In the paper, the numerical analysis of thermal processes proceeding in the domain of biological tissue subjected to an external heat source is presented. Heat transfer in the skin tissue was assumed to be transient and two-dimensional. The bioheat transfer in the domain considered is described by the system of Pennes equations determining the temperature field in successive skin layers. Between the layers the ideal contact is assumed. On the selected part of skin surface the Neumann condition determining the value of external heat source is given, on the conventionally assumed internal surface of the tissue the no-flux condition is accepted. For time *t*=0 the initial distribution of temperature is known. The degree of the skin burn can be predicted on the basis of the so-called Henriques integrals and the main subject of the paper is the sensitivity analysis of these integrals with respect to the skin parameters. On the stage of numerical computations the boundary element method has been used. In the final part of the paper the results obtained are shown.
*Keywords:* bioheat transfer, burn integrals, sensitivity analysis, boundary element method.

I. ©pacapan, M. Premrov. Modal analysis of wave motion in inhomogeneous waveguides which are modelled by FEM. CAMES 2004 (11)

This paper presents a simple computing procedure for the analysis of the wave motion in infinite layered waveguides via the analysis of the propagating wave modes. Waveguides may have irregular inclusions, which yields complicated reflections of waves, and an analytical solution is practically not feasible. The section of the waveguide, where we want to analyze the displacements and stress waves, is modelled by finite elements using standard programs for FEM. The external problem is solved as an internal one, while the radiation conditions are satisfied exactly. The procedure only some simple mathematical manipulations and is performed in the frequency domain. It yields exact results and a clear insight into the propagating wave modes. The results of the first presented numerical example are compared to the exact ones, while in the second example the foundation represents an irregularity in the waveguide composed of two layers

M. Premrov, I. ©pacapan. Solving wave problems in infinite domain by using variable local DtN operators. CAMES 2004 (11)

This paper presents an iterative method for solving two-dimensional wave problems in infinite domains. The method yields a solution that satisfies Sommerfeld's radiation condition, as required for the correct solution of infinite domains excited only locally. This problem occurs in the solution of the wave equation in infinite domains when using an asymptotic local DtN (Dirichlet-to-Neumann) map in computational procedures applied to a finite domain. We are demonstrating that the amplitudes of the reflected fictive harmonics depend upon the wave number, the location of the fictive boundary, as well as on the DtN operator used in the computations. A constant value of the operator cannot sufficiently eliminate the amplitudes of all reflected waves, while the results are poor especially for higher harmonics. Thus, we are proposing an iterative method, which varies the tangential dependence of the operator in each computational step.
*Keywords:* wave motion, infinite domains, fictive boundary, radiation condition, DtN operators.

S. D. Rajan, D. T. Nguyen, M. D. Deshpande, L. Harrell. Optimal design of engineering systems using MPI-enabled genetic algorithm. CAMES 2004 (11)

The focus of this paper is on the development and implementation of a genetic algorithm (GA)-based software system using message passing interface (MPI) protocol and library. A customized form of simple GA used in previous research [1-4] is parallelized. This MPI-enabled version is used to find the solution to finite element based design optimization problems. Results show that an almost linear speedup is obtained on homogenous hardware cluster and, with proper reworking of the software, on heterogeneous hardware cluster.
*Keywords:* parallel processing, genetic algorithm, MPI, structural optimization.

S. F. Araslanov. Artificial relations between quantities at nearest nodes or cells and the Newton iteration procedure for the modified pressure correction method. CAMES 2004 (11)

