Design of optimal Runge-Kutta methods - FEniCS Project

More documents

Recommendations

Info

Beyond linear stability Classical stability theory and its extensions focus on weak bounds: �u n � ≤ C(t) linear problems inner product norms For hyperbolic PDEs, we are often interested in strict bounds �u n � ≤ C nonlinear problems L1, L∞, TV , or positivity We refer to bounds of the latter types as strong stability properties. For example: �u n �TV ≤ �u n−1 �TV D. Ketcheson (KAUST) 21 / 36
Strong stability preservation Designing fully-discrete schemes with strong stability properties is notoriously difficult! D. Ketcheson (KAUST) 22 / 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 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: Nonlinear accuracy Besides the cond
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

Design of optimal Runge-Kutta methods - FEniCS Project

Create successful ePaper yourself

Delete template?

Save as template?