Spin models in three dimensions: Adaptive lattice spacing

Entropic lattice Boltzmann models for hydrodynamics in three dimensions.

Efficient, nonlinearly stable entropic lattice Boltzmann models for computational fluid dynamics are presented. A new method of fast evaluation of equilibria to machine precision is proposed. Analytical solution is found for the collision step which guarantees stability and thermodynamic consistency of the scheme. As an example, a novel 15-velocity lattice Boltzmann model is derived and validat...

Monte Carlo studies of antiferromagnetic spin models in three dimensions

The study of antiferromagnetic models (AFM) may give us some insights on the formulation of non trivial relativistic quantum field theories, as they present a very rich phase space and, presumably, new universality classes [1]. They are also interesting as related with models describing high temperature superconductors [2]; the two dimensional quantum Heisenberg antiferromagnet in the low tempe...

Lattice and spin polarons in two dimensions

Adaptive BDDC in three dimensions

The adaptive BDDC method is extended to the selection of face constraints in three dimensions. A new implementation of the BDDC method is presented based on a global formulation without an explicit coarse problem, with massive parallelism provided by a multifrontal solver. Constraints are implemented by a projection and sparsity of the projected operator is preserved by a generalized change of ...

The Optimal Lattice Quantizer in Three Dimensions

The body-centered cubic lattice is shown to have the smallest mean squared error of any lattice quantizer in three dimensions, assuming that the input to the quantizer has a uniform distribution.