一种新的减基法中的采样方法及误差估计

A novel sampling method with error estiomation for the reduced basis method

针对减基法中求解精度受减基空间完备性影响的问题,提出了一种基于向量空间逼近原理的采样方法及相应的误差估计。该方法使每一步采样得到的特征向量与之前已得到的特征向量所张成的向量空间角度最大,从而保证了每步采样所对应的特征向量都具有最弱相关性,进而使最终得到的特征向量基空间更具完备性。并且由该方法产生了一种先验特征值误差界,使得减基法所产生的特征值误差能被控制在预先设定的范围之内。文中算例显示了该方法的有效性。

The vector-space approximation sampling method is proposed here for the reduced basis method in which the precision of solution is influenced by completeness of basis space. The method can enable the corresponding eigenvector obtained in every step to have the biggest angle with the space constructed by early sampling eigenvectors, and then it makes the constructed eigenvector basis space have the weakest correlation and thus be more complete. Furthermore, this method can bring on a prior eigenvalue error bound which can ensure the eigenvalue errors produced by the reduced basis methods to be limited in the previously set scopes. The numerical example demonstrates the validity of the proposed sampling method.