相关论文: On discretizations of axisymmetric systems

We consider a family of conforming space-time finite element discretizations for the wave equation based on splines of maximal regularity in time. Traditional techniques may require a CFL condition to guarantee stability. Recent works by O.…

In this paper we study the stability of explicit finite difference discretizations of linear advection-diffusion equations (ADE) with arbitrary order of accuracy in the context of method of lines. The analysis first focuses on the stability…

We consider a family of conforming space-time discretizations for the wave equation based on a first-order-in-time formulation employing maximal regularity splines. In contrast with second-order-in-time formulations, which require a CFL…

A method of the formal diagonalization of the discrete linear operator with a parameter is studied. In the case when the operator provides a Lax operator for a nonlinear quad system the formal diagonalization method allows one to describe…

As global ocean general circulation models are run at eddy-permitting resolutions, reproducing accurate growth rates of baroclinic instabilities is a major concern when choosing a discretization of the equations of motion. From this…

We consider the finite difference discretization of isotropic elastic wave equations on nonuniform grids. The intended applications are seismic studies, where heterogeneity of the earth media can lead to severe oversampling for simulations…

We review asymptotic stability of solitary waves for nonlinear dispersive equations set on the line. Our focus is threefold: first, the nonlinear Schrodinger equation; second, the notion of full asymptotic stability (which states that…

This thesis aims at investigating the first steps toward an unconditionally stable space-time isogeometric method, based on splines of maximal regularity, for the linear acoustic wave equation. The unconditional stability of space-time…

We consider a scalar diffusion equation with a sign-changing coefficient in its principle part. The well-posedness of such problems has already been studied extensively provided that the contrast of the coefficient is non-critical.…

We present natural axisymmetric variants of schemes for curvature flows introduced earlier by the present authors and analyze them in detail. Although numerical methods for geometric flows have been used frequently in axisymmetric settings,…

We present a theorem that allows to simplify linear stability analysis of periodic and quasiperiodic nonlinear regimes in N-particle mechanical systems (both conservative and dissipative) with different kinds of discrete symmetry. This…

We revisit second-order-in-time space-time discretizations of the linear and semilinear wave equations by establishing precise equivalences with first-order-in-time formulations. Focusing on schemes using continuous piecewise-polynomial…

Astrophysical discs which are sufficiently massive and cool are linearly unstable to the formation of axisymmetric structures. In practice, linearly stable discs of surface density slightly below the threshold needed for this instability…

We present an approach to simulate the 3D isotropic elastic wave propagation using nonuniform finite difference discretization on staggered grids. Specifically, we consider simulation domains composed of layers of uniform grids with…

An exact discretization method is being developed for solving linear systems of ordinary fractional-derivative differential equations with constant matrix coefficients (LSOFDDECMC). It is shown that the obtained linear discrete system in…

Mathematical descriptions of flow phenomena usually come in the form of partial differential equations. The differential operators used in these equations may have properties such as symmetry, skew-symmetry, positive or negative…

In recent publications, the author and his coworkers have proposed a multigrid method for solving linear systems arizing from the discretization of partial differential equations in isogeometric analysis and have proven that the convergence…

In this paper, we consider the problem of stabilizing discrete-time linear systems by computing a nearby stable matrix to an unstable one. To do so, we provide a new characterization for the set of stable matrices. We show that a matrix $A$…

Astrophysical disks that are sufficiently cold and dense are linearly unstable to the formation of axisymmetric rings as a result of the disk's gravity. In practice, spiral structures are formed, which may in turn produce bound fragments.…

This paper extends previous work on finitedifference schemes over staggered grids for infinite-dimensional port-Hamiltonian systems. In the one-dimensional setting, it generalizes the discretization approach originally developed for the…