Design of optimal Runge-Kutta methods - FEniCS Project
Design of optimal Runge-Kutta methods - FEniCS Project Design of optimal Runge-Kutta methods - FEniCS Project
Time Integration Using a better time integrator is usually simple but can be highly beneficial. Using a different time integrator can: Reduce the number of RHS evaluations required Alleviate timestep resrictions due to D. Ketcheson (KAUST) 6 / 36
Time Integration Using a better time integrator is usually simple but can be highly beneficial. Using a different time integrator can: Reduce the number of RHS evaluations required Alleviate timestep resrictions due to Linear stability D. Ketcheson (KAUST) 6 / 36
- Page 1 and 2: Design of optimal Runge-Kutta metho
- Page 3 and 4: Outline 1 High order Runge-Kutta me
- Page 5 and 6: Solution of hyperbolic PDEs The fun
- Page 7 and 8: Solution of hyperbolic PDEs The fun
- Page 9 and 10: Solution of hyperbolic PDEs The fun
- Page 11: Time Integration Using a better tim
- Page 15 and 16: 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
Time Integration<br />
Using a better time integrator is usually simple but can be highly<br />
beneficial.<br />
Using a different time integrator can:<br />
Reduce the number <strong>of</strong> RHS evaluations required<br />
Alleviate timestep resrictions due to<br />
Linear stability<br />
D. Ketcheson (KAUST) 6 / 36
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