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

A New Reduced Basis Method for Parabolic Equations Based on Single-Eigenvalue Acceleration