Comparison of Different-Ordered Polynomial Acceleration Methods

The polynomial interpolation acceleration method for time history analysis is presented, in which accelerations between several equal neighboring time steps are assumed to be polynomial function of time. In term of Taylor deployment theorem, with the increase of degree of polynomial, higher order precision of the solution of dynamic equation can be achieved thus wider time step can be used to solve the dynamic equation with truncation error in the acceptable limit. However, when higher degree of polynomial is used, the stabilization field of the method narrow down, which leads to restriction of the time step size. Once time step is larger than the limit of smaller convergence field, the transferred error will be magnified many times and results in the failure of solution. Numerical analysis shows that the higher order polynomial interpolation acceleration method unnecessarily leads to wider acceptable time step. Stabilization field and convergence accuracy taken into account, the square acceleration method is superior to linear and third-degree polynomial acceleration method.