勷勤数学•专家报告

题      目：Efficient multiscale preconditioners for large-scale highly heterogeneous flow

报  告  人：付书彬 助理教授  (邀请人：钟柳强)

                                   宁波东方理工大学（暂名）

时      间：5月12日  16：00-17：00

地     点：数科院东楼401

报告人简介:

       付书彬博士现为宁波东方理工大学（暂名）助理教授，博士生导师，曾入选浙江省海外引才计划。他本科毕业于四川大学数学学院，随后在德州农工大学获得博士学位。曾在香港中文大学和威斯康星大学麦迪逊分校完成博士后训练。他的主要研究兴趣是多尺度有限元方法和模型降阶方法及其跨学科应用。主要成果发表在SIAM J. Sci. Comput., Multiscale Model. Simul., J. Comput. Phys., Comput. Methods Appl. Mech. Engrg., Water Resour. Res.和Geophys. J. Int.等期刊

摘      要：

       We propose efficient and robust preconditioners for large-scale incompressible flow in highly heterogeneous porous media. We start from the discretization of the first-order form for the single phase incompressible flow and apply a velocity elimination strategy to obtain an equation with pressure as the only unknown. Then an efficient two-grid preconditioner is designed to solve this equation. The key component of the preconditioner is adoption of a non-standard coarse space that contains the media’s heterogeneity information. We solve a carefully constructed spectral problem in each coarse element to form the non-standard coarse space. Rich numerical tests with several types of large-scale three-dimensional highly heterogeneous permeability fields are presented. The experimental results show that our generalized multiscale space based preconditioner is robust with respect to the contrast, size and geometry of the permeability fields. We also successfully apply this preconditioner for multiphase flow simulation and transport problems arising from reservoir simulation. We will also introduce how to extend this two-grid preconditioner to multigrid regime.

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