β Scribed by S. Zhao
No coin nor oath required. For personal study only.
In this paper, the origins of spurious solutions occurring in the high-order finite difference methods are studied. Based on a uniform mesh, spurious modes are found in the high-order one-sided finite difference discretizations of many eigenvalue problems. Spurious modes are classified as spectral pollution and non-spectral pollution. The latter can be partially avoided by mesh refinement, while the former persists when the mesh is refined. Through numerical studies of some prototype eigenvalue problems, such as those of the Helmholtz and beam equations, we show that perfect central differentiation schemes do not produce any spurious modes. Nevertheless, high-order central difference schemes encounter difficulties in implementing complex boundary conditions. We further show that the central difference schemes will produce spurious modes as well, if asymmetric approximation is involved in boundary treatments. In general, central difference schemes are less likely to produce spurious modes than one-sided difference schemes.
π SIMILAR VOLUMES
This work investigates the mitigation and elimination of scheme-related oscillations generated in compact and classical fourth-order finite difference solutions of stiff problems, represented here by the Burgers and Reynolds equations. The regions where severe gradients are anticipated are refined b
## Abstract Although unconditionally stable (US), the accuracy of ADIβFDTD is not so high as that of conventional FDTD. In this paper, a highβorder USβFDTD based on the weighted finiteβdifference method is presented. A strict analysis of stability shows that it is unconditionally stable. And, more