Related papers: Detection of time-varying heat sources using an an…
A non-classical initial and boundary value problem for a non-homogeneous one-dimensional heat equation for a semi-infinite material with a zero temperature boundary condition at the face $x=0$ is studied with the aim of finding explicit…
In this paper, the results of numerical experiments verifying a novel setup for laser beam profiling are presented. The experimental setup is based on infrared thermography and includes laser beam illuminating a thin metal plate. The method…
The paper is concerned with an inverse point source problem for the Helmholtz equation. It consists of recovering the locations and amplitudes of a finite number of radiative point sources inside a given inhomogeneous medium from the…
This work is concerned with the inverse source problem of locating multiple multipolar sources from boundary measurements for the Helmholtz equation. We develop simple and effective sampling schemes for location acquisition of the sources…
Three inverse boundary value problems for the heat equations in one space dimension are considered. Those three problems are: extracting an unknown interface in a heat conductive material, an unknown boundary in a layered material or a…
When the variations of surface temperature are measured both spatially and temporally, analytical expressions that correctly account for multi-dimensional transient conduction can be applied. To enhance the accessibility of these accurate…
Within the field of optimal experimental design, \emph{sensor placement} refers to the act of finding the optimal locations of data collecting sensors, with the aim to optimise reconstruction of an unknown parameter from finite data. In…
The present article is dedicated to the forward and backward solution of a transient one-phase Stefan problem. In the forward problem, we compute the evolution of the initial domain for a Stefan problem where the melting temperature varies…
Temperature monitoring during the life time of heat source components in engineering systems becomes essential to guarantee the normal work and the working life of these components. However, prior methods, which mainly use the interpolate…
We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part…
This paper presents a statistical forward model for a Compton imaging system, called Compton imager. This system, under development at the University of Illinois Urbana Champaign, is a variant of Compton cameras with a single type of…
This paper deals with the numerical methods for the reconstruction of source term in linear parabolic equation from final overdetermination. We assume that the source term has the form f(x)h(t) and h(t) is given, which guarantees the…
History Matching is a technique used to calibrate complex computer models, that is, finding the input settings which lead to the simulated output matching up with real world observations. Key to this technique is the construction of…
This paper proposes strategies to detect time reversibility in stationary stochastic processes by using the properties of mixed causal and noncausal models. It shows that they can also be used for non-stationary processes when the trend…
We develop a computational approach to locate the source of a steady-state gradient of diffusing particles from the fluxes through narrow windows distributed either on the boundary of a three dimensional half-space or on a sphere. This…
Imaging point sources in heterogeneous environments from boundary or far-field measurements has been extensively studied in the past. In most existing results, the environment, represented by the refractive index function in the model…
In this paper, we investigate the pointwise time analyticity of three differential equations. They are the biharmonic heat equation, the heat equation with potentials and some nonlinear heat equations with power nonlinearity of order $p$.…
This paper studies a prototype of inverse initial boundary value problems whose governing equation is the heat equation in three dimensions. An unknown discontinuity embedded in a three-dimensional heat conductive body is considered. A {\it…
We prove logarithmic stability in the parabolic inverse problem of determining the space-varying factor in the source, by a single partial boundary measurement of the solution to the heat equation in an infinite closed waveguide, with…
We employ adaptive mesh refinement, implicit time stepping, a nonlinear multigrid solver and parallel computation, to solve a multi-scale, time dependent, three dimensional, nonlinear set of coupled partial differential equations for three…