一种快速高精度Duhamel积分算法

A fast precise algorithm for Duhamel integrals

基于快速傅里叶变换(FFT)和数值积分理论,提出了一种应用于振型叠加法的龙贝格快速傅里叶变换(R-FFT)积分算法.将单自由度二阶微分方程的Duhamel积分的求解转换为一系列快速卷积项和梯形积分修正项的加权叠加,充分利用了系统脉冲响应和激励的整个时间序列的信息.R-FFT借助于成熟的FFT方法实现快速计算,并利用不同阶次的龙贝格积分格式改善收敛精度.数值算例表明该算法具有快速、精度高、适应性强的特点.

A Romberg-fast Fourier transform （R-FFT） integration algorithm based on fast Fourier transform （FFT） and numerical integration theory was proposed for modal superposition method. The algorithm transforms Duhamel integral into weighted superposition of some rapid convolutions and a correction term of trapezoidal integration, which making the best use of the whole time information of impulse response and exciting forces. Taking advantages of excellent FFT algorithms, the calculation is much more rapid than the classical recurrent methods, and the precision is improved with different order Romberg integral schemes. Numerical results show the high speed, high accuracy and good adaptability of R-FFT.