Particle Based gPC Methods for Mean-Field Models of Swarming with Uncertainty
Particle Based gPC Methods for Mean-Field Models of Swarming with Uncertainty
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DOI：
10.4208/cicp.oa-2017-0244
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发表时间：
2017-12
影响因子：
3.7
通讯作者：
J. Carrillo;L. Pareschi;M. Zanella
中科院分区：
文献类型：
--
作者：
J. Carrillo;L. Pareschi;M. Zanella
在这项工作中，我们专注于建设的数值方案的近似随机平均场方程保持非负的解决方案。这里开发的方法利用平均场蒙特卡罗方法的物理变量结合广义多项式混沌（gPC）在随机空间中的扩展。与直接应用的随机Galerkin方法，这是非常准确的，但会导致损失的积极性，所提出的计划是能够实现高精度的随机空间，而不会失去非负性的解决方案。几个应用程序的计划平均场模型的集体行为的报告。
In this work we focus on the construction of numerical schemes for the approximation of stochastic mean--field equations which preserve the nonnegativity of the solution. The method here developed makes use of a mean-field Monte Carlo method in the physical variables combined with a generalized Polynomial Chaos (gPC) expansion in the random space. In contrast to a direct application of stochastic-Galerkin methods, which are highly accurate but lead to the loss of positivity, the proposed schemes are capable to achieve high accuracy in the random space without loosing nonnegativity of the solution. Several applications of the schemes to mean-field models of collective behavior are reported.