Ensemble Timestepping Algorithms for the Heat Equation with Uncertain Conductivity
For researchers in computational heat transfer and uncertainty quantification, this work provides efficient algorithms for ensemble simulations, though the method is incremental and domain-specific.
This paper introduces two ensemble timestepping algorithms for solving heat conduction problems with uncertain conductivity, achieving reduced storage and computational costs by solving a linear system with a shared coefficient matrix for multiple right-hand sides. Stability and convergence are proven under a condition on conductivity fluctuations, and numerical tests confirm the theory.
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.