In many transport-chemistry models, a huge system of ODE's of the advection-diffusion-reaction type has to be integrated in time. Typically, this is done with the help of operator splitting. Operator splitting is attractive for complex large-scale transport-chemistry models because it allows to handle different processes separately in different parts of the computer program. Rosenbrock schemes ...

The valence-band electronic structure of a clean Ni(111) surface is investigated by spin-resolved photoemission. At room temperature the orientation of the photoelectron spins on the Bloch sphere and the exchange splitting of surface and bulk states along the surface normal (Γ̅ ) are determined. All investigated states are found to have a sizable exchange splitting >50 meV. Since the splitting i...

In this paper we describe an iterative operator-splitting method for unbounded operators. We derive error bounds for iterative splitting methods in the presence of unbounded operators and semigroup operators. Here mixed applications of hyperbolic and parabolic type are allowed and discussed in the applications. Mixed experiments are applied to ordinary differential equations and evolutionary Sc...

We consider force-gradient, also called modified potential, operator splitting methods for problems with unbounded operators. We prove that force-gradient operator splitting schemes retain their classical orders of accuracy for time-dependent partial differential equations of parabolic or Schrödinger type, provided that the solution is sufficiently regular.

Using the principle that characteristic polynomials of matrices obtained from elements of a reductive group G over Q typically have splitting field with Galois group isomorphic to the Weyl group of G, we construct an explicit monic integral polynomial of degree 240 whose splitting field has Galois group the Weyl group of the exceptional group of type E8.

This paper shows, by means of a new type of operator called a splitting operator, that the Douglas-Rachford splitting method for finding a zero of the sum of two monotone operators is a special case of the proximal point algorithm. Therefore, applications of Douglas-Rachford splitting, such as the alternating direction method of multipliers for convex programming decomposition, are also special...

The splitting of eh(A+B) into a single product of eh A and eh B results in symplectic integrators when A and B are classical Lie operators. However, at high orders, a single product splitting, with exponentially growing number of operators, is very difficult to derive. This work shows that, if the splitting is generalized to a sum of products, then a simple choice of the basis product reduces t...

Photon splitting is a QED process that can potentially suppress pair production in the inner magnetosphere of a pulsar with a super-strong magnetic field, and hence, may quench radio emission from these objects. While it is unknown how many splitting modes really operate in supercritical fields, we derive gap parameters of a high magnetic field pulsar for both the vacuum-type gap and the space-...

The present work introduces a modified scheme for the solution of compressible 2-D full Navier-Stokes equations, using Flux Vector Splitting method. As a result of this modification, numerical diffusion is reduced. The computer code which is developed based on this algorithm can be used easily and accurately to analyze complex flow fields with discontinuity in properties, in cases such as shock...

Over the last ten years, robustness of schemes has raised an increasing interest among the CFD community. The objective of this article is to solve the quasi-one-dimensional compressible flow inside a “Shubin nozzle” and to investigate Bean-Warming and flux vector splitting methods for numerical solution of compressible flows. Two different conditions have been considered: first, there is a sup...