Domain Decomposition Methods for Convection-Diffusion-Reaction Equations with Finite Volume Discretizations

In this dissertation, fast solvers for the convection-diffusion-reaction (CDR) model with the finite volume discretization are studied. Both overlapping and non-overlapping domain decom- position (DD) preconditioning methods are considered. With overlapping DD preconditioners, we work on a time dependent CDR model. The additive Runge-Kutta (ARK) scheme is used for the time discretization and the fourth-order finite volume is applied for the spacial discretization. With the non-overlapping DD methods, some preconditioners based on the Schur complement with low-rank corrections (SLR) are introduced. A time independent CDR model with the second-order finite volume discretization is studied by applying these non-overlapping DD preconditioners. In both overlapping and non-overlapping DD methods, two level preconditioners with a coarse prob- lem are introduced. We demonstrate the scalability of the two level preconditioners by numerical experiments. The finite volume element methods (FVEMs) is a special class of finite volume meth- ods. It shares properties of both finite element and finite volume methods. We develop an adaptive balancing domain decomposition by constraints (BDDC) preconditioner for the FVEMs and pro- vide an convergence analysis. Numerical experiments are provided to demonstrate our theoretical results.

Name thesis:degree_name

Ph.D.

Discipline thesis:degree_discipline

Mathematics

Grantor dc:publisher

University of Kansas

Year dc:date.issued

2022

Author dc:creator

• Su, Yanru

Advisor dc:contributor.advisor

• Tu, Xuemin

• BDDC preconditioner
• domain decomposition methods
• finite volume methods
• Schur complement preconditioning

Language dc:language.iso

en

Dc Identifier Other

https://www.proquest.com/LegacyDocView/DISSNUM/29254328

OAI identifier oai:identifier

oai:kuscholarworks.ku.edu:1808/38234