The key to the design of advanced micro electro–mechanical devices is an accurate evaluation of the circuit-integrated piezoelectric oscillator that accounts for its complicated configuration. Here, the direct numerical modeling of this oscillator leads to a general formulation as a structure–piezoelectric–circuit interaction. Hence, this study developed a strongly coupled partitioned iterative method for the structure–piezoelectric–circuit interaction. The proposed method was constructed using hierarchical decomposition, the partitioned iterative method for two coupled fields, and loop union. That is, the whole system of the coupled multiphysics is hierarchically decomposed into coupled two-field subsystems, partitioned iterative algorithms for two coupled fields are applied to these subsystems, and the coupling algorithms for these subsystems are reduced to a single coupling algorithm. In the proposed method, three distinct direct piezoelectric, inverse piezoelectric, and circuit solvers are strongly coupled with each other. The inverse piezoelectric solver uses shell finite elements to analyze the response of the thin oscillator efficiently, while the direct piezoelectric solver uses solid finite elements to accurately describe the three-dimensional distribution of the electric potential in the piezoelectric continuum. The proposed method can accurately analyze coupling phenomena in the RC circuit, piezoelectric shunt damping, and piezoelectric energy harvesting.

设计先进的微机电设备的关键是对电路集成压电振荡器进行准确评估，这说明了其复杂的配置。在这里，该振荡器的直接数值建模导致了结构-压电-电路相互作用的一般公式。因此，本研究开发了一种用于结构-压电-电路相互作用的强耦合分区迭代方法。所提出的方法是使用层次分解、两个耦合场的分区迭代方法和循环联合构建的。即，将耦合多物理场的整个系统分层分解为耦合两场子系统，对这些子系统应用两个耦合场的分区迭代算法，并且这些子系统的耦合算法被简化为单一的耦合算法。在所提出的方法中，三个不同的直接压电、逆压电和电路求解器彼此强耦合。逆压电求解器使用壳有限元有效地分析薄振子的响应，而直接压电求解器使用固体有限元精确描述压电连续体中电位的三维​​分布。该方法可以准确分析RC电路、压电并联阻尼和压电能量收集中的耦合现象。和电路求解器彼此强耦合。逆压电求解器使用壳有限元有效地分析薄振子的响应，而直接压电求解器使用固体有限元精确描述压电连续体中电位的三维​​分布。该方法可以准确分析RC电路、压电并联阻尼和压电能量收集中的耦合现象。和电路求解器彼此强耦合。逆压电求解器使用壳有限元有效地分析薄振子的响应，而直接压电求解器使用固体有限元精确描述压电连续体中电位的三维​​分布。该方法可以准确分析RC电路、压电并联阻尼和压电能量收集中的耦合现象。