Domain decomposition algorithms for indefinite weakly singular integral equations: the h and p versions

We extend the approach of Cai and Widlund (Domain decompositionalgorithms for indefinite elliptic problems, SIAM J. Sci. Stat.Comput. 13 (1992), 243-258), which was designed for finite elementdiscretizations, to boundary element discretizations of indefiniteweakly singular integral equations. Both the h and p versionsof the Galerkin approximation are considered. We prove thatthe additive Schwarz method suggested by Cai and Widlund canbe used for this equation as an efficient preconditioner forGMRES, an iterative method of conjugate gradient type. For bothversions, the rates of convergence of this iterative methodare shown to approach 1 only logarithmically as the degreesof freedom tend to infinity.     

Anisotropic magnetoresistance of two-dimensional holes in GaAs

Experiments on high-quality GaAs (311)A two-dimensional holes at low temperatures reveal a remarkable dependence of the magnetoresistance, measured with an in-plane magnetic field ( B), on the direction of B relative to both the crystal axes and the current direction. The magnetoresistance features, and in particular the value of B above which the resistivity exhibits an insulating behavior, depend on the orientation of B. To explain the data, the anisotropic band structure of the holes and a repopulation of the spin subbands in the presence of B, as well as the coupling of the orbital motion to B, need to be taken into account.     

Highly anisotropic g-factor of two-dimensional hole systems

Coupling the spin degree of freedom to the anisotropic orbital motion of two-dimensional (2D) hole systems gives rise to a highly anisotropic Zeeman splitting with respect to different orientations of an in-plane magnetic field B relative to the crystal axes. This mechanism has no analog in the bulk band structure. We obtain good, qualitative agreement between theory and experimental data, taken in GaAs 2D hole systems grown on (113) substrates, showing the anisotropic depopulation of the upper spin subband as a function of in-plane B.