论文标题
数据同化问题的动态域分解的平行框架研究KALMAN滤清器算法的案例研究
Parallel framework for Dynamic Domain Decomposition of Data Assimilation problems a case study on Kalman Filter algorithm
论文作者
论文摘要
我们专注于通过变异方法和Kalman Filter算法解决的基于部分微分方程（PDE）的数据同化问题（DA）。最近，我们提出了一个域分解框架（我们称之为DD-DA，简称为DD-DA），沿空间和时间方向执行整个物理域的分解，并加入Schwarz的方法和平行的方法。为了有效的DD-DA算法并行化，必须平均分配给子域的计算负载。通常，计算成本与分配给分区的数据实体数量成正比。高质量的分区还需要在计算过程中的沟通量最低。为了处理观测值不均匀且稀疏的DD-DA问题，在目前的工作中，我们采用基于自适应和动态定义DD界限的平行负载平衡算法 - 旨在根据数据位置平衡工作负载。我们称其为dydd。由于由所谓的离散化 - 最优化的方法引起的DA问题的数值模型是受约束的最小平方模型（CLS），因此我们将使用CLS作为参考状态估计问题，并且我们在不同方案上验证DYDD。
We focus on Partial Differential Equation (PDE) based Data Assimilatio problems (DA) solved by means of variational approaches and Kalman filter algorithm. Recently, we presented a Domain Decomposition framework (we call it DD-DA, for short) performing a decomposition of the whole physical domain along space and time directions, and joining the idea of Schwarz' methods and parallel in time approaches. For effective parallelization of DD-DA algorithms, the computational load assigned to subdomains must be equally distributed. Usually computational cost is proportional to the amount of data entities assigned to partitions. Good quality partitioning also requires the volume of communication during calculation to be kept at its minimum. In order to deal with DD-DA problems where the observations are nonuniformly distributed and general sparse, in the present work we employ a parallel load balancing algorithm based on adaptive and dynamic defining of boundaries of DD -- which is aimed to balance workload according to data location. We call it DyDD. As the numerical model underlying DA problems arising from the so-called discretize-then-optimize approach is the constrained least square model (CLS), we will use CLS as a reference state estimation problem and we validate DyDD on different scenarios.
