APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 4th International ConferenceAMiTaNS '12 Memorial Volume devoted to Prof. Christo I. Christov
 PLENARY TALKS


Mathematical modling of the 3D separated viscous fluid flows
View Description Hide DescriptionThe 3D homogeneous and density stratified viscous fluid flows around a sphere and a circular cylinder have been investigated by means of the direct numerical simulation on supercomputers and the visualization of the 3D vortex structures in the wake. These flows have been simulated on the basis of the NavierStokes equations (NSE) in the Boussinesq approximation. The different transitions in sphere wakes (2D3D, laminarturbulent and others) with increasing of Reynolds number Re (1<Re<500000) and decreasing of Froude number Fr (0.005<Fr<1000) have been investigated in details. The classifications of flow regimes have been refined. It was found also that the values of the maximum phase difference along the circular cylinder axis are approximately equal to 0.10.2 T (for mode A, 191<Re≤300) and 0.0150.030 T (for mode B, 300≤Re≤400), where the time T is the period of the flow.

Semicoarsening AMLI preconditioning of higher order elliptic problems
View Description Hide DescriptionThe present paper presents the construction of a robust multilevel preconditioner for anisotropic bicubic finite element (FE) elliptic problems. More precisely, the behavior of the constant in the strengthened CBS inequality, which is important for studying (approximate) block factorizations of FE stiffness matrices, is analyzed in the case when the underlying conforming FE space consists of piecewise bicubic functions, and is decomposed according to hierarchical splittings that are based on semicoarsening of the FE mesh. The presented theoretical estimates are further confirmed by numerically computed CBS constants for a rich set of parameters (coarsening factor and anisotropy ratio). The problem of solving efficiently systems with the pivot block matrices arising in the hierarchical basis twolevel matrices is also addressed in this paper. Finally, combining the proven uniform estimates with the theory of the Algebraic Multilevel Iteration (AMLI) methods an optimal order multilevel algorithm whose total computational cost is proportional to the size of the discrete problem with a proportionality constant independent of the anisotropy ratio is obtained.

Fourstage computational technology with adaptive numerical methods for computational aerodynamics
View Description Hide DescriptionComputational aerodynamics is a key technology in aircraft design which is ahead of physical experiment and complements it. Of course all three components of computational modeling are actively developed: mathematical models of real aerodynamic processes, numerical algorithms, and highperformance computing. The most impressive progress has been made in the field of computing, though with a considerable complication of computer architecture. Numerical algorithms are developed more conservative. More precisely, they are offered and theoretically justified for more simple mathematical problems. Nevertheless, computational mathematics now has amassed a whole palette of numerical algorithms that can provide acceptable accuracy and interface between modern mathematical models in aerodynamics and highperformance computers. A significant step in this direction was the European Project ADIGMA whose positive experience will be used in International Project TRISTAM for further movement in the field of computational technologies for aerodynamics. This paper gives a general overview of objectives and approaches intended to use and a description of the recommended fourstage computer technology.

Vortex safety in aviation
View Description Hide DescriptionThe objective is the general review of impact of aircraft wake vortices on the follower aircraft encountering the wake. Currently, the presence of wake vortices past aircraft limits the airspace capacity and flight safety level for aircraft of different purposes. However, wake vortex nature and evolution have not been studied in full measure. A mathematical model simulating the process of near wake generation past bodies of different shapes, as well as the wake evolution after rollingup into wake vortices (far wake) is developed. The processes are suggested to be modeled by means of the Method of Discrete Vortices. Far wake evolution is determined by its complex interaction with the atmosphere and ground boundary layer. The main factors that are supposed to take into account are: wind and ambient turbulence 3Ddistributions, temperature stratification of the atmosphere, wind shear, as well as some others which effects will be manifested as considerable during the investigation. The ground boundary layer effects on wake vortex evolution are substantial at low flight altitudes and are determined through the boundary layer separation.

 SPECIAL SESSIONS

 HPC GRID APPLICATIONS IN COMPUTATIONAL PHYSICS AND COMPUTATIONAL CHEMISTRY

Web service module for access to gLite
View Description Hide DescriptionGLite is a lightweight grid middleware for grid computing installed on all clusters of the European Grid Infrastructure (EGI). The middleware is partially serviceoriented and does not provide welldefined Web services for job management. The existing Web services in the environment cannot be directly used by grid users for building service compositions in the EGI. In this article we present a module of welldefined Web services for job management in the EGI. We describe the architecture of the module and the design of the developed Web services. The presented Web services are composable and can participate in service compositions (workflows). An example of usage of the module with tools for service compositions in gLite is shown.

Numerical study of the wind energy potential in Bulgaria  Some preliminary results
View Description Hide DescriptionThe new energy efficiency politics of the EU requires till year 2020 16% of Bulgarian electricity to be produced from renewable sources. The wind is one of renewable energy sources. The ecological benefits of all the kinds of "green" energy are obvious. It is desirable, however, the utilization of renewable energy sources to be as much as possible economically effective. This means that installment of the respective devices (wind farms, solar farms, etc.) should be based on a detailed and reliable evaluation of the real potential of the country. Detailed study of the wind energy potential of the country  spatial distribution, temporal variation, mean and extreme values, fluctuations and statistical characteristics; evaluation from a point of view of industrial applicability can not be made only on the basis of the existing routine meteorological data  the measuring network is not dense enough to catch all the details of the local flow systems, hence of the real wind energy potential of the country spatial distribution. That is why the measurement data has to be supplemented by numerical modeling. The wind field simulations were performed applying the 5th generation PSU/NCAR MesoMeteorological Model MM5 for years 20002007 with a spatial resolution of 3 km over Bulgaria. Some preliminary evaluations of the country wind energy potential, based on the simulation output are demonstrated in the paper.

