This paper proposes improving the solve time of a bootstrap algebraic multigrid (AMG) designed previously by the authors. This is achieved by incorporating the information, a set of algebraically smooth vectors, generated by the bootstrap algorithm, in a single hierarchy by using sufficiently large aggregates, and these aggregates are compositions of aggregates already built throughout the bootstrap algorithm. The modified AMG method has good convergence properties and shows significant reduction in both memory and solve time.

The morphology of a mixture made of a polar active gel immersed in an isotropic passive fluid is studied numerically. Lattice Boltzmann method is adopted to solve the Navier-Stokes equation and coupled to a finite-difference scheme used to integrate the dynamic equations of the concentration and of the polarization of the active component. By varying the relative amounts of the mixture phases, different structures can be observed.

We present here a comparison between collision-streaming and finite-difference lattice Boltzmann (LB) models. This study provides a derivation of useful formulae which help one to properly compare the simulation results obtained with both LB models. We consider three physical problems: the shock wave propagation, the damping of shear waves, and the decay of Taylor-Green vortices, often used as benchmark tests. Despite the different mathematical and computational complexity of the two methods, we show how the physical results can be related to obtain relevant quantities.

We investigate nonlinear elliptic Dirichlet problems whose growth is driven by a general anisotropic N-function, which is not necessarily of power-type and need not satisfy the ? nor the ? -condition. Fully anisotropic, non-reflexive Orlicz-Sobolev spaces provide a natural functional framework associated with these problems. Minimal integrability assumptions are detected on the datum on the right-hand side of the equation ensuring existence and uniqueness of weak solutions.

Let X={X1,X2,...,Xm} be a system of smooth vector fields in R^n satisfying the Hörmander's finite rank condition. We prove the following Sobolev inequality with reciprocal weights in Carnot-Carathéodory space G associated to system X (1?BRK(x)dx?BR|u|tK(x)dx)1/t<=CR??1?BR1K(x)dx?BR|Xu|2K(x)dx??1/2, where Xu denotes the horizontal gradient of u with respect to X. We assume that the weight K belongs to Muckenhoupt's class A_2 and Gehring's class G_?, where ? is a suitable exponent related to the homogeneous dimension.

We study an eigenvalue problem involving a fully anisotropic elliptic differential operator in arbitrary Orlicz-Sobolev spaces. The relevant equations are associated with constrained minimization problems for integral functionals depending on the gradient of competing functions through general anisotropic N-functions. In particular, the latter need neither be radial, nor have a polynomial growth, and are not even assumed to satisfy the so called \Delta_2-condition. The resulting analysis requires the development of some new aspects of the theory of anisotropic Orlicz-Sobolev spaces.

We investigate how the Z-type dynamic approach can be applied to control backward bifurcation phenomena in epidemic models. Because of its rich phenomenology, that includes stationary or oscillatory subcritical persistence of the disease, we consider the SIR model introduced by Zhou & Fan in [Nonlinear Analysis: Real World Applications, 13(1), 312-324, 2012] and apply the Z-control approach in the specific case of indirect control of the infective population.

In this paper, we deploy the hybrid Lattice Boltzmann - Particle Dynamics (LBPD) method to investigate the transport properties of blood flow within arterioles and venules. The numerical approach is applied to study the transport of Red Blood Cells (RBC) through plasma, highlighting significant agreement with the experimental data in the seminal work by Fahraeus and Lindqvist. Moreover, the results provide evidence of an interesting hand-shaking between the range of validity of the proposed hybrid approach and the domain of viability of particle methods.

We discuss the state of art of Lattice Boltzmann (LB) computing, with special focus on prospective LB schemes capable of meeting the forthcoming Exascale challenge. After reviewing the basic notions of LB computing, we discuss current techniques to improve the performance of LB codes on parallel machines and illustrate selected leading-edge applications in the Petascale range. Finally, we put forward a few ideas on how to improve the communication/computation overlap in current largescale LB simulations, as well as possible strategies towards fault-tolerant LB schemes.