Design of optimal Runge-Kutta methods - FEniCS Project

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Acknowledgments Some parts of this are joint work with: Aron Ahmadia Matteo Parsani D. Ketcheson (KAUST) 2 / 36
Outline 1 High order Runge-Kutta methods 2 Linear properties of Runge-Kutta methods 3 Nonlinear properties of Runge-Kutta methods 4 Putting it all together: some optimal methods and applications D. Ketcheson (KAUST) 3 / 36
Page 1: Design of optimal Runge-Kutta metho
Page 5 and 6: Solution of hyperbolic PDEs The fun
Page 11 and 12: Time Integration Using a better tim
Page 17 and 18: Runge-Kutta Methods To solve the in
Page 19 and 20: Outline 1 High order Runge-Kutta me
Page 21 and 22: The Stability Function For the line
Page 23 and 24: Absolute Stability For the linear e
Page 25 and 26: Stability optimization This leads n
Page 27 and 28: Stability Optimization: a toy examp
Page 29 and 30: Stability Optimization: a toy examp
Page 31 and 32: Stability Optimization: one more ex
Page 33 and 34: Stability Optimization: one more ex
Page 35 and 36: Nonlinear accuracy Besides the cond
Page 37 and 38: Strong stability preservation Desig
Page 39 and 40: Strong stability preservation Desig
Page 41 and 42: The Forward Euler condition Recall
Page 43 and 44: Runge-Kutta methods as a convex com
Page 45 and 46: Example: A highly oscillatory flow
Page 47 and 48: Low storage methods 3S Algorithm S3
Page 49 and 50: Two-step optimization process Our o
Page 51 and 52: Two-step optimization process Our o
Page 53 and 54:
Optimizing for the SD spectrum On r
Page 55 and 56:
Optimizing for the SD spectrum Prim
Page 57 and 58:
Application: flow past a wedge Dens
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Design of optimal Runge-Kutta methods - FEniCS Project

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