The initial-boundary value problem for quasi-linear parabolic equation with distribution coefficient modelling the nonlinear filtration is discussed. The presented results constitute extension of the earlier works of the authors concerning the filtration problem in the domains without sources to the case of filtration in the presence of sources.

A parameter identification problem for nonlinear parabolic equation describing the prelinear filtration phenomenon is considered. It is shown that the problem admits a non-empty solution set which is stable with respect to perturbations in the cost functional and the data. The numerical method for solving the inverse problem is given and the computational results are presented.

We examine S-continued fraction bounds on the effective dielectric constant epsilon_e of a two-phase composite for the case where the dielectric coefficients epsilon_1 and epsilon_2 are complex. The starting point for our study is a power series expansion of epsilon_e at z=0, z=epsilon_2/epsilon_1-1. The S-continued fractions to the expansions of epsilon_e(z) have an interesting mathematical structure. Its convergents represent the best bounds derived earlier by Milton, and independently by Bergman. Specific examples of calculation of complex S-continued fraction bounds on epsilon_e are provided.

The aim of this contribution is to present two-point Padé approximants method for the determination of upper and lower estimates on the effective transport coefficients of two-phase composite materials. The obtained formulae improve the corresponding one-point Padé approximants bounds. As an example, a set of narrowing bounds for the overall conductivity of a square array of cylinders has been evaluated.

Two topics are discussed. Firstly, exact formulae for the homogenized coefficients of a layered thermopiezoelectric composite are derived. Secondly, by applying the Ritz method, the local problems are solved approximately. Specific cases are also examined and illustrated.

The present paper further develops the boundary element technique to provide an efficient and accurate method of analysing the crack propagation processes in 2-D linear elastic structures. Based on both the direct boundary integral equations, for source points located on the external boundary of the plane elastic region, and the indirect boundary integral equations, for the resultant forces acting on one side of the crack surfaces, this technique allows to avoid problems associated with other numerical methods for fracture mechanics computation. In the first part of this paper, the proposed boundary element technique and also the strain energy density criterion, which determines the crack increment in a mixed-mode loading situations, are described. In the second part, two numerical examples are enclosed to demonstrate the capabilities of the boundary element technique as a tool for modelling an arbitrary crack, predicting its growth and updating the model geometry to simulate the next crack increment.

Distributed programming paradigm in key stages of CAD process is proposed, as an alternative to the conventional single-computer--single-user approach. Object-oriented technology is suggested for cooperative design and implementation of large scale engineering computations. Complex ideas concerning specification and design of the new system are presented. In addition, an example of the transformation of the old CAD system to the new environment is described.