Ghost variables are assignable variables that appear in program annotations but do not correspond to physical entities. They are used to facilitate specification and verification, e.g., by using a ghost variable to count the number of iterations of a loop, and also to express extra-functional behaviours. In this paper we give a formal model of ghost variables and show how they can be eliminated...

We consider implicit integration methods for the numerical solution of sti initial-value problems. In applying such methods, the implicit relations are usually solved by Newton iteration. However, it often happens that in subintervals of the integration interval the problem is nonsti or mildly sti with respect to the stepsize. In these nonsti subintervals, we do not need the (expensive) Newton ...

We present numerical experiments for a nonoverlapping domain decomposition method with interface relaxation for general selfadjoint and non-selfadjoint elliptic problems in two dimensions. The procedure contains two steps in each full iteration. The transmission condition on the interface is taken to be Dirichlet in the rst step and Neumann in the second. However, in the presence of interior su...

This paper presents a model which provides a smooth transition between a kinetic and a diffusion domain. The idea is to use a buffer zone, in which both diffusion and kinetic equations will be solved. The solution of the original kinetic equation will be recovered as the sum of the solutions of these two equations. We use an artificial connecting function which makes the equation on each domain...

This paper presents a fast iterative solver for Lippmann-Schwinger equation for highfrequency waves scattered by a smooth medium with a compactly supported inhomogeneity. The solver is based on the sparsifying preconditioner [63] and a domain decomposition approach similar to the method of polarized traces [64]. The iterative solver has two levels, the outer level in which a sparsifying precond...

In this article, we consider the iterated Runge–Kutta (IRK) method which is an iteration method based on a predictor–corrector scheme for the solution of ordinary differential equations. The method uses embedded formulae to control the stepsize. We present different algorithms of the IRK method on distributed memory multiprocessors using appropriate communication primitives. The theoretical per...

The piecewise variational iteration method (VIM) for solving Riccati differential equations (RDEs) provides a solution as a sequence of iterates. Therefore, its application to RDEs leads to the calculation of terms that are not needed and more time is consumed in repeated calculations for series solutions. In order to overcome these shortcomings, we propose an easy-to-use piecewise-truncated VI...

This paper deals with the parallel simulation of delamination problems at the mesoscale by means of multi-scale methods, the aim being the Virtual Delamination Testing of Composite parts. In the non-linear context, Domain Decomposition Methods are mainly used as a solver for the tangent problem to be solved at each iteration of a Newton-Raphson algorithm. In case of strongly non linear and hete...

We analyze a space-time domain decomposition iteration, for a model advection diiusion equation in one and two dimensions. The asymptotic convergence rate is superlinear, and it is governed by the diiusion of the error across the overlap between subdomains. Hence, it depends on both the size of this overlap and the diiusion coeecient in the equation. However, it is independent of the number of ...

For nonselfadjoint elliptic boundary value problem which are preconditioned by a sub-structuring method, i.e., nonoverlapping domain decomposition, we introduce and study the concept of subspace orthogonalization. In subspace orthogonalization variants of Krylov methods the computation of inner products and vector updates, and the storage of basis elements is restricted to a (presumably small) ...