Convergence theories and a deluxe dual and primal finite element tearing and interconnecting algorithm are developed for a hybrid staggered DG finite element approximation of H(curl) elliptic problems in two dimensions. In addition to the advantages of staggered DG methods, the basis functions of the new hybrid staggered DG method are all locally supported in the triangular elements, and a Lagrange multiplier approach is applied to enforce the global connections of these basis functions. The interface problem on the Lagrange multipliers is further reduced to the resulting problem on the subdomain interfaces, and a dual and primal finite element tearing and interconnecting algorithm with an enriched weight factor is then applied to the resulting problem. Our algorithm is shown to give a condition number bound of <i>C</i>(1+log(<i>H</i><i>h</i>))², independent of the two parameters, where <i>H</i><i>h</i> is the number of

In this paper, a class of FETI-DP preconditioners is developed for a fast solution of the linear system arising from staggered discontinuous Galerkin discretization of the two-dimensional Stokes equations. The discretization has been recently developed and has the distinctive advantages that it is optimally convergent and has a good local conservation property. In order to efficiently solve the linear system, two kinds of FETI-DP preconditioners, namely, lumped and Dirichlet preconditioners, are considered and analyzed. Scalable bounds C (H/h) and C (1+ log (H/h)) 2 are proved for the lumped and Dirichlet preconditioners, respectively, with the constant C depending on the infsup constant of the discrete spaces but independent of any mesh parameters. Here H/h stands for the number of elements across each subdomain. Numerical results are presented to confirm the theoretical estimates.

The most general admissible boundary conditions are derived for an idealized AharonovBohm flux intersecting the plane at the origin on the background of a homogeneous magnetic field. A standard technique based on self-adjoint extensions yields a four-parameter family of boundary conditions; the other two parameters of the model are the AharonovBohm flux and the homogeneous magnetic field. The generalized boundary conditions may be regarded as a combination of the AharonovBohm effect with a point interaction. Spectral properties of the derived Hamtonians are studied in detail.

We investigate a charged two-dimensional particle in a homogeneous magnetic field interacting with a periodic array of point obstacles. We show that while Landau levels remain to be infinitely degenerate eigenvalues, between them the system has bands of absolutely continuous spectrum and exhibits thus a transport along the array. We also compute the band functions and the corresponding probability current.

In this paper, we consider the numerical approximation of the three-dimensional poroelastic wave equations in the spherical coordinate system. One difficulty in the design of an efficient numerical scheme is that the problem is singular in the center and the polar axes of the computational domain. Nevertheless, we develop a hybrid finite difference/control volume method for solving this problem. Our method is explicit and is second order accurate in both space and time. Numerical results are shown to confirm the convergence rate of our method and the effectiveness to simulate wave propagation in poroelastic media in the spherical coordinate system.