AI 中文总结
该研究针对准静态电孔隙弹性的五场系统，提出迭代解耦方法，可几何收敛至整体解，数值实验验证了其无闭锁性能。
AI 中文摘要
准静态电孔隙弹性通过电场与压力梯度间的电动耦合，将麦克斯韦方程与Biot孔隙弹性理论耦合。引入总压力后，电孔隙弹性方程被重新表述为五场系统，以解决近不可压缩区域的孔隙弹性闭锁问题。针对所得五场系统，推导了整体弱形式并给出连续稳定性估计。随后引入二阶向后差分公式（BDF2）时间离散与混合有限元空间离散，得到全离散整体格式。基于该格式，开发了一种迭代解耦方法，在电磁学子问题与孔隙弹性子问题间交替求解，并在物理耦合条件下，证明其以显式、与网格无关的收缩因子几何收敛至整体解。还提出了代数等价的简化形式，其中电磁块每时间步仅求解一次，而孔隙弹性块则迭代求解，同时通过压力梯度反馈获得电场修正更新。数值实验验证了理论预测，并展示了无闭锁性能。
英文摘要
Quasi-static electroporoelasticity couples Maxwell's equations with Biot's poroelasticity through electrokinetic coupling between the electric field and the pressure gradient. By introducing the total pressure, the electroporoelasticity equations are reformulated as a five-field system to address poroelastic locking in the nearly incompressible regime. For the resulting five-field system, a monolithic weak formulation is derived, together with a continuous stability estimate. A second-order backward differentiation formula (BDF2) time discretization and a mixed finite- element spatial discretization are then introduced, yieling to a fully discrete monolithic scheme. Building on this scheme, we develop an iterative decoupling method that alternates between an electromagnetic subproblem and a poroelastic subproblem, and prove its geometric convergence to the monolithic solution with an explicit mesh-independent contraction factor under the physical coupling condition. An algebraically equivalent reduced form is also presented, in which the electromagnetic block is solved only once per time step, while the poroelastic block is solved iteratively with electric-field correction updates obtained from the pressure-gradient feedback. Numerical experiments verify the theoretical predictions and demonstrate the locking-free performance.
