A novel efficient method for real-time computation of parameterized dynamic equations with large-scale dimension

摘要

This paper presents an efficient method for solving the parameterized dynamic linear equilibrium equations of large dimensions. This technique uses the conception of the reduced-basis method and is developed by the combination of time integration and least square projection to treat dynamic problems, in which the characteristic matrices are characterized and influenced by a number of independent parameters. Time integration is developed for constructing basis spaces, and least square projection is used for dimensional reduction. Three distinct kinds of reduced-basis spaces can be obtained by integration of the displacement, velocity, and acceleration basis vectors in the time field, respectively. Then, via performing least square projection of the original problem onto the reduced-basis spaces of much smaller dimension, and conducting the offline-online computational procedures, the approximate solutions of the dynamic problems are computed efficiently and accurately. Also, the computations under singularity condition are taken into consideration. Both theoretical analyses and numerical discussions have shown that substantial time efficiency and sufficient reliability can be achieved for real-time computation by using the suggested method.