Strongly coupled partitioned iterative method for the structure–piezoelectric–circuit interaction using hierarchical decomposition

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