Useful resources

- Numerical Recipes in C

- Will Hossack's Java example page including Runge-Kutta integrator examples

ToDo List

Schedule for next 2 weeks (30/07 - 14/08)

• Read around and understand Runge-Kutta 4 (RK4) integration method and its computational implementation.

1. Consider attempt to integrate a self-regulating stepsize control into RK4 functions. eg. Variable stepsize depending on difference between k2 and k3 (2nd and 3rd gradients calculated).
2. Adaptive step-size achieved through error analysis during RK4 loop

• Research and work through Electromagnetic equation of motion involving RK4 method.
• Understand RK4 in reference to a parabolic path.
• Understand errors in all of above (accuracy of method).
• Write and run through C++ program showing electron trajectory in simple EM field.

1. C++ RK4 integrator up and running using Lorentz differential equation to track particle in EM field. Seems to be accurate to 0.07% in 14 million steps.

• Create simple EM field Geant4 example in vacumn (or very low density gas) and run electrons through it to compare trajectories with previous C++ code.
• Port current C++ RK4 version to CUDA.

1. Above involves deciding how to change RK4 algorithm to parallel, what to put in CUDA kernal.
2. Investigate speed ups from port.

• Fully understand G4ClassicalRK4 and G4ConstRK4 and Richardson Extrapolation error correction method in G4MagErrorStepper, as well as ( 1 << IntegrationOrder()) section in MagErrorStepper (possible bitwise operator?)
• Investigate and understand Nystrom RK4 method for time indep fields and read ATLAS paper on Nystrom method.

-- PhilipClark - 30-Jul-2010