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jonapost / field_propagation

Module for integrating a track's trajectory in a field, whether magnetic, electric, combined electromagnetic, or also including gravity or other forces.
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Implement G4VRevisedChordFinder #18

Open dmitrySorokin opened 8 years ago

dmitrySorokin commented 8 years ago

G4RevisedChordFinder class should be able to provide different strategies for finding the next chord and location of the intersection point for drivers with and without interpolation.

dmitrySorokin commented 8 years ago

This is a class diagram for the field propagation project. The new class G4ReviseChordFinder can apply different algorithms for drivers with interpolation (Bulirsch-Stoer, Bogacki-Shampine45) and without it.

uml For drivers with interpolation I have decided to use the following algorithm:

  1. Do one good step with error control (possibly large step).
  2. Divide it to substeps satisfying the chord condition (d < fDeltaChord) using interpolation
  3. If the track intersects with geometry use interpolation to find the intersection point
dmitrySorokin commented 8 years ago

For testing purposes I have created a test called SimplePropatation. This test simulates movement of 1 MeV proton in uniform magnetic field directed along Y axe. Initial momentum direction is (sqrt(2)/2, sqrt(2)/2, 0). In this test it is possible to compare position and intersection points with analytical solution. The only one used process is transportation.

track

Using this test I have tested ClassicalRK, CashKarp and Bulirsch-Stoer algorithms. All of them are producing exactly the same output:

Step# X(mm) Y(mm) Z(mm) KinE(MeV) dE(MeV) StepLeng TrackLeng NextVolume ProcName
0 0 -742 -102 1 0 0 0 World initStep
1 -0.171 -100 -102 1 0 908 908 Cube Transportation
2 94.7 100 38.3 1 0 283 1.19e+03 World Transportation
3 -71.2 300 73.3 1 0 283 1.47e+03 Cube2 Transportation
4 -41.1 500 -93.6 1 0 283 1.76e+03 World Transportation
5 -99.4 1e+03 23.7 1 0 707 2.46e+03 OutOfWorld Transportation

Number of field evaluations is shown in the table below.

Algorithm Number of field evaluatons error
ClassicalRK 4307 2.06e-06
CashKarp 1457 2.00e-05
Bulirsch-Stoer (dense) 1195 6.54e-05
Bulirsch-Stoer (non-dense) 2182 1.83e-06

The error has been calculated using difference between analytical and numerical solutions:

In this test I used the following parameters: DeltaOneStep: 0.0001 DeltaIntersection: 1e-05. It is clearly seen from the table that for each algorithm misplacement error doesn't exceed the DeltaOneStep value.

dmitrySorokin commented 8 years ago

Running testNTST I've got the following results. run2a.mac

UPD1: Add results of Bogacki-Shampine45 (non-dese) UPD2: Add results of Bogacki-Shampine45 (dense)

Algorithm Number of field evaluations
ClassicalRK 258'202'511
CashKarp 197'812'070
Bogacki-Shampine45 (non-dense) 196'841'663
Bulirsch-Stoer (non-dense) 165'822'246
Bulirsch-Stoer (dense) 70'629'309
Bogacki-Shampine45 (dense) 33'267'828

run2b.mac

Algorithm Number of field evaluations
ClassicalRK 1'310'095'739
CashKarp 637'558'303
Bogacki-Shampine45 (non-dense) 584'907'614
Bulirsch-Stoer (non-dense) 881'546'608
Bulirsch-Stoer (dense) 325'747'133
Bogacki-Shampine45 (dense) 203'119'876

run2c.mac

Algorithm Number of field evaluations
ClassicalRK 4'359'099'222
CashKarp 1'996'530'125
Bogacki-Shampine45 (non-dense) 1'763'054'970
Bulirsch-Stoer (non-dense) 2'705'914'123
Bulirsch-Stoer (dense) 1'731'185'999
Bogacki-Shampine45 (dense) 1'250'251'457
jonapost commented 8 years ago

Results are very promising indeed !! Great to see.