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25 //
26 // class G4HelixMixedStepper
27 //
28 // Class description:
29 //
30 // G4HelixMixedStepper split the Method used for Integration in two:
31 //
32 // If Stepping Angle ( h / R_curve) < pi/3
33 // use Stepper for small step(ClassicalRK4 by default)
34 // Else use HelixExplicitEuler Stepper
35 //
36 // Created: T.Nikitina, CERN - 18.05.2007, derived from G4ExactHelicalStepper
37 // -------------------------------------------------------------------------
38
39 #include "G4HelixMixedStepper.hh"
40 #include "G4PhysicalConstants.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"
61 #include "G4LineSection.hh"
62
63 // ---------------------------------------------------------------------------
64 G4HelixMixedStepper::
65 G4HelixMixedStepper(G4Mag_EqRhs* EqRhs,
66 G4int stepperNumber,
67 G4double angleThreshold)
68 : G4MagHelicalStepper(EqRhs)
69 {
70 if( angleThreshold < 0.0 )
71 {
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 (original)
82 stepperNumber = 745; // Default is DormandPrince745 (ie DoPri5)
83 // stepperNumber = 8; // Default is CashKarp
84 }
85
86 fStepperNumber = stepperNumber; // Store the choice
87 fRK4Stepper = SetupStepper(EqRhs, fStepperNumber);
88 }
89
90 // ---------------------------------------------------------------------------
91 G4HelixMixedStepper::~G4HelixMixedStepper()
92 {
93 delete fRK4Stepper;
94 if (fVerbose>0) { PrintCalls(); }
95 }
96
97 // ---------------------------------------------------------------------------
98 void G4HelixMixedStepper::Stepper( const G4double yInput[], // [7]
99 const G4double dydx[], // [7]
100 G4double Step,
101 G4double yOut[], // [7]
102 G4double yErr[])
103 {
104 // Estimation of the Stepping Angle
105 //
106 G4ThreeVector Bfld;
107 MagFieldEvaluate(yInput, Bfld);
108
109 G4double Bmag = Bfld.mag();
110 const G4double* pIn = yInput+3;
111 G4ThreeVector initVelocity = G4ThreeVector( pIn[0], pIn[1], pIn[2] );
112 G4double velocityVal = initVelocity.mag();
113
114 const G4double R_1 = std::abs(GetInverseCurve(velocityVal,Bmag));
115 // curv = inverse Radius
116 G4double Ang_curve = R_1 * Step;
117 // SetAngCurve(Ang_curve);
118 // SetCurve(std::abs(1/R_1));
119
120 if(Ang_curve < fAngle_threshold)
121 {
122 ++fNumCallsRK4;
123 fRK4Stepper->Stepper(yInput,dydx,Step,yOut,yErr);
124 }
125 else
126 {
127 constexpr G4int nvar = 6 ;
128 constexpr G4int nvarMax = 8 ;
129 G4double yTemp[nvarMax], yIn[nvarMax], yTemp2[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 can be aliases for same array
137 //
138 for(G4int i=0; i<nvar; ++i)
139 {
140 yIn[i]=yInput[i];
141 }
142
143 G4double halfS = Step * 0.5;
144
145 // 1. Do first half step and full step
146 //
147 AdvanceHelix(yIn, Bfld, halfS, yTemp, yTemp2); // yTemp2 for s=2*h (halfS)
148
149 MagFieldEvaluate(yTemp, Bfld_midpoint) ;
150
151 // 2. Do second half step - with revised field
152 // NOTE: Could avoid this call if 'Bfld_midpoint == Bfld'
153 // or diff 'almost' zero
154 //
155 AdvanceHelix(yTemp, Bfld_midpoint, halfS, yOut);
156 // Not requesting y at s=2*h (halfS)
157
158 // 3. Estimate the integration error
159 // should be (nearly) zero if Bfield= constant
160 //
161 for(G4int i=0; i<nvar; ++i)
162 {
163 yErr[i] = yOut[i] - yTemp2[i];
164 }
165 }
166 }
167
168 // ---------------------------------------------------------------------------
169 void G4HelixMixedStepper::DumbStepper( const G4double yIn[],
170 G4ThreeVector Bfld,
171 G4double h,
172 G4double yOut[] )
173 {
174 AdvanceHelix(yIn, Bfld, h, yOut);
175 }
176
177 // ---------------------------------------------------------------------------
178 G4double G4HelixMixedStepper::DistChord() const
179 {
180 // Implementation : must check whether h/R > 2 pi !!
