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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
33 // use Stepper for small step(Classical 33 // use Stepper for small step(ClassicalRK4 by default)
34 // Else use HelixExplicitEuler Stepper 34 // Else use HelixExplicitEuler Stepper
35 // 35 //
36 // Created: T.Nikitina, CERN - 18.05.2007, der << 36 // History:
>> 37 // Derived from ExactHelicalStepper 18/05/07
>> 38 //
37 // ------------------------------------------- 39 // -------------------------------------------------------------------------
38 40
39 #include "G4HelixMixedStepper.hh" 41 #include "G4HelixMixedStepper.hh"
40 #include "G4PhysicalConstants.hh" 42 #include "G4PhysicalConstants.hh"
41 #include "G4ClassicalRK4.hh" 43 #include "G4ClassicalRK4.hh"
42 #include "G4CashKarpRKF45.hh" 44 #include "G4CashKarpRKF45.hh"
43 #include "G4SimpleRunge.hh" 45 #include "G4SimpleRunge.hh"
44 #include "G4HelixImplicitEuler.hh" 46 #include "G4HelixImplicitEuler.hh"
45 #include "G4HelixExplicitEuler.hh" 47 #include "G4HelixExplicitEuler.hh"
46 #include "G4HelixSimpleRunge.hh" 48 #include "G4HelixSimpleRunge.hh"
47 #include "G4ExactHelixStepper.hh" 49 #include "G4ExactHelixStepper.hh"
48 #include "G4ExplicitEuler.hh" 50 #include "G4ExplicitEuler.hh"
49 #include "G4ImplicitEuler.hh" 51 #include "G4ImplicitEuler.hh"
50 #include "G4SimpleHeum.hh" 52 #include "G4SimpleHeum.hh"
51 #include "G4RKG3_Stepper.hh" 53 #include "G4RKG3_Stepper.hh"
52 #include "G4NystromRK4.hh" 54 #include "G4NystromRK4.hh"
53 55
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" 56 #include "G4ThreeVector.hh"
61 #include "G4LineSection.hh" 57 #include "G4LineSection.hh"
62 58
63 // ------------------------------------------- << 59 G4HelixMixedStepper::G4HelixMixedStepper(G4Mag_EqRhs *EqRhs,G4int fStepperNumber, G4double angleThr)
64 G4HelixMixedStepper:: << 60 : G4MagHelicalStepper(EqRhs), fNumCallsRK4(0), fNumCallsHelix(0)
65 G4HelixMixedStepper(G4Mag_EqRhs* EqRhs, <<
66 G4int stepperNumber <<
67 G4double angleThreshol <<
68 : G4MagHelicalStepper(EqRhs) <<
69 { 61 {
70 if( angleThreshold < 0.0 ) << 62 SetVerbose(1);
71 { << 63 if( angleThr < 0.0 ){
72 fAngle_threshold = (1.0/3.0)*pi; << 64 fAngle_threshold= 0.33*pi;
73 } << 65 }else{
74 else << 66 fAngle_threshold= angleThr;
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 } 67 }
85 68
86 fStepperNumber = stepperNumber; // Store th << 69 if(fStepperNumber<0)
>> 70 fStepperNumber=4; // Default is RK4
87 fRK4Stepper = SetupStepper(EqRhs, fStepper 71 fRK4Stepper = SetupStepper(EqRhs, fStepperNumber);
88 } 72 }
89 73
90 // ------------------------------------------- <<
91 G4HelixMixedStepper::~G4HelixMixedStepper() 74 G4HelixMixedStepper::~G4HelixMixedStepper()
92 { 75 {
93 delete fRK4Stepper; << 76 delete(fRK4Stepper);
94 if (fVerbose>0) { PrintCalls(); } << 77 if (fVerbose>0){ PrintCalls();};
95 } 78 }
96 79
97 // ------------------------------------------- << 80 void G4HelixMixedStepper::Stepper( const G4double yInput[7],
98 void G4HelixMixedStepper::Stepper( const G4do << 81 const G4double dydx[7],
99 const G4do << 82 G4double Step,
100 G4do << 83 G4double yOut[7],
101 G4do << 84 G4double yErr[])
102 G4do << 85
103 { 86 {
104 // Estimation of the Stepping Angle << 87 //Estimation of the Stepping Angle
105 // << 88
106 G4ThreeVector Bfld; 89 G4ThreeVector Bfld;
107 MagFieldEvaluate(yInput, Bfld); 90 MagFieldEvaluate(yInput, Bfld);
108 91
109 G4double Bmag = Bfld.mag(); 92 G4double Bmag = Bfld.mag();
