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Meeting 2015 09 18

Results from previous meeting

Last week we didn't have the opportunity to discuss the results.
Please review the corresponding wiki entry

General comments

The goal for this week was to add basic geometries and check whether the results differed from the previous ones.
We decided to add planes in constant x values, covering all the y and z values.
The planes were positioned in:
-40mm, -32mm, 24mm, -16mm, -8mm, 0mm, 8mm, 16mm, 24mm, 32mm, 40mm

/N02/det/trackMaxSteps 1000000000
/N02/det/trackMaxLen 1 km
/gun/energy 10.9181415106 MeV
/N02/prec/setDeltaOne 1.0e-2 mm
/N02/prec/setDeltaInt 1.0e-5 mm
/N02/prec/setEpsilonMin 1.0e-5
/N02/prec/setEpsilonMax 1.0e-5
/N02/prec/setDeltaChord 0.25 mm
/N02/det/stepMax 20. mm

  • All measured times correspond to executions (both of G4 or PD) which don't produce output at all (or produce a minimum logging).
  • MSE is the Mean Squared Error of the position
  • MSE = 1/N * sum_{i=1}^{N} (G4x_i - ANx_i)^2 + (G4y_i - ANy_i)^2
  • N = Number of output points
  • r_Error = sqrt(MSE)
  • max(X_Error) is the maximum of all the absolute errors in x, i.e. max(abs(G4x_i - ANx_i))

G4 comparison

As can be seen in subsequent the table and the figures, the solutions crossing and without crossing the geometry seem to be the same.
The time for the simulation with geometry crossing, however, seems to be larger. Further analysis should be done to verify this hypothesis.

Simulation Time RHS evaluation steps r_Error [mm] Max(X_Error) [mm]
Crossing Geometry 1.57s 1.65e6 1.73 3.12
Without Crossing Geometry 1.42s 1.65e6 1.73 3.12

Position Comparison


Figure 1: X_position without crossing geometries


Figure 2: X_position crossing geometries


Figure 3: Y_position without crossing geometries


Figure 4: Y_position crossing geometries

Position Comparison for first oscillations


Figure 5: X_position for first oscillations without crossing geometries


Figure 6: X_position for first oscillations crossing geometries


Figure 7: Y_position for first oscillations without crossing geometries


Figure 8: Y_position for first oscillations crossing geometries

Error Comparison:


Figure 9: X_error without crossing geometries


Figure 10: X_error crossing geometries

PD comparison

As can be seen in the subsequent table and the figures, the solutions crossing and without crossing the geometry seem to be the same.
The simulation time seems to be similar. Further analysis should be done to verify this hypothesis.

Simulated with QSS3 method
DeltaQmin = DeltaQ * 1e-3 = 1e-5 * 1e-3

Simulation Time Equivalent in PD to RHS eval steps r_Error [mm] Max(X_Error) [mm]
Crossing Geometry 3.95s 3.08e6 1.09 2.20
Without Crossing Geometry 3.90s 3.08e6 1.09 2.20

Position Comparison


Figure 11: X_position without crossing geometries


Figure 12: X_position crossing geometries


Figure 13: Y_position without crossing geometries


Figure 14: Y_position crossing geometries

Position Comparison for first oscillations


Figure 15: X_position for first oscillations without crossing geometries


Figure 16: X_position for first oscillations crossing geometries


Figure 17: Y_position for first oscillations without crossing geometries


Figure 18: Y_position for first oscillations crossing geometries

Error Comparison:


Figure 19: X_error without crossing geometries


Figure 20: X_error crossing geometries