论文标题
Smoluchowski Type方程的模型降低
Model reduction in Smoluchowski-type equations
论文作者
论文摘要
在本文中，我们利用适当的正交分解方法（POD）方法来减少对Smoluchowski聚合方程的应用，并带有源和下沉项。特别是，我们在实践中表明，存在一个低维空间，可以近似聚合方程的解决方案。我们还证明，可以仅取决于此类空间的维度，而不是原始问题大小对聚合过程进行建模。此外，我们提出了一种重建必要空间的方法，而无需解决完整的进化问题，这可以导致大量的计算加速，示例也会列出。
In this paper we utilize the Proper Orthogonal Decomposition (POD) method for model order reduction in application to Smoluchowski aggregation equations with source and sink terms. In particular, we show in practice that there exists a low-dimensional space allowing to approximate the solutions of aggregation equations. We also demonstrate that it is possible to model the aggregation process with the complexity depending only on dimension of such a space but not on the original problem size. In addition, we propose a method for reconstruction of the necessary space without solving of the full evolutionary problem, which can lead to significant acceleration of computations, examples of which are also presented.
