Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematical Sciences

Committee Chair/Advisor

Hyesuk Lee

Committee Member

Qingshan Chen

Committee Member

Fei Xue

Committee Member

Shitao Liu


We introduce two global-in-time domain decomposition methods, namely the Steklov-Poincare method and Schwarz waveform relaxation (SWR) method using Robin transmission conditions (or the Robin method), for solving fluid-structure interaction systems involving elastic, porous, or poroelastic structure. These methods allow us to formulate the coupled system as a space-time interface problem and apply iterative algorithms directly to the evolutionary problem. Each time-dependent fluid and the structure subdomain problem is solved independently, which enables the use of different time discretization schemes and time step sizes in the subsystems. This leads to an efficient way of simulating time-dependent multiphysics phenomena. For the fluid-porous structure interaction system, we consider the SWR method. The coupled system is formulated as a time-dependent interface problem based on Robin-Robin transmission conditions, for which the decoupling SWR algorithm is proposed and proved for convergence. For the fluid-poroelastic structure interaction (FPSI) system, we use interface conditions to define Steklov-Poincare type operators. These operators are used to transform the coupled system into a non-linear space-time interface problem, which is then solved using a nested iteration algorithm. For the system that involves elastic structure, we implement both the Steklov-Poincare method and the SWR method.

Additionally, we present a temporal numerical discretization scheme for the interaction between a 3D fluid and a 2D plate structure. We show the stability of this scheme and propose a numerical algorithm that sequentially solves the fluid and plate subsystems through an effective decoupling approach. We perform numerical tests using P2Morley elements for the plate subproblem that involves the biharmonic operator.

Numerical tests are presented for both non-physical and physical problems with various mesh sizes and time step sizes to illustrate the accuracy and efficiency of the proposed methods.



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