In this article a method for calculation of the finite-difference Navier-Stokes equations with a time step *Δt=h/u*_{flow} (*h* is the average cell's size, uflow flow velocity) at the minimal expenses of computer time is suggested.
To realize the Newton-type iteration scheme and in order to avoid solving large-volume linear systems of equations for points *k*, which contain the variations of unknowns not only at the point *k* but also at points *k*' neighbouring with the point *k*, we replace the unknown relations between the variations of quantities at nearest points *k* and *k'* with artificial ones. Therefore the unknowns at the point *k* can be directly determined via equations at the point *k* and one does not need to apply complicated technique. The introduction of artificial relations between the variations of quantities at nearest nodes or cells and the use of approximate equality **c**'≈-**c** relating geometric coefficients of both displaced and usual cells make it possible to obtain formulas for correct rates of change of the residuals of the equations. Consequently, only four global iterations and 4 to 5 (in average) inner pressure correction iterations for every global iteration suffice to provide the convergence.
*Keywords:* heat transfer flows, approximation technique, Newton iteration method, pressure correction.

I. Georgiev, S. Margenov. DD-MIC(0) preconditioning of rotated trilinear FEM elasticity systems. CAMES 2004 (11)

New results about preconditioning of rotated trilinear nonconforming FEM elasticity systems in the case of mesh anisotropy are presented. The solver of the arising linear system is based on the constructed efficient preconditioner of the coupled stiffness matrix. Displacement decomposition of the stiffness matrix is used as a first step of the algorithm. At the second step, modified incomplete factorization MIC(0) with perturbation is applied to a proper auxiliary M-matrix to get an approximate factorization of the obtained block-diagonal matrix. The derived condition number estimates and the presented numerical tests well illustrate the behaviour of the theoretically studied algorithms as well as their robustness for some more realistic benchmark problems.

Z. Gáspár, R. Németh. Discrete model of twisted rings. CAMES 2004 (11)

A discrete model consisting N straight links and N springs is defined. The originally straight model is bent into a discrete torus, then it is twisted. The C_{2} symmetric shapes can be determined by four parameters, and there are three constrains. The equilibrium paths are determined by the simplex method (piecewise linear approximation). Global bifurcation diagrams, spatial equilibrium shapes and parasitic solutions are analysed.

S. L. Skorokhodov, V. I. Vlasov. The Multipole method for the Laplace equation in domains with polyhedral corners. CAMES 2004 (11)

A new analytic-numerical method has been developed for solving the Laplace equation in domains with cones of arbitrary base, in particular with polyhedral corners. The solution is represented as an expansion involving singular functions (the Multipoles), which play the role of basic functions. The method enables to find these functions explicitly and to compute efficiently their singularity exponents. The method possesses exponential rate of convergence and provides precise computation of the solution, its derivatives and intensity factors at the edges and at the corner point. In addition, an asymptotic expansion of the solution near the edges of polyhedral corner has been obtained.

F. Konkol, V. Kompi¹. Trefftz polynomials reciprocity based boundary element formulations for elastodynamics. CAMES 2004 (11)

In this paper Trefftz polynomials are used for the BEM (Boundary Element Method) based on the reciprocity relations. BEM provides a powerful tool for the calculation of dynamic structural response in the frequency and time domains. Field equations of motion and boundary conditions are cast into boundary integral equations (BIE), which are discretized only on the boundary [1]. Trefftz polynomials or other non-singular (e.g. harmonic), Trefftz functions [2] (i.e. functions satisfying all governing differential equations but not the boundary conditions) used in the Betti's reciprocity relations lead to corresponding BIE that do not contain any (weak, strong, hyper) singularities. Fundamental solutions are not needed and evaluation of the field variables inside the domain is simpler.

Z. Mi¹koviæ. Model for the determination of the load carrying capacity of the RC walls. CAMES 2004 (11)

The paper presents the possibility of the limit stress state approximation of the reinforced concrete wall structures by discontinuous stress fields with variable configuration. Heuristic optimization technique, *simulated annealing*, is applied to determine optimal configuration for approximation of *load carrying capacity* based on *lower bound theorem* of theory of plasticity. Model was tested by comparing with the results of several experimental tested beams, as well as with other numerical models.
*Keywords:* concrete stuctures, plastic design, carrying capacity, numerical methods, heuristic optimization, simulated annealing.