A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems
A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems
复制标题
高度非线性随机多物理场系统的紧耦合域分解方法
DOI：
10.1016/j.jcp.2016.10.052
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
D. Tartakovsky
中科院分区：
文献类型：
--
作者：
S. Taverniers;D. Tartakovsky
多物理场模拟通常涉及由内部生成或外部施加的随机波动驱动的非线性组件。当与域分解（DD）算法一起使用时，这些组件必须以一种既能准确地传播子域之间的噪声，又能使其自身稳定且具有成本效益的时间积分的方式耦合。我们开发了一个保守的DD方法，其中紧耦合是通过使用Jacobian自由牛顿-克雷洛夫（JfNK）方法与广义最小残差迭代线性求解器。该策略是测试上的耦合的非线性扩散系统的截断高斯噪声在边界处强迫。在子域之间的界面处，强制执行状态变量及其通量的路径连续性，而不是平均值的连续性，使得DD算法能够在整个计算域中正确地传播边界波动。依赖于单次牛顿迭代（显式耦合），而不是完全收敛的JfNK（隐式）耦合，可能会增加一个数量级的解决方案误差。DD组件之间的通信频率的增加降低了显式耦合的误差，但对于所考虑的所有噪声强度，在可比的误差水平下，使显式耦合的效率低于隐式耦合。最后，DD算法与隐式JfNK耦合解决时间相关波动的边界噪声时，后者的相关时间超过一些倍数的适当定义的特征扩散时间。
Multiphysics simulations often involve nonlinear components that are driven by internally generated or externally imposed random fluctuations. When used with a domain-decomposition (DD) algorithm, such components have to be coupled in a way that both accurately propagates the noise between the subdomains and lends itself to a stable and cost-effective temporal integration. We develop a conservative DD approach in which tight coupling is obtained by using a Jacobian-free Newton–Krylov (JfNK) method with a generalized minimum residual iterative linear solver. This strategy is tested on a coupled nonlinear diffusion system forced by a truncated Gaussian noise at the boundary. Enforcement of path-wise continuity of the state variable and its flux, as opposed to continuity in the mean, at interfaces between subdomains enables the DD algorithm to correctly propagate boundary fluctuations throughout the computational domain. Reliance on a single Newton iteration (explicit coupling), rather than on the fully converged JfNK (implicit) coupling, may increase the solution error by an order of magnitude. Increase in communication frequency between the DD components reduces the explicit coupling's error, but makes it less efficient than the implicit coupling at comparable error levels for all noise strengths considered. Finally, the DD algorithm with the implicit JfNK coupling resolves temporally-correlated fluctuations of the boundary noise when the correlation time of the latter exceeds some multiple of an appropriately defined characteristic diffusion time.
日本儿童和学生对 TIMSS 科学论文式任务的反应特征 (7) - 9 项任务分析结果的趋势 -
DOI：
--
发表时间：
2005
期刊：
日本科学教育学会年会論文集 第29号
影响因子：
--
作者：
中山 迅;大場裕子;猿田祐嗣
通讯作者：
猿田祐嗣