1205.3808 (Hasan Almanasreh)

hp-Cloud Approximation Of The Dirac Eigenvalue Problem: The Way Of
Stability    [PDF]

Hasan Almanasreh

We apply hp-cloud method to the radial Dirac eigenvalue problem. The difficulty of occurrence of spurious values among the genuine eigenvalues is treated. The method of treatment is based on assuming hp-cloud Petrov-Galerkin scheme to construct the weak formulation of the problem which adds a consistent diffusivity to the variational formulation without deforming the equation. The size of the artificially added diffusion term is controlled by a derived stability parameter ($\tau$). The derivation of $\tau$ considers the limit behavior of the eigenvalues at infinity. The importance of $\tau$ is of being applicable for generic basis functions. This is together with choosing appropriate intrinsic enrichments in the construction of the cloud shape functions.

View original: http://arxiv.org/abs/1205.3808