Table of contents
The box method and some error estimation
This article focuses its attention on practical use of the box method for solving certain type of partial differential equations. The heat conduction problem of the oil transformer under stationary load is described by this equation. The knowledge of the transformer operating temperature is important for ensuring correct functionality and lifespan of transformer. We consider an elliptic partial differential equation of second order with the Newton boundary condition on a rectangular domain. The...
The combination technique for a two-dimensional convection-diffusion problem with exponential layers
Convection-diffusion problems posed on the unit square and with solutions displaying exponential layers are solved using a sparse grid Galerkin finite element method with Shishkin meshes. Writing for the maximum number of mesh intervals in each coordinate direction, our “combination” method simply adds or subtracts solutions that have been computed by the Galerkin FEM on , and meshes. It is shown that the combination FEM yields (up to a factor ) the same order of accuracy in the associated...
The Convergence rate and Complexity of Precondotioned Iterative methods based on Approximate finite Element matrix Factorization
The CUDA implementation of the method of lines for the curvature dependent flows
We study the use of a GPU for the numerical approximation of the curvature dependent flows of graphs - the mean-curvature flow and the Willmore flow. Both problems are often applied in image processing where fast solvers are required. We approximate these problems using the complementary finite volume method combined with the method of lines. We obtain a system of ordinary differential equations which we solve by the Runge-Kutta-Merson solver. It is a robust solver with an automatic choice of the...
The island model as a Markov dynamic system
Parallel multi-deme genetic algorithms are especially advantageous because they allow reducing the time of computations and can perform a much broader search than single-population ones. However, their formal analysis does not seem to have been studied exhaustively enough. In this paper we propose a mathematical framework describing a wide class of island-like strategies as a stationary Markov chain. Our approach uses extensively the modeling principles introduced by Vose, Rudolph and their collaborators....
The mesh chopping algorithm for singularly perturbed boundary value problem.
The numerical solution of compressible flows in time dependent domains
This work is concerned with the numerical solution of inviscid compressible fluid flow in moving domains. Specifically, we assume that the boundary part of the domain (impermeable walls) are time dependent. We consider the Euler equations, which describe the movement of inviscid compressible fluids. We present two formulations of the Euler equations in the ALE (Arbitrary Lagrangian-Eulerian) form. These two formulations are discretized in space by the discontinuous Galerkin method. We apply a semi-implicit linearization...
The SOR Method on Parallel Computers.
The use of graphics card and nVidia CUDA architecture in the optimization of the heat radiation intensity
The paper focuses on the acceleration of the computer optimization of heat radiation intensity on the mould surface. The mould is warmed up by infrared heaters positioned above the mould surface, and in this way artificial leathers in the automotive industry are produced (e.g. for car dashboards). The presented heating model allows us to specify the position of infrared heaters over the mould to obtain approximately even heat radiation intensity on the whole mould surface. In this way we can obtain...
Three dimensional modelling of the peach in MAPLE
Linearized Gauss-Newton iteration method is used to determine main axes of the three-dimensional ellipsoid approximating a peach. Three independent photos displaying the peach as ground, side, and front view are used as data sources. System MAPLE 11 was used as a computer environment. A practical example is presented in order to demonstrate the usage of all required commands. The quality of approximation is evaluated as a final part of the paper.
Three-dimensional numerical model of neutron flux in hex-Z geometry
We present a method for solving the equations of neutron transport with discretized energetic dependence and angular dependence approximated by the diffusion theory. We are interested in the stationary solution that characterizes neutron fluxes within the nuclear reactor core in an equilibrium state. We work with the VVER-1000 type core with hexagonal fuel assembly lattice and use a nodal method for numerical solution. The method effectively combines a whole-core coarse mesh calculation with a more...
Transputer implementation of block regularized filtering
Triangulation automatique d’un polyèdre en dimension
Two implementations of the preconditioned conjugate gradient method on heterogeneous computing grids
Efficient iterative solution of large linear systems on grid computers is a complex problem. The induced heterogeneity and volatile nature of the aggregated computational resources present numerous algorithmic challenges. This paper describes a case study regarding iterative solution of large sparse linear systems on grid computers within the software constraints of the grid middleware GridSolve and within the algorithmic constraints of preconditioned Conjugate Gradient (CG) type methods. We identify...