‎Using the explicit forms of eigenstates for linearized operator related to a matrix version of Nonlinear Schrödinger equation‎, ‎soliton perturbation theory is developed for the $F=1$ bright spinor Bose-Einstein condensates‎. ‎A small disturbance of the integrability condition can be considered as a small correction to the integrable equation‎. ‎By choosing appropriate perturbation‎, ‎the soli...

In this paper we discuss new domain decomposition preconditioners for piecewise linear finite element discretisations of boundary-value problems for the model elliptic problem −∇ · (A∇u) = f , (1) in a bounded polygonal or polyhedral domain Ω ⊂ R, d = 2 or 3 with suitable boundary data on the boundary ∂Ω. The tensor A(x) is assumed isotropic and symmetric positive definite, but may vary with ma...

Associated to a symplectic quotient $M/\!/G$ is Lagrangian correspondence $\Lambda_G$ from $M$. In this note, we construct in two examples quilts with seam condition on such correspondence, the case of $S^1$ acting $\mathbb{CP}^2$ $\mathbb{CP}^2/\!/ S^1 = \mathbb{CP}^1$. First, study quilted strips that would, if not for figure eight bubbling, identify Floer chain groups $CF(\gamma,S_{\text{Cl}...

In this paper we consider the full discretization of linear Maxwell’s equations on spatial grids which are locally refined. For such problems, explicit time integration schemes become ine cient because the smallest mesh width results in a strict CFL condition. Recently locally implicit time integration methods have become popular in overcoming the problem of so called grid-induced sti↵ness. Var...

For many flow problems modeled by Large Eddy Simulation (LES), the computational meshes are such that a large number of the elements would allow for explicit timestepping, but the CFL-condition is highly limited by the smaller stretched elements in the boundary layers. We propose an implicit-explicit time-integration scheme that uses an implicit solver only for the smaller portion of the domain...

Conventional explicit nite diierence schemes for the advection equations are subject to the time step restrictions dictated by the CFL condition. In many situations, time step sizes are not chosen to satisfy accuracy requirements but rather to satisfy the CFL condition. In this paper we present explicit algorithms which are stable far beyond the CFL restriction. Similar or even better accuracy ...