Ensemble time‐stepping algorithms for the heat equation with uncertain conductivity
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Publication:4623413
DOI10.1002/NUM.22267zbMATH Open1407.65102arXiv1708.00893OpenAlexW2963160198WikidataQ115397940 ScholiaQ115397940MaRDI QIDQ4623413
Author name not available (Why is that?)
Publication date: 15 February 2019
Published in: (Search for Journal in Brave)
Abstract: Motivated by applications to 3D printing, this paper presents two algorithms for calculating an ensemble of solutions to heat conduction problems. The ensemble average is the most likely temperature distribution and its variance gives an estimate of prediction reliability. Solutions are calculated by solving a linear system, involving a shared coefficient matrix, for multiple right-hand sides at each timestep. Storage requirements and computational costs to solve the system are thereby reduced. Stability and convergence of the method are proven under a condition involving the ratio between fluctuations of the thermal conductivity and the mean. A series of numerical tests are provided which confirm the theoretical analyses and illustrate uses of ensemble simulations.
Full work available at URL: https://arxiv.org/abs/1708.00893
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