In this second part, we carry out a numerical comparison between two Vlasov solvers, which solve directly the Vlasov equation on a grid of the phase space. The two methods are based on the semi-Lagrangian method as presented in Part I: the first one (LOSS) uses a uniform mesh of the phase space whereas the second one (OBI) is an adaptive method. The numerical comparisons are performed by solvin...

In this era of precision cosmology, a detailed physical understanding on the evolution of cosmic baryons is required. Cosmic magnetic fields, though still poorly understood, may represent an important component in the global cosmic energy flow that affects the baryon dynamics. We have developed an Eulerianbased cosmological magnetohydrodynamics code (CosmoMHD) with modern shock capturing scheme...

In this paper, we suggest a new Heterogeneous Multiscale Method (HMM) for the Helmholtz equation with high contrast. The method is constructed for a setting as in Bouchitté and Felbacq (C.R. Math. Acad. Sci. Paris 339(5):377–382, 2004), where the high contrast in the parameter leads to unusual effective parameters in the homogenized equation. We revisit existing homogenization approaches for th...

Let U ⊆ H(OP1×P1 (2, 1)) be a basepoint free four-dimensional vector space. The sections corresponding to U determine a regular map φU : P1 × P1 −→ P3. We study the associated bigraded ideal IU ⊆ k[s, t;u, v] from the standpoint of commutative algebra, proving that there are exactly six numerical types of possible bigraded minimal free resolution. These resolutions play a key role in determinin...

This paper introduces a new method for accelerating current sluggish FEM and improving memory demand in FEM problems with high node resolution or bulky structures. Like most of the numerical methods, FEM results to a matrix equation which normally has huge dimension. Breaking the main matrix equation into several smaller size matrices, the solving procedure can be accelerated. For implementing ...