# 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

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] 1.57s 1.65e6 1.73 3.12 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] 3.95s 3.08e6 1.09 2.20 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