181 // If( h/R < pi) use G4LineSection::DistLine
182 // Else DistChord=R_helix
183 //
184 G4double distChord;
185 G4double Ang_curve=GetAngCurve();
186
187 if(Ang_curve<=pi)
188 {
189 distChord=GetRadHelix()*(1-std::cos(0.5*Ang_curve));
190 }
191 else
192 {
193 if(Ang_curve<twopi)
194 {
195 distChord=GetRadHelix()*(1+std::cos(0.5*(twopi-Ang_curve)));
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 calls to smallStepStepper = "
210 << fNumCallsRK4
211 << " and Number of calls to Helix = " << fNumCallsHelix << G4endl;
212 }
213
214 // ---------------------------------------------------------------------------
215 G4MagIntegratorStepper*
216 G4HelixMixedStepper::SetupStepper(G4Mag_EqRhs* pE, G4int StepperNumber)
217 {
218 G4MagIntegratorStepper* pStepper;
219 if (fVerbose>0) { G4cout << " G4HelixMixedStepper: ";
220 }
221 switch ( StepperNumber )
222 {
223 // Robust, classic method
224 case 4:
225 pStepper = new G4ClassicalRK4( pE );
226 if (fVerbose>0) { G4cout << "G4ClassicalRK4"; }
227 break;
228
229 // Steppers with embedded estimation of error
230 case 8:
231 pStepper = new G4CashKarpRKF45( pE );
232 if (fVerbose>0) { G4cout << "G4CashKarpRKF45"; }
233 break;
234 case 13:
235 pStepper = new G4NystromRK4( pE );
236 if (fVerbose>0) { G4cout << "G4NystromRK4"; }
237 break;
238
239 // Lowest order RK Stepper - experimental
240 case 1:
241 pStepper = new G4ImplicitEuler( pE );
242 if (fVerbose>0) { G4cout << "G4ImplicitEuler"; }
243 break;
244
245 // Lower order RK Steppers - ok overall, good for uneven fields
246 case 2:
247 pStepper = new G4SimpleRunge( pE );
248 if (fVerbose>0) { G4cout << "G4SimpleRunge"; }
249 break;
250 case 3:
251 pStepper = new G4SimpleHeum( pE );
252 if (fVerbose>0) { G4cout << "G4SimpleHeum"; }
253 break;
254 case 23:
255 pStepper = new G4BogackiShampine23( pE );
256 if (fVerbose>0) { G4cout << "G4BogackiShampine23"; }
257 break;
258
259 // Higher order RK Steppers
260 // for smoother fields and high accuracy requirements
261 case 45:
262 pStepper = new G4BogackiShampine45( pE );
263 if (fVerbose>0) { G4cout << "G4BogackiShampine45"; }
264 break;
265 case 145:
266 pStepper = new G4TsitourasRK45( pE );
267 if (fVerbose>0) { G4cout << "G4TsitourasRK45"; }
268 break;
269 case 745:
270 pStepper = new G4DormandPrince745( pE );
271 if (fVerbose>0) { G4cout << "G4DormandPrince745"; }
272 break;
273
274 // Helical Steppers
275 case 6:
276 pStepper = new G4HelixImplicitEuler( pE );
277 if (fVerbose>0) { G4cout << "G4HelixImplicitEuler"; }
278 break;
279 case 7:
280 pStepper = new G4HelixSimpleRunge( pE );
281 if (fVerbose>0) { G4cout << "G4HelixSimpleRunge"; }
282 break;
283 case 5:
284 pStepper = new G4HelixExplicitEuler( pE );
285 if (fVerbose>0) { G4cout << "G4HelixExplicitEuler"; }
286 break; // Since Helix Explicit is used for long steps,
287 // this is useful only to measure overhead.
288 // Exact Helix - likely good only for cases of
289 // i) uniform field (potentially over small distances)
290 // ii) segmented uniform field (maybe)
291 case 9:
292 pStepper = new G4ExactHelixStepper( pE );
293 if (fVerbose>0) { G4cout << "G4ExactHelixStepper"; }
294 break;
295 case 10:
296 pStepper = new G4RKG3_Stepper( pE );
297 if (fVerbose>0) { G4cout << "G4RKG3_Stepper"; }
298 break;
299
300 // Low Order Steppers - not good except for very weak fields
301 case 11:
302 pStepper = new G4ExplicitEuler( pE );
303 if (fVerbose>0) { G4cout << "G4ExplicitEuler"; }
304 break;
305 case 12:
306 pStepper = new G4ImplicitEuler( pE );
307 if (fVerbose>0) { G4cout << "G4ImplicitEuler"; }
308 break;
309
310 case 0:
311 case -1:
312 default:
313 pStepper = new G4DormandPrince745( pE ); // Was G4ClassicalRK4( pE );
314 if (fVerbose>0) { G4cout << "G4DormandPrince745 (Default)"; }
315 break;
316 }
317
318 if(fVerbose>0)
319 {
320 G4cout << " chosen as stepper for small steps in G4HelixMixedStepper."
321 << G4endl;
322 }
323
324 return pStepper;
325 }
326