Computational Inverse Techniques: Theory, Numerical Analysis and Application

摘要

This paper describes in brief the theory, principles, computational algorithms, and practical applications of the computational inverse techniques. First, regularization methods are introduced for the treatment of ill-posed inverse problems. Robust and practical optimization algorithms are then introduced, including the combination of different types of optimization methods, such as gradient based methods with genetic algorithms, intergeneration projection genetic algorithms, progressive neural networks, reduce-basis methods, etc. Last, several numerical examples for force/source reconstructions, crack detection, material property characterization, and heat coefficients identification, have been presented to briefly demonstrate the applications of these computational inverse techniques.