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Multiscale multilevel iterative substructuring

多尺度多级迭代子结构

基本信息

批准号：
1521563
负责人：
Bedrich Sousedik
金额：
$ 19.99万
依托单位：
University of Maryland Baltimore County
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2015
资助国家：
美国
起止时间：
2015-09-01 至 2019-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1521563&HistoricalAwards=false
关键词：
Multiscale multilevel iterative substructuring

项目摘要

The PI will develop novel algorithms that can be used for the simulation of flow through porous media in real-world reservoir models. The simulation of flow in porous media finds applications in a number of areas, such as water management, oil and gas recovery, carbon dioxide (CO2) sequestration, and nuclear waste disposal, to name a few. The underlying mathematical models and efficient numerical simulation is challenging due to several aspects. The reservoirs are typically very large, so the discretized mathematical model leads to systems of equations with hundreds of millions of unknowns, they have irregular structure, which complicates the model geometry, and they consist of materials that significantly differ in geological properties, which translates in the model to jumps in coefficients over several orders of magnitude. Moreover, the geological formations quite often also contain fractures that alter the effective permeabilities, and therefore need to be be accurately incorporated into the numerical model. For example, the flow of water in granite rock, which represents one of the suitable sites for nuclear waste deposit, is conducted by the complex system of vugs, cavities and fractures with various topology and sizes. Alternatively, the fractures might result from the engineering activities, for example hydraulic fracturing (also known as fracking) used for the extraction of natural gas.The PI will develop novel algorithms for solving saddle-point linear systems combining numerical upscaling techniques with parallel, domain decomposition iterative solvers. There are many aspects of multiscale and domain decomposition methods that are quite well understood, but the major drawback of current methodologies is that they do not take full advantage of their potential by using the multiscale phenomena in the design of the solvers, which results in their inefficiency. Multiscale methods also frequently consist in fact only of two scales, whereas in a porous medium there are typically many scales. At the same time, advances in multicore architectures, networking, high end computers, and large data stores, are ushering in a new era of high performance parallel and distributed simulations. Naturally, with these new capabilities come new challenges in computing and system modeling. The goal of this project is to open new avenues to tackle these issues. In particular, the PI will develop multiscale methods that allows for a multiple of scales, and uses the upscaling algorithm to build a multilevel preconditioner for the iterative solver. The components of the method are thus recycled, which significantly decreases the computational cost. Moreover, this approach can be applied recursively and thus naturally offers a multilevel multiscale potential, unlike many traditional multiscale approaches that consist in fact of only two scales. It is expected that understanding of the issues related to design of multiscale and multilevel methods for extremely large problems will ultimately contribute to development of the next generation of parallel iterative solvers suitable for implementation on future exascale supercomputers.

PI将开发新的算法，可用于模拟真实世界油藏模型中的多孔介质流动。多孔介质中流动的模拟在许多领域中找到应用，例如水管理、石油和天然气回收、二氧化碳（CO2）封存和核废料处理，仅举几例。由于几个方面的原因，底层的数学模型和有效的数值模拟是具有挑战性的。储层通常非常大，因此离散化数学模型导致具有数亿个未知量的方程系统，它们具有不规则的结构，这使模型几何形状复杂化，并且它们由地质性质显著不同的材料组成，这在模型中转化为几个数量级的系数跳跃。此外，地质构造通常还包含改变有效渗透率的裂缝，因此需要准确地纳入数值模型。例如，花岗岩是核废料存款的合适场所之一，花岗岩中的水流是由具有各种拓扑结构和尺寸的溶洞、洞穴和裂缝组成的复杂系统引导的。或者，裂缝可能来自工程活动，例如用于开采天然气的水力压裂（也称为压裂）。PI将开发新的算法，用于解决鞍点线性系统，将数值放大技术与并行区域分解迭代求解器相结合。有很多方面的多尺度和区域分解方法，是相当好理解的，但目前的方法的主要缺点是，他们没有充分利用其潜力，通过使用多尺度现象在设计的求解器，这导致其效率低下。多尺度方法也经常实际上仅由两个尺度组成，而在多孔介质中通常有许多尺度。与此同时，多核架构、网络、高端计算机和大型数据存储的进步正在迎来一个高性能并行和分布式仿真的新时代。当然，这些新功能也带来了计算和系统建模方面的新挑战。该项目的目标是为解决这些问题开辟新的途径。特别是，PI将开发允许多个尺度的多尺度方法，并使用升尺度算法为迭代求解器构建多级预处理器。因此，该方法的组件被回收，这显着降低了计算成本。此外，这种方法可以递归地应用，从而自然地提供了一个多层次的多尺度潜力，不像许多传统的多尺度方法，实际上只包括两个尺度。预计了解的问题，设计的多尺度和多级方法的极大的问题，最终将有助于开发下一代的并行迭代求解器，适用于未来的exascale超级计算机上的实施。