This work presents a strongly coupled partitioned method for fluid-structure interaction (FSI) problems based on a monolithic formulation of the system which employs a Lagrange multiplier. We prove that both the semi-discrete and fully discrete formulations are well-posed. To derive a partitioned scheme, a Schur complement equation, which implicitly expresses the Lagrange multiplier and the fluid pressure in terms of the fluid velocity and structural displacement, is constructed based on the monolithic FSI system. Solving the Schur complement system at each time step allows for the decoupling of the fluid and structure subproblems, making the method non-iterative between subdomains. We investigate bounds for the condition number of the Schur complement matrix and present initial numerical results to demonstrate the performance of our approach, which attains the expected convergence rates.

翻译：本文提出了一种强耦合分区方法用于求解流体-结构相互作用(FSI)问题，该方法基于采用拉格朗日乘子的整体系统公式。我们证明了半离散和完全离散公式均具有适定性。为推导分区格式，基于整体FSI系统构建了Schur补方程，该方程隐式地将拉格朗日乘子和流体压力表示为流体速度和结构位移的函数。在每个时间步求解Schur补系统可实现流体与结构子问题的解耦，使得该方法在子域间无需迭代。我们研究了Schur补矩阵条件数的界，并给出初步数值结果以验证该方法的性能，其达到了预期的收敛阶。