Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Optimization by Vector Space Methods
Optimization by Vector Space Methods
Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
Perspectives in Flow Control and Optimization
Perspectives in Flow Control and Optimization
Identification of a Temperature Dependent Heat Conductivity from Single Boundary Measurements
SIAM Journal on Numerical Analysis
A computational framework for the regularization of adjoint analysis in multiscale PDE systems
Journal of Computational Physics
Convex Optimization
Inverse Problem Theory and Methods for Model Parameter Estimation
Inverse Problem Theory and Methods for Model Parameter Estimation
Discretization of Dirac delta functions in level set methods
Journal of Computational Physics
The numerical approximation of a delta function with application to level set methods
Journal of Computational Physics
Understanding And Implementing the Finite Element Method
Understanding And Implementing the Finite Element Method
Two methods for discretizing a delta function supported on a level set
Journal of Computational Physics
Geometric integration over irregular domains with application to level-set methods
Journal of Computational Physics
Short Note: A proof that a discrete delta function is second-order accurate
Journal of Computational Physics
Nonlinear Optimization
Journal of Computational Physics
Discretizing delta functions via finite differences and gradient normalization
Journal of Computational Physics
Hi-index | 31.45 |
We develop an optimization-based approach to the problem of reconstructing temperature-dependent material properties in complex thermo-fluid systems described by the equations for the conservation of mass, momentum and energy. Our goal is to estimate the temperature dependence of the viscosity coefficient in the momentum equation based on some noisy temperature measurements, where the temperature is governed by a separate energy equation. We show that an elegant and computationally efficient solution of this inverse problem is obtained by formulating it as a PDE-constrained optimization problem which can be solved with a gradient-based descent method. A key element of the proposed approach, the cost functional gradients are characterized by mathematical structure quite different than in typical problems of PDE-constrained optimization and are expressed in terms of integrals defined over the level sets of the temperature field. Advanced techniques of integration on manifolds are required to evaluate numerically such gradients, and we systematically compare three different methods. As a model system we consider a two-dimensional unsteady flow in a lid-driven cavity with heat transfer, and present a number of computational tests to validate our approach and illustrate its performance.