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The Second Order Adjoint Analysis

The Second Order Adjoint Analysis. Team of Stochastic Department Of Civil Engineering Chuo University. Kawahara Lab. Taylor Expansion. What is Hessian?. Performance Function. : The model solution. : Observation. 0. The First Order. Hessian. The Second Order. SOA.

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The Second Order Adjoint Analysis

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  1. The Second Order Adjoint Analysis Team of Stochastic Department Of Civil Engineering Chuo University Kawahara Lab.

  2. Taylor Expansion What is Hessian? Performance Function : The model solution : Observation

  3. 0 The First Order

  4. Hessian The Second Order

  5. SOA ( Second Order Adjoint ) Hessian Action Calculation DFP method High computational burden EFGS method

  6. Basic Equation Thermal Conduction Equation Specific heat Density Temperature Thermal Conductivity Initial Condition

  7. Boundary Condition Heat Flux Error

  8. Uncertain Estimation via Hessian Calculation Performance Function Exact Solution Noisy Solution

  9. Lagrange Multiplier Method First Order Adjoint Variation

  10. First Order Adjoint (FOA) The First Order Adjoint Equation Boundary Conditions Final Condition

  11. Tangent Linear Tangent Liner Problem Boundary Conditions Initial Condition

  12. Second Order Adjoint (SOA) The Second Order Adjoint Equation Boundary Conditions Final Condition

  13. and The Hessian Action

  14. Newton’s Method Gradient Hessian

  15. Numerical Example

  16. Performance Function

  17. Heat Flux

  18. Temperature

  19. Conclusion • The calculation of the Hessian can be performed using the solution of the SOA problem. • The optimal control of thermal conduction can be analyzed using Hessian.

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