R. Čiegis

Numerical algorithms for simulation of multisection lasers by using traveling wave model

Abstract Sequential and parallel algorithms for the simulation of the dynamics of high‐power semiconductor lasers is presented. The model equations describing the multisection broad–area semiconductors lasers are solved by the finite difference scheme, which is constructed on staggered grids. This nonlinear scheme is linearized applying the predictor‐corrector method. The algorithm is implemented by using the ParSol tool of parallel linear algebra objects. For parallelization we adopt the domain partitioning method, the domain is split along the longitudinal axis. Results of computational experiments are presented, the obtained speed‐up and efficiency of the parallel algorithm agree well with the theoretical scalability analysis.

Parallel algorithms for solution of nonlinear diffusion problems in image smoothing 1

Abstract In this work we consider parallel algorithms for solution of nonlinear parabolic PDEs. First mathematical models describing nonlinear diffusion filters are presented. The finite‐volume method is used to approximate differential equations. Parallel algorithms are based on the domain decomposition method. The algorithms are implemented by using ParSol parallelization tool and a brief description of this tool is also presented. The efficiency of proposed parallel algorithms is investigated and results of the scalability analysis are given. Theoretical predictions are compared with results of computational experiments. Application of nonlinear diffusion filters for analysis of computer tomography images is discussed in the last section of the paper.

Numerical simulation of the heat conduction in electrical cables

Abstract The modelling of the heat conduction in electrical cables is a complex mathematical problem. To get a quantitative description of the thermo‐electrical characteristics in the electrical cables, one requires a mathematical model for it. It must involve the different physical phenomena occurring in the electrical cables, i.e. heat conduction, convection and radiation effects, description of heat sources due to current transitions. Since the space in mobile systems is limited and weight is always reduced, wire conductor sizes must be kept as small as possible. Thus the main aim is to determine optimal conductor cross‐sections for long standing loads. In this paper we develop and validate a set of mathematical models and numerical algorithms for the heat transfer simulation in cable bundles. The numerical algorithms are targeted to the two‐dimensional transient heat transfer mathematical models. Finally, a validation procedure for the coefficient validation of the differential equations is carried ou...

Template realization of generalized branch and bound algorithm

Abstract In this work we consider a template for implementation of parallel branch and bound algorithms. The main aim of this package to ease implementation of covering and combinatorial optimization methods for global optimization. Standard parts of global optimization algorithms are implemented in the package and only method specific rules should be implemented by the user. The parallelization part of the tool is described in details. Results of computational experiments are presented and discussed.

Numerical solution of hyperbolic heat conduction equation

Abstract Hyperbolic heat conduction problem is solved numerically. The explicit and implicit Euler schemes are constructed and investigated. It is shown that the implicit Euler scheme can be used to solve efficiently parabolic and hyperbolic heat conduction problems. This scheme is unconditionally stable for both problems. For many integration methods strong numerical oscillations are present, when the initial and boundary conditions are discontinuous for the hyperbolic problem. In order to regularize the implicit Euler scheme, a simple linear relation between time and space steps is proposed, which automatically introduces sufficient amount of numerical viscosity. Results of numerical experiments are presented.

An implementation of a parallel generalized branch and bound template

Abstract Branch and bound (BnB) is a general algorithm to solve optimization problems. We present a template implementation of the BnB paradigm. A BnB template is implemented using C++ object oriented paradigm. MPI is used for underlying communications. A paradigm of domain decomposition (data parallelization) is used to construct a parallel algorithm. To obtain a better load balancing, the BnB template has the load balancing module that allows the redistribution of search spaces among the processors at run time. A parallel version of users algorithm is obtained automatically. A new derivative‐free global optimization algorithm is proposed for solving nonlinear global optimization problems. It is based on the BnB algorithm and its implementation is done by using the developed BnB algorithm template library. The robustness of the new algorithm is demonstrated by solving a selection of test problems.

Mathematical modeling of wood drying process 1

Abstract This work focuses on the development of mathematical models describing moisture movement in wood, when the wood is considered as porous medium. Main moisture transport mechanisms are discussed. It is shown how the wood can be described as a two‐ or three‐phase system. Summaries of several multiphase flow models are presented in the hierarchical order: from the most general models to more simple examples. The approximation steps are described explicitly, and all assumptions are given in detail. It shown how models for specific applications in wood drying or saturation can be obtained.

Numerical simulation of the heat conduction in composite materials

Abstract In this paper we develop and validate mathematical models and numerical algorithms for the heat transfer simulation in composite materials. The main features of the problem deal with the dependence of the heat source on the solution, discontinuous diffusion coefficients and nonlinear convection and radiation boundary conditions. The differential problem is approximated by the finite volume discrete scheme. It is proved that for a sufficiently small parameter, which defines the dependence of the source term on the solution, the discrete problem has a unique solution which converges to the solution of the differential problem. Linearization of the nonlinear problem is done by using the Picard method and the convergence of the iterations is proved. Results of numerical experiments are presented.

Finite‐difference scheme for one problem of nonlinear optics

Abstract We consider a mathematical model, which describes Q‐switching process. The finite difference scheme is developed for approximation of the given system of nonlinear PDEs. It is constructed by using the staggered grid, such a strategy enables an automatic linearization of the algorithm. The transport equations are approximated along characteristics z±t, thus no discretization error is introduced at this stage. But such algorithm puts a strong relation between time and space steps of the discrete grid. The convergence analysis of this scheme is done using the method developed in [2]. First some estimates of the boundedness of the exact solution are proved. Then the boundedness of the discrete solution is investigated. On the basis of these estimates the main stability inequality is proved. The second order convergence rate with respect the space and time coordinates follows from this estimate.

Mathematical modeling of grain drying 1

Abstract In this paper we consider the mathematical model which describes the grain drying process. The air and grain moisture and temperature are described by a system of PDE. A finite difference scheme is proposed for finding a numerical solution. The convergence of the discrete solution is proved for a simplified model, when the temperature is assumed to be given a priori. Results of numerical experiments are presented.