Noise reconstruction for the inverse heat conduction problem

AbstractA new automatic procedure to numerically recover the sample root mean square norm of the data error for the linear inverse heat conduction problem (IHCP)—when this information is not readily available—is presented. Numerical results are described which illustrate the accuracy of the algorithm

Mollified hyperbolic method for coefficient identification problems

AbstractWe introduce a stable numerical method for the identification of a transmissivity coefficient in a one-dimensional parabolic equation. It is a combination of the Mollification Method and a well-known space marching implementation of the Hyperbolic Regularization procedure. The new method succesfully restores a certain type of continuity with respect to the initial condition and the boundary data. The accuracy of the algorithm is demonstrated by means of several examples where exact and perturbed data are considered

Surface fitting and numerical gradient computations by discrete mollification

AbstractWe review the δ-mollification procedure for automatic fitting of surfaces defined from discrete noisy data functions in R2. As a further application, the stable numerical computation of gradient fields from discrete noisy data is also investigated. The main features of the algorithm are: 1.1. information about the noise is needed;2.2. the mollification parameters are chosen automatically by means of the Generalized Cross Validation (GCV) procedure.A complete error analysis of the method is provided together with several numerical examples of interest

Numerical experiments in 2-D IHCP on bounded domains Part I: The “interior” cube problem

AbstractDifferent space marching implementations of the Mollification Method are introduced to numerically recover the temperature and heat flux histories at interior points of bounded subdomains of a finite two-dimensional rectangular body when the temperature and heat flux functions are approximately measured at one boundary side

Automatic numerical differentiation by discrete mollification

AbstractA new, very simple, totally automated and powerful technique for numerical differentiation based on the computation of the derivative of a suitable filtered version of the noisy data by discrete mollification is presented. Several numerical examples of interest are also analyzed

Identification of source terms in 2-D IHCP

AbstractWe introduce a stable numerical space marching scheme based on discrete mollification—implemented as an automatic adaptive filter—for the approximate identification of temperature, temperature gradient, and source terms in the two-dimensional inverse heat conduction problem (IHCP).The stability and error analysis of the algorithm, together with some numerical examples, are provided