Reducing the Computational Requirements of the Differential Quadrature Method

TL;DR

This paper reveals that the weighting coefficient matrices in the differential quadrature method are centrosymmetric or skew-centrosymmetric under symmetric grid spacings, enabling a 75% reduction in computational effort for matrix operations.

Contribution

It introduces the properties of centrosymmetric and skew-centrosymmetric matrices in DQM, significantly reducing computational costs regardless of grid spacing equality.

Findings

75% reduction in computational effort demonstrated

Matrices are centrosymmetric or skew-centrosymmetric with symmetric grid spacings

Numerical examples validate the computational advantages

Abstract

This paper shows that the weighting coefficient matrices of the differential quadrature method (DQM) are centrosymmetric or skew-centrosymmetric if the grid spacings are symmetric irrespective of whether they are equal or unequal. A new skew centrosymmetric matrix is also discussed. The application of the properties of centrosymmetric and skew centrosymmetric matrix can reduce the computational effort of the DQM for calculations of the inverse, determinant, eigenvectors and eigenvalues by 75%. This computational advantage are also demonstrated via several numerical examples.