Two improved isogeometric quadratic elements and the central difference scheme are used to formulate the solution procedures of transient wave propagation prob- lems. In the proposed procedures, the lumped matrices co...Two improved isogeometric quadratic elements and the central difference scheme are used to formulate the solution procedures of transient wave propagation prob- lems. In the proposed procedures, the lumped matrices corresponding to the isogeomet- ric elements are obtained. The stability conditions of the solution procedures are also acquired. The dispersion analysis is conducted to obtain the optimal Courant-Friedrichs- Lewy （CFL） number or time-step sizes corresponding to the spatial isogeometric elements. The dispersion analysis shows that the isogeometric quadratic element of the fourth-order dispersion error （called the isogeometric analysis （IGA）-f quadratic element） provides far more desirable numerical dissipation/dispersion than the element of the second-order dis- persion error （called the IGA-s quadratic element） when appropriate time-step sizes are selected. The numerical simulations of one-dimensional （1D） transient wave propagation problems demonstrate the effectiveness of the proposed solution procedures.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11602004 and11325210)
文摘Two improved isogeometric quadratic elements and the central difference scheme are used to formulate the solution procedures of transient wave propagation prob- lems. In the proposed procedures, the lumped matrices corresponding to the isogeomet- ric elements are obtained. The stability conditions of the solution procedures are also acquired. The dispersion analysis is conducted to obtain the optimal Courant-Friedrichs- Lewy （CFL） number or time-step sizes corresponding to the spatial isogeometric elements. The dispersion analysis shows that the isogeometric quadratic element of the fourth-order dispersion error （called the isogeometric analysis （IGA）-f quadratic element） provides far more desirable numerical dissipation/dispersion than the element of the second-order dis- persion error （called the IGA-s quadratic element） when appropriate time-step sizes are selected. The numerical simulations of one-dimensional （1D） transient wave propagation problems demonstrate the effectiveness of the proposed solution procedures.
