In this paper we investigate performance of global communications in a particular parallel code. The code simulates dynamics of expansion of premixed spherical flames using an asymptotic model of Sivashinsky type and a spectral numerical algorithm. As a result, the code heavily relies on global all-to-all interprocessor communications implementing transposition of the distributed data array in ...

The dissertation is divided into two separate parts. First part We propose an e cient and generic algorithm for rigorous integration forward in time of systems of equations originating from partial di erential equations written in the Fourier basis. By rigorous integration we mean a procedure, which operates on sets, and return sets which are guaranteed to contain the exact solution. The algori...

This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method can be extended to functional differential and integro-differential equations. For showing efficiency of the method we give some numerical examples.

The nonlinear nonlocal Michelson-Sivashinsky equation for isolated crests of unstable flames is studied, using pole-decompositions as starting point. Polynomials encoding the numerically computed 2N flame-slope poles, and auxiliary ones, are found to closely follow a MeixnerPollaczek recurrence; accurate steady crest shapes ensue for N3. Squeezed crests ruled by a discretized Burgers equation ...

In this work, we study the one-dimensional stabilized Kuramoto Sivashinsky equation with additive uncorrelated stochastic noise. The Eckhaus stable band of the deterministic equation collapses to a narrow region near the center of the band. This is consistent with the behavior of the phase diffusion constants of these states. Some connections to the phenomenon of state selection in driven out o...