S hur omplement pre onditioning for ellipti systems of partial di erential equations D. Loghin and A. J. Wathen One su essful approa h in the design of solution methods for saddle-point problems requires the eÆ ient solution of the asso iated S hur omplement problem ([26℄, [19℄). In the ase of problems arising from partial di erential equations the fa torization of the symbol of the operator an...

The optical eld in a weakly guiding homogeneous waveguide satis es scalar Helmholtz equations in both the core and cladding, and transmission conditions on the boundary. The transverse wavenumbers of the two scalar Helmholtz equations for the core and cladding are di erent and both of them depend on the propagation constants in the longitudinal direction of the waveguide. Two di erent systems o...

Smoothed Particle Hydrodynamics SPH is a meshless Lagrangian parti cle method for solving a system of hydrodynamic equations for compressible uids SPH is especially suited for problems with free boundaries a commonplace situation in as trophysics Rather than solving the equations on a grid the equations are solved at the positions of the so called particles each representing a mass packet with ...

The intention of this special session on ”Advances in the numerical solution of nonlinear evolution equations” is to gather mathematicians and theoretical physicists, interconnected through their field of application, the analytical tools, or the numerical methods used. The scope of topics includes but is not limited to Schrödinger type equations, highly oscillatory equations, parabolic problem...

So called \recursive equations" have been introduced by Baccelli et al. as a convenient way of characterizing the behavior of stochastic Petri net models in terms of transition ring instances and of creation and destruction times for tokens in places [1, 2]. Such equations have been used to prove model properties as well as to speed up simulation by parallel processing techniques in the case of...

Newton's method is a fundamental technique underlying many numerical methods for solving systems of nonlinear equations and optimization problems. However, it is often not fully appreciated that Newton's method can produce signi cantly di erent behavior when applied to equivalent systems, i.e., problems with the same solution but di erent mathematical formulations. In this paper, we investigate...

The Euler-Poincaré di↵erential (EPDi↵) equations are of general interest as evolution equations on Riemannian manifolds endowed with Sobolev metrics. The EPDi↵ equations describe geodesic motion on the di↵eomorphism group. The deformation between the reference and the target templates, following the path of minimum energy, satisfies the EPDi↵ equations. The EPDi↵ equations can be written as a f...

We develop a discontinuous ®nite element method for advection±di€usion equations arising in contaminant transport problems, based on the Local Discontinuous Galerkin (LDG) method of Cockburn B and Shu CW. (The local discontinuous Garlerkin method for time-dependent convection±di€usion systems. SIAM J Numer Anal 1998;35:2440±63). This method is de®ned locally over each element, thus allowing for...

The paper introduces an approach for the derivation of discrete time approximations for solutions of stochastic di erential equations with time delay. The suggested approximations converge in a strong sense. Furthermore, explicit solutions for linear stochastic delay equations are given.

Symbolic Reachability Computation for Families of Linear Vector Fields Gerardo Lafferriere Department of Mathematical Sciences Portland State University, P.O. Box 751, Portland, OR 97207-0751. [email protected] George J. Pappas Department of Electrical Engineering University of Pennsylvania, 200 South 33rd Street, Philadelphia, PA 19104. [email protected] Sergio Yovine VERIMAG Centre Equat...