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Tsunami Prediction Using Adjoint Methods
Brisa Davis
Motivation
• Tsunami simulations can be used for– Prediction and warning systems– Analyzing data
Accuracy(gained via mesh refinement)
vs.
Computational Time
• Adaptive Mesh Refinement – Clusters grid points in areas of interest
• Goal: – predict what areas of the wave will hit
Crescent City, and– use Adaptive Mesh Refinement on just those
areas
Acoustics Example
• Acoustics Equation:
+ A + B = 0
from t = 0 to T
Zero velocity at boundaries
• Adjoint Equation:
+ + = 0
from t = T to 0
Zero velocity at boundaries
Path Towards Targeted AMR
• Solve these two equations• Look at where the inner product is high• Refine at those places
Solving the Acoustics Equation
Solving the Adjoint Equationfrom t = T to t = 0
Contours of the Inner Product
3 Levels of Refinement
Timing Improvements
• Fine Grid: 12.552 seconds• Traditional AMR: 9.944 seconds• Adjoint Method: 3.464
Future Work
• Apply this method to shallow water equations
Impact
• Development of improved software• Hazard modeling and mitigation
Time’s Up!
• About you:– Name: Brisa Davis– Department: Applied Math– Contact Information: [email protected]