In this paper, we develop a new reduced basis (RB) method, named as Single Eigenvalue Acceleration Method (SEAM), for second-order parabolic equations with homogeneous Dirichlet boundary conditions. The high-fidelity numerical method adopts the backward Euler scheme and conforming finite elements for the temporal and spatial discretization, respectively. Under the assumption that the time step size is sufficiently small and time steps are not very large, we show that the singular value distribution of the high-fidelity solution matrix $U$ is close to that of a rank one matrix. We select the eigenfunction associated with the principal eigenvalue of the matrix $U^\top U$ as the basis of the Proper Orthogonal Decomposition (POD) method to obtain SEAM and a parallel SEAM. Numerical experiments confirm the efficiency of the new method.

翻译：在本文中,我们开发了一种新的降低基数(RB)方法,称为单一电子价值加速法(SEAM),用于具有同质二极分立边界条件的二级抛物线方程式;高纤维数字法分别采用后向极分法和符合时间和空间分解的限定元素;假设时间步骤大小足够小,时间步骤也不大,我们表明高纤维溶解矩阵的单值分布值为1美元接近于一等矩阵。我们选择与基体主电子值U ⁇ top U$相联系的元功能作为适当矫形分解法的基础,以获得SEAM和平行的SEAM。数字实验证实了新方法的效率。