Original Article
Muhammad Abid; Madiha Bibi; Nasir Yasin; Muhammad Shahid
Abstract
Accurate numerical solution of parabolic and elliptic partial differential equations governing two-dimensional heat transfer is critical for engineering simulations but computationally challenging.This work employs key numerical techniques finite differences, conjugate gradients, and Crank-Nicolson time ...
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Accurate numerical solution of parabolic and elliptic partial differential equations governing two-dimensional heat transfer is critical for engineering simulations but computationally challenging.This work employs key numerical techniques finite differences, conjugate gradients, and Crank-Nicolson time stepping to solve the heat diffusion equation and analyze method performance.The Poisson equation is discretized using second-order central finite differences and solved with the conjugate gradient approach to determine the steady state solution. The transient heat equation is integrated in time via the Crank-Nicolson implicit scheme, also utilizing conjugate gradients.The methods effectively compute solutions matching analytical and boundary conditions. Convergence and stability are achieved while capturing transient thermal evolution. Insights are gained into discretization and iteration parameter impacts.The numerical framework demonstrates accurate and efficient simulation of two-dimensional conductive heat transfer. It provides a template for extension to more complex geometries and multiphysics phenomena, contributing to advances in computational engineering.
Original Article
Dipak Dulal; Ramin Goudarzi Karim; Carmeliza Navasca
Abstract
In this paper, we use tensor models to analyze the Covid-19 pandemic data. First, we use tensor models, canonical polyadic, and higher-order Tucker decompositions to extract patterns over multiple modes. Second, we implement a tensor completion algorithm using canonical polyadic tensor decomposition ...
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In this paper, we use tensor models to analyze the Covid-19 pandemic data. First, we use tensor models, canonical polyadic, and higher-order Tucker decompositions to extract patterns over multiple modes. Second, we implement a tensor completion algorithm using canonical polyadic tensor decomposition to predict spatiotemporal data from multiple spatial sources and to identifyCovid-19 hotspots. We apply a regularized iterative tensor completion technique with a practical regularization parameter estimator to predict the spread of Covid-19 cases and to find and identify hotspots. Our method can predict weekly, and quarterly Covid-19 spreads with high accuracy. Third, we analyze Covid-19 data in the US using a novel sampling method for alternating leastsquares. Moreover, we compare the algorithms with standard tensor decompositions concerning their interpretability, visualization, and cost analysis. Finally, we demonstrate the efficacy of the methods by applying the techniques to the New Jersey Covid-19 case tensor data.
