Related papers: Detection of time-varying heat sources using an an…
The modeling and simulation of heat source trajectories through phase-change materials is a relevant problem both for space exploration and for terrestrial climate research, among other fields. In space, the DLR and NASA are both interested…
Iron loss determination in the magnetic core of an electrical machine, such as a motor or a transformer, is formulated as an inverse heat source problem. The sensor positions inside the object are optimized in order to minimize the…
This paper is concerned with the numerical simulation of three dimensional time-dependent inverse source problems of acoustic waves. The reconstructions of both multiple stationary point sources and a moving point source are considered. The…
We discuss inverse problems of determining the time-dependent source coefficient for a general class of subelliptic heat equations. We show that a single data at an observation point guarantees the existence of a (smooth) solution pair for…
In this paper, we investigate the direct and linear inverse problems of identifying time-dependent and time-independent source terms in a time-fractional diffusion-wave equation, using measured data at an interior point of the time…
We present a family of integral equation-based solvers for the linear or semilinear heat equation in complicated moving (or stationary) geometries. This approach has significant advantages over more standard finite element or finite…
In this paper, we consider the problem of identifying a single moving point source for a three-dimensional wave equation from boundary measurements. Precisely, we show that the knowledge of the field generated by the source at six different…
We develop a numerical solver for radiative transfer problems based on the weighted essentially nonoscillatory (WENO) scheme modified with anti-diffusive flux corrections, in order to solve the temperature and ionization profiles around a…
Dynamical energy analysis was recently introduced as a new method for determining the distribution of mechanical and acoustic wave energy in complex built up structures. The technique interpolates between standard statistical energy…
We address the inverse problem of identifying a time-dependent source coefficient in a one-dimensional heat equation with a fractional Laplacian subject to Dirichlet boundary conditions and an integral nonlocal data. An a priori estimate is…
This paper considerers the problem of computing the value of a solution of the heat equation at a given point inside a bounded domain after the initial time. It is assumed that the initial value of the solution inside the domain (possibly…
This paper investigates the inverse problems of determining a space-dependent source for thermoelastic systems of type III under adequate time-averaged or final-in-time measurements and conditions on the time-dependent part of the sought…
Recent developments of ultrafast laser pulse techniques enable us to study the subpicosecond scale dynamics out of thermal equilibrium. Multiple temperature models are frequently used to describe such dynamics where the total system is…
In this work we have proposed a geometric model that is employed to devise a scheme for identifying the hotspots and zones in a chip. These spots or zone need to be guarded thermally to ensure performance and reliability of the chip. The…
In this work we investigate an inverse problem of recovering point sources and their time-dependent strengths from {a posteriori} partial internal measurements in a subdiffusion model which involves a Caputo fractional derivative in time…
We investigate the identification of the time-dependent source term in the diffusion equation using boundary measurements. This facilitates tracing back the origins of environmental pollutants. Employing the concept of dynamic complex…
Let $\Omega_\epsilon$ be a metallic plate whose top inaccessible surface has been damaged by some chemical or mechanical agent. We heat the opposite side and collect a sequence of temperature maps $u^\epsilon$. Here, we construct a formal…
We present a fast adaptive method for the evaluation of heat potentials, which plays a key role in the integral equation approach for the solution of the heat equation, especially in a non-stationary domain. The algorithm utilizes a…
In this paper, we establish existence and uniqueness of weak solutions to general time fractional equations and give their probabilistic representations. We then derive sharp two-sided estimates for fundamental solutions of a family of time…
We present a cost-effective method for model calibration and solution of source inversion problems in atmospheric dispersion modelling. We use Gaussian process emulations of atmospheric dispersion models within a Bayesian framework for…