110 const G4double* pIn = yInput+3; << 93 const G4double *pIn = yInput+3;
111 G4ThreeVector initVelocity = G4ThreeVector( << 94 G4ThreeVector initVelocity= G4ThreeVector( pIn[0], pIn[1], pIn[2]);
112 G4double velocityVal = initVelocity.mag(); << 95 G4double velocityVal = initVelocity.mag();
113 << 96 G4double R_1;
114 const G4double R_1 = std::abs(GetInverseCurv << 97 G4double Ang_curve;
115 // curv = inverse Radius << 98
116 G4double Ang_curve = R_1 * Step; << 99 R_1=std::abs(GetInverseCurve(velocityVal,Bmag));
117 // SetAngCurve(Ang_curve); << 100 Ang_curve=R_1*Step;
118 // SetCurve(std::abs(1/R_1)); << 101 SetAngCurve(Ang_curve);
119 << 102 SetCurve(std::abs(1/R_1));
120 if(Ang_curve < fAngle_threshold) << 103
121 { << 104 if(Ang_curve< fAngle_threshold){
122 ++fNumCallsRK4; << 105 fNumCallsRK4++;
123 fRK4Stepper->Stepper(yInput,dydx,Step,yOut 106 fRK4Stepper->Stepper(yInput,dydx,Step,yOut,yErr);
124 } 107 }
125 else 108 else
126 { 109 {
127 constexpr G4int nvar = 6 ; << 110 fNumCallsHelix++;
128 constexpr G4int nvarMax = 8 ; << 111 const G4int nvar = 6 ;
129 G4double yTemp[nvarMax], yIn[nvarMax] << 112 G4int i;
130 G4ThreeVector Bfld_midpoint; << 113 G4double yTemp[7], yIn[7], yTemp2[7];
131 << 114 G4ThreeVector Bfld_midpoint;
132 SetAngCurve(Ang_curve); << 115
133 SetCurve(std::abs(1.0/R_1)); << 116 // Saving yInput because yInput and yOut can be aliases for same array
134 ++fNumCallsHelix; << 117 for(i=0;i<nvar;i++) yIn[i]=yInput[i];
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 } <<
142 118
143 G4double halfS = Step * 0.5; 119 G4double halfS = Step * 0.5;
144 <<
145 // 1. Do first half step and full step 120 // 1. Do first half step and full step
146 // << 121 AdvanceHelix(yIn, Bfld, halfS, yTemp, yTemp2); // yTemp2 for s=2*h (halfS)
147 AdvanceHelix(yIn, Bfld, halfS, yTemp, yTem << 122 //**********
148 123
149 MagFieldEvaluate(yTemp, Bfld_midpoint) ; 124 MagFieldEvaluate(yTemp, Bfld_midpoint) ;
150 125
151 // 2. Do second half step - with revised f 126 // 2. Do second half step - with revised field
152 // NOTE: Could avoid this call if 'Bfld_m << 127 // NOTE: Could avoid this call if 'Bfld_midpoint == Bfld' or diff 'almost' zero
153 // or diff 'almost' zero << 128 AdvanceHelix(yTemp, Bfld_midpoint, halfS, yOut); // Not requesting y at s=2*h (halfS)
154 // << 129 //**********
155 AdvanceHelix(yTemp, Bfld_midpoint, halfS, <<
156 // Not requesting y at s=2*h (halfS) <<
157 130
158 // 3. Estimate the integration error << 131 // 3. Estimate the integration error - should be (nearly) zero if Bfield= constant
159 // should be (nearly) zero if Bfield= c << 132 for(i=0;i<nvar;i++) {
160 // << 133 yErr[i] = yOut[i] - yTemp2[i] ;
161 for(G4int i=0; i<nvar; ++i) <<
162 { <<
163 yErr[i] = yOut[i] - yTemp2[i]; <<
164 } 134 }
165 } 135 }
166 } 136 }
167 137
168 // ------------------------------------------- << 138 void
169 void G4HelixMixedStepper::DumbStepper( const G << 139 G4HelixMixedStepper::DumbStepper( const G4double yIn[],
170 G << 140 G4ThreeVector Bfld,
171 G << 141 G4double h,
172 G << 142 G4double yOut[])
173 { 143 {
174 AdvanceHelix(yIn, Bfld, h, yOut); 144 AdvanceHelix(yIn, Bfld, h, yOut);
175 } 145 }
176 146
177 // ------------------------------------------- << 147 G4double G4HelixMixedStepper::DistChord() const
178 G4double G4HelixMixedStepper::DistChord() cons <<
179 { 148 {
180 // Implementation : must check whether h/R > 149 // Implementation : must check whether h/R > 2 pi !!
