用于具有不确定导热系数的热方程的集合时间步进算法
Ensemble Timestepping Algorithms for the Heat Equation with Uncertain Conductivity
AI总结：
本文提出两种算法计算热传导问题的解集，通过共享系数矩阵减少存储和计算成本，证明了方法的稳定性与收敛性，并通过数值实验验证了理论分析。
摘要：
受3D打印应用的启发，本文提出了两种算法用于计算热传导问题的解集。解集的平均值是最可能的温度分布，其方差估计预测可靠性。通过求解包含共享系数矩阵的线性系统，对多个右端进行求解，从而减少存储需求和计算成本。在热导率波动与均值的比值条件下证明了方法的稳定性与收敛性。提供了一系列数值实验，验证了理论分析并展示了集合模拟的应用。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
