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We present a simple, analytic point source model for both static and time-varying point-like heat sources and the resulting temperature profile that solves the heat equation in dimension three. Simple algorithms to detect the location and…
Computing solutions to partial differential equations using the fast Fourier transform can lead to unwanted oscillatory behavior. Due to the periodic nature of the discrete Fourier transform, waves that leave the computational domain on one…
The local and overall responses of nonlinear composites are classically investigated by the Finite Element Method. We propose an alternate method based on Fourier series which avoids meshing and which makes direct use of microstructure…
We develop a space-time spectral element method for topology optimization of transient heat conduction. The forward problem is discretized with summation-by-parts (SBP) operators, and interface/boundary and initial/terminal conditions are…
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…
This study introduces pre-orthogonal adaptive Fourier decomposition (POAFD) to obtain approximations and numerical solutions to the fractional Laplacian initial value problem and the extension problem of Caffarelli and Silvestre…
Accurately predicting nonlinear transient thermal fields in two-dimensional domains is a significant challenge in various engineering fields, where conventional analytical and numerical methods struggle to balance physical fidelity with…
The main goal of this paper is applying the cut-off projection for solving one-dimensional backward heat conduction problem in a two-slab system with a perfect contact. In a constructive manner, we commence by demonstrating the…
Laminated composite materials are widely used in most fields of engineering. Wave propagation analysis plays an essential role in understanding the short-duration transient response of composite structures. The forward physics-based models…
In this paper, we present a numerical algorithm for the accurate and efficient computation of the convolution of the frequency domain layered media Green's function with a given density function. Instead of compressing the convolution…
In the present study, soot formation in the turbulent lifted diffusion flame, consisting of ethylene-air is numerically investigated using three different soot modeling approaches and is comprehensively reported. For turbulence-chemistry…
The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…
Modern package designs make use of technologies such as backside power delivery (BSPD) and 3D stacked chiplets that require accounting for the heterogeneity in back end of the line (BEOL) structures in hot-spot prediction. Multiscale…
Materials with complex inner structure can be challenging to characterize in an effective way. First, it is difficult to determine the representative volume for such a heterogeneous material. Second, the effective material parameters…
Existing algorithms with iterations as the principle for 3D inverse heat conduction problems (IHCPs) are usually time-consuming. With the recent advancements in deep learning techniques, it is possible to apply the neural network to compute…
Finite element models without simplifying assumptions can accurately describe the spatial and temporal distribution of heat in machine tools as well as the resulting deformation. In principle, this allows to correct for displacements of the…
Robust and non-destructive material classification is a challenging but crucial first-step in numerous vision applications. We propose a physics-guided material classification framework that relies on thermal properties of the object. Our…
Inverse problems of recovering heat transfer coefficient from integral measurements are considered. The heat transfer coefficient occurs in the transmission conditions of imperfect contact type or the Robin type boundary conditions. It is…
In this paper, we propose and analyze a new semi-implicit stochastic multiscale method for the radiative heat transfer problem with additive noise fluctuation in composite materials. In the proposed method, the strong nonlinearity term…
We introduce a model-agnostic forward diffusion process for time-series forecasting that decomposes signals into spectral components, preserving structured temporal patterns such as seasonality more effectively than standard diffusion.…