Lower order RK Steppers - ok overall, <<
246 case 2: <<
247 pStepper = new G4SimpleRunge( pE ); <<
248 if (fVerbose>0) { G4cout << "G4SimpleR <<
249 break; <<
250 case 3: <<
251 pStepper = new G4SimpleHeum( pE ); <<
252 if (fVerbose>0) { G4cout << "G4SimpleH <<
253 break; <<
254 case 23: <<
255 pStepper = new G4BogackiShampine23( pE <<
256 if (fVerbose>0) { G4cout << "G4Bogacki <<
257 break; <<
258 <<
259 // Higher order RK Steppers <<
260 // for smoother fields and high accuracy <<
261 case 45: <<
262 pStepper = new G4BogackiShampine45( pE <<
263 if (fVerbose>0) { G4cout << "G4Bogacki <<
264 break; <<
265 case 145: <<
266 pStepper = new G4TsitourasRK45( pE ); <<
267 if (fVerbose>0) { G4cout << "G4Tsitour <<
268 break; <<
269 case 745: <<
270 pStepper = new G4DormandPrince745( pE <<
271 if (fVerbose>0) { G4cout << "G4Dormand <<
272 break; <<
273 <<
274 // Helical Steppers <<
275 case 6: <<
276 pStepper = new G4HelixImplicitEuler( p <<
277 if (fVerbose>0) { G4cout << "G4HelixIm <<
278 break; <<
279 case 7: <<
280 pStepper = new G4HelixSimpleRunge( pE <<
281 if (fVerbose>0) { G4cout << "G4HelixSi <<
282 break; <<
283 case 5: <<
284 pStepper = new G4HelixExplicitEuler( p <<
285 if (fVerbose>0) { G4cout << "G4HelixEx <<
286 break; // Since Helix Explicit is use <<
287 // this is useful only to measu <<
288 // Exact Helix - likely good only for ca <<
289 // i) uniform field (potentia <<
290 // ii) segmented uniform field <<
291 case 9: <<
292 pStepper = new G4ExactHelixStepper( pE <<
293 if (fVerbose>0) { G4cout << "G4ExactHe <<
294 break; <<
295 case 10: <<
296 pStepper = new G4RKG3_Stepper( pE ); <<
297 if (fVerbose>0) { G4cout << "G4RKG3_St <<
298 break; <<
299 <<
300 // Low Order Steppers - not good except <<
301 case 11: <<
302 pStepper = new G4ExplicitEuler( pE ); <<
303 if (fVerbose>0) { G4cout << "G4Explici <<
304 break; <<
305 case 12: <<
306 pStepper = new G4ImplicitEuler( pE ); <<
307 if (fVerbose>0) { G4cout << "G4Implici <<
308 break; <<
309 <<
310 case 0: <<
311 case -1: <<
312 default: <<
313 pStepper = new G4DormandPrince745( pE <<
314 if (fVerbose>0) { G4cout << "G4Dormand <<
315 break; <<
316 } 142 }
317 << 143 else{
318 if(fVerbose>0) << 144 distChord=GetRadHelix();
319 { <<
320 G4cout << " chosen as stepper for small st <<
321 << G4endl; <<
322 } 145 }
323 << 146
324 return pStepper; << 147 return distChord;
>> 148
325 } 149 }
326 150