181 // If( h/R < pi) use G4LineSection::DistL 150 // If( h/R < pi) use G4LineSection::DistLine
182 // Else DistChord=R_helix 151 // Else DistChord=R_helix
183 // 152 //
184 G4double distChord; 153 G4double distChord;
185 G4double Ang_curve=GetAngCurve(); 154 G4double Ang_curve=GetAngCurve();
186 155
187 if(Ang_curve<=pi) << 156 if(Ang_curve<=pi){
188 { <<
189 distChord=GetRadHelix()*(1-std::cos(0.5*An 157 distChord=GetRadHelix()*(1-std::cos(0.5*Ang_curve));
190 } 158 }
191 else 159 else
192 { 160 {
193 if(Ang_curve<twopi) << 161 if(Ang_curve<twopi){
194 { <<
195 distChord=GetRadHelix()*(1+std::cos(0.5* 162 distChord=GetRadHelix()*(1+std::cos(0.5*(twopi-Ang_curve)));
196 } 163 }
197 else << 164 else{
198 { <<
199 distChord=2.*GetRadHelix(); 165 distChord=2.*GetRadHelix();
200 } 166 }
201 } 167 }
202 168
203 return distChord; 169 return distChord;
204 } 170 }
205 171
206 // ------------------------------------------- 172 // ---------------------------------------------------------------------------
207 void G4HelixMixedStepper::PrintCalls() 173 void G4HelixMixedStepper::PrintCalls()
208 { 174 {
209 G4cout << "In HelixMixedStepper::Number of c << 175 G4cout<<"In HelixMixedStepper::Number of calls to smallStepStepper = "<<fNumCallsRK4
210 << fNumCallsRK4 << 176 <<" and Number of calls to Helix = "<<fNumCallsHelix<<G4endl;
211 << " and Number of calls to Helix = <<
212 } 177 }
213 178
214 // ------------------------------------------- <<
215 G4MagIntegratorStepper* 179 G4MagIntegratorStepper*
216 G4HelixMixedStepper::SetupStepper(G4Mag_EqRhs* 180 G4HelixMixedStepper::SetupStepper(G4Mag_EqRhs* pE, G4int StepperNumber)
217 { 181 {
218 G4MagIntegratorStepper* pStepper; 182 G4MagIntegratorStepper* pStepper;
219 if (fVerbose>0) { G4cout << " G4HelixMixedSt << 183 if (fVerbose>0)
220 } << 184 G4cout<<"In G4HelixMixedStepper: Choosing Stepper for small steps. Choice is ";
221 switch ( StepperNumber ) 185 switch ( StepperNumber )
222 { << 186 {
223 // Robust, classic method << 187 case 0:
224 case 4: << 188 case 4: pStepper = new G4ClassicalRK4( pE ); if (fVerbose>0)G4cout<<"G4ClassicalRK4"<<G4endl; break;
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 } <<
317 <<
318 if(fVerbose>0) <<
319 { <<
320 G4cout << " chosen as stepper for small st <<
321 << G4endl; <<
322 } <<
323 189
>> 190 // Steppers with embedded estimation of error
>> 191 case 1: pStepper = new G4NystromRK4( pE ); if (fVerbose>0)G4cout<<"G4NystromRK4"<<G4endl; break;
>> 192 case 8: pStepper = new G4CashKarpRKF45( pE ); if (fVerbose>0)G4cout<<"G4CashKarpRKF45"<<G4endl; break;
>> 193
>> 194 // Lower order RK Steppers - ok overall, good for uneven fields
>> 195 case 2: pStepper = new G4SimpleRunge( pE ); if (fVerbose>0)G4cout<<"G4SimpleRunge"<<G4endl; break;
>> 196 case 3: pStepper = new G4SimpleHeum( pE ); if (fVerbose>0)G4cout<<"G4SimpleHeum"<<G4endl;break;
>> 197
>> 198 // Helical Steppers -
>> 199 // Since these are used for long steps, less useful
>> 200 case 5: pStepper = new G4HelixExplicitEuler( pE ); if (fVerbose>0)G4cout<<"G4HelixExplicitEuler"<<G4endl; break;
>> 201 case 6: pStepper = new G4HelixImplicitEuler( pE ); if (fVerbose>0)G4cout<<"G4HelixImplicitEuler"<<G4endl; break;
>> 202 case 7: pStepper = new G4HelixSimpleRunge( pE ); if (fVerbose>0)G4cout<<"G4HelixSimpleRunge"<<G4endl; break;
>> 203
>> 204 // Exact Helix - only for cases of i)uniform field
>> 205 // ii) segmented uniform field (maybe)
>> 206 case 9: pStepper = new G4ExactHelixStepper( pE ); if (fVerbose>0)G4cout<<"G4ExactHelixStepper"<<G4endl; break;
>> 207
>> 208 case 10: pStepper = new G4RKG3_Stepper( pE ); if (fVerbose>0)G4cout<<"G4RKG3_Stepper"<<G4endl; break;
>> 209
>> 210 // Low Order Steppers - not good except for very weak fields
>> 211 case 11: pStepper = new G4ExplicitEuler( pE ); if (fVerbose>0)G4cout<<"G4ExplicitEuler"<<G4endl; break;
>> 212 case 12: pStepper = new G4ImplicitEuler( pE ); if (fVerbose>0)G4cout<<"G4ImplicitEuler"<<G4endl; break;
>> 213
>> 214 case -1:
>> 215 default: pStepper = new G4ClassicalRK4( pE );G4cout<<"G4ClassicalRK4 (Default)."<<G4endl; break;
>> 216
>> 217 }
324 return pStepper; 218 return pStepper;
325 } 219 }
326 220