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AdamMarekWermus02

Hello and welcome to my research page. My focus is on applying the Parker-Sochacki Method to different physical simulations comparing it against numerical methods currently used in the animation industry.

There is also a section for Motion Capture, Stereoscopy, and Trumpet Research.

 

N-Body Gravity: Comparing Different Integrators

Here you will see images of a 3-body gravity problem all under the same initial conditions following this pattern:PS_3

I am going to show that at higher orders, Parker-Sochacki can take the largest time step maintaining accuracy compared to Forward Euler, Semi-Implicit Euler, Velocity Verlet, Runge-Kutta 2 Midpoint Method, and Runge-Kutta 4th Order. At 8th Order, Parker-Sochacki can take a time step of 0.001 for this 3 body problem. I will show what the other integrators look like at that same time step followed by what time step they need to have the same accuracy as Parker-Sochacki.

Forward_Euler_1

Semi_Implicit_Euler_1Velocity_Verlet.PNG

RK2_Midpoint_1.PNG

RK4_1

Forward Euler, Runge-Kutta 2 Midpoint Method, and Runge-Kutta 4th Order blow up. Semi-Implicit Euler and Velocity Verlet are stable but not accurate.

To see N-body patterns, refer to the Particle Systems section.