Asymptotic behaviour of splitting schemes involving time-subcycling techniques

Asymptotic behavior of splitting schemes involving time-subcycling techniques

In order to integrate numerically a well-posed multiscale evolutionary problem such as a Cauchy problem for an ODE system or a PDE system, using time-subcycling techniques consists in splitting the vector field in a fast part and a slow part and taking advantage of this decomposition, for example by integrating the fast equation on a much smaller time step than the slow equation (instead of hav...

Splitting schemes for unsteady problems involving the grad-div operator

In this paper we consider various splitting schemes for unsteady problems containing the grad-div operator. The fully implicit discretization of such problems would yield at each time step a linear problem that couples all components of the solution vector. In this paper we discuss various possibilities to decouple the equations for the different components that result in unconditionally stable...

Asymptotic Behaviour of Some Infinite Products Involving Prime Numbers

Asymptotic behaviour of some infinite products involving prime numbers

The asymptotic behaviour of some entire functions defined via infinite products is investigated as the parameter z tends to infinity in the sector | arg z| < π. These functions arise in the distributions of the number of prime factors of integers and of the number of irreducible factors of monic polynomials over a finite field. Our approach is based on the Mellin transform with a suitable conto...

Asymptotic behaviour of graded components of local cohomology modules

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