The back and forth error compensation and correction (BFECC) method advects the solution forward and then backward in time. The result is compared to the original data to estimate the error. Although inappropriate for parabolic and other nonreversible partial differential equations, it is useful for often troublesome advection terms. The error estimate is used to correct the data before advecti...

The paper studies a splitting method for the numerical time-integration of the system of partial differential equations describing the motion of viscous incompressible fluid with free boundary subject to surface tension forces. The method splits one time step into a semi-Lagrangian treatment of the surface advection and fluid inertia, an implicit update of viscous terms and the projection of ve...

Modeling reactive transport in porous media, using a local chemical equilibrium assumption, leads to a system of advection-diffusion PDE’s coupled with algebraic equations. When solving this coupled system, the algebraic equations have to be solved at each grid point for each chemical species and at each time step. This leads to a coupled non-linear system. In this paper a global solution appro...

Semi-Lagrangian (SL) methods have been very popular in the Vlasov simulation community [28, 2, 3, 18, 31, 4, 23, 25]. In this paper, we propose a new Strang split SL discontinuous Galerkin (DG) method for solving the Vlasov equation. Specifically, we apply the Strang splitting for the Vlasov equation [5], as a way to decouple the nonlinear Vlasov system into a sequence of linear equations. To e...

Online and stochastic learning has emerged as powerful tool in large scale optimization. In this work, we generalize the Douglas-Rachford splitting (DRs) method for minimizing composite functions to online and stochastic settings (to our best knowledge this is the first time DRs been generalized to sequential version). We first establish an O(1/ √ T ) regret bound for batch DRs method. Then we ...

A new algorithm for volume tracking which is based on the concept of flux-corrected transport (FCT) is introduced. It is applicable to incompressible 2D flow simulations on finite volume and difference meshes. The method requires no explicit interface reconstruction, is direction-split and can be extended to 3D and orthogonal curvilinear meshes in a straightforward manner. A comparison of the n...

In a bi-directional Community Antenna Television (CATV) Network the use of a Contention Resolutions Algorithm (CRA) is essential in order to allocate the bandwidth of the multiaccess medium in the upstream direction between the active stations. Two of the CRAs known as exponential backoff algorithm and splitting tree algorithm, have recently been adopted by the Digital Video Broadcasting (DVB)/...

The action of high-intensity ultraviolet pulse laser radiation on a 161 bp fragment of pBR 322 DNA (EcoRI-MspI fragment) was studied. At doses up to 5 X 10(18) photons/cm2 the N-glycosidic bond splitting is negligible. The action of hot piperidine on irradiated DNA leads to chain splitting at the residues, modified via biphotonic processes. The modification and, hence, splitting efficiencies de...

Abstract We present a new rank-adaptive tensor method to compute the numerical solution of high-dimensional nonlinear PDEs. The combines functional train (FTT) series expansions, operator splitting time integration, and algorithm based on thresholding criterion that limits component PDE velocity vector normal FTT manifold. This yields scheme can add or remove modes adaptively from as integratio...