Comparison of some approximation schemes for convective terms for solving gas flow past a square in a microchannel
View Description Hide DescriptionRapidly emerging microelectromechanical devices create new potential microfluidic applications. A simulation of an internal and external gas flows is important for their design. For small Knudsen number Kn < 0.1 (Kn = l _{0}/L, where l _{0} is the mean free path of the gas molecules and L is the characteristic length), a continuum approach based on modified NavierStokesFourier or extended hydrodynamic continuum models with corresponding velocityslip and temperaturejump boundary conditions is still applicable and, respectively, preferable. We restrict ourself to the use of NavierStokesFourier continuum model. A development of the algorithm to solve a specific class of problems is closely related to numerical schemes used for approximation of equations terms. Higherorder approximation schemes can reduce the number of mesh nodes and respectively computational time, but it is possible to obtain physical unrealistic results. In this paper we study influence of some approximation schemes for convective terms over the spatial steps. It is compared upwind, central difference and total variation diminishing (TVD) schemes MinMod, QUICK and SUPERBEE. A test case is gas flow past a square in a microchannel at subsonic speed (Mach number M = 0.1) and supersonic speed (M = 2.43), available in a literature.

Operational pollution forecast for the region of Bulgaria
View Description Hide DescriptionAn operational prototype of the Integrated Bulgarian Chemical Weather Forecasting and Information System is presented. This version of the system is limited to relatively low resolution (10 km) but covers all Bulgaria. It is based on the US EPA Models3 System (MM5, SMOKE and CMAQ). The meteorological input to the system is the Bulgarian operational numerical weather forecast. The boundary conditions are taken from analogous Greek system (Aristotle University of Thessaloniki). Bulgarian system runs automatically twice a day (00 and 12 UTC) and produces 48hour forecast. The part of the results of each System's run is postprocessed in a way to be visualized and uploaded to a respective web site. In the paper, description of the System is given together with a demonstration of its products. In addition highlights of Systems upgrade will be given.

Using analytic hierarchy process approach in ontological multicriterial decision making  Preliminary considerations
View Description Hide DescriptionIn this paper we consider combining ontologically demarcated information with Saaty's Analytic Hierarchy Process (AHP) [1] for the multicriterial assessment of offers during contract negotiations. The context for the proposal is provided by the Agents in Grid project (AiG; [2]), which aims at development of an agentbased infrastructure for efficient resource management in the Grid. In the AiG project, software agents representing users can either (1) join a team and earn money, or (2) find a team to execute a job. Moreover, agents form teams, managers of which negotiate with clients and workers terms of potential collaboration. Here, ontologically described contracts (Service Level Agreements) are the results of autonomous multiround negotiations. Therefore, taking into account relatively complex nature of the negotiated contracts, multicriterial assessment of proposals plays a crucial role. The AHP method is based on pairwise comparisons of criteria and relies on the judgement of a panel of experts. It measures how well does an offer serve the objective of a decision maker. In this paper, we propose how the AHP method can be used to assess ontologically described contract proposals.

Numerical experiments with applying approximate LUfactorizations as preconditioners for solving SLAEs with coefficient matrices from the "Sparse Matrix Market"
View Description Hide DescriptionThe solution of systems of linear algebraic equations (SLAEs) is very often the most timeconsuming part of the computational process during the treatment of the original problems, because these systems can be very large (containing up to many millions of equations). It is, therefore, important to select fast, robust and reliable methods for the solution of SLAEs when large applications are to be run, also in the case where fast modern computers are available. Since the coefficient matrices of the systems are normally sparse (i.e., most of their elements are zeros), the first requirement is to exploit efficiently the sparsity. However, this is normally not sufficient when the systems are very large. The computation of preconditioners based on approximate LUfactorizations and their use in the efforts to increase further the efficiency of the calculations will be discussed in this paper. Computational experiments based on comprehensive comparisons of many numerical results that are obtained by using ten wellknown methods for solving SLAEs (the direct Gaussian elimination and nine iterative methods) when the coefficient matrices are chosen from the "Sparse Matrix Market" are reported in this paper. Most of the methods are preconditioned Krylov subspace algorithms.

An algebraic method for reconstruction of harmonic functions via radon projections
View Description Hide DescriptionWe consider an algebraic method for reconstruction of a harmonic function via a finite number of values of its Radon projections. More precisely, for given values of some Radon projections, we seek a harmonic polynomial which matches these data exactly. In the present work, we focus mostly on the case where these measurements are taken along equally spaced chords of the unit circle. We present an efficient reconstruction algorithm which is robust with respect to noise in the input data and provide numerical examples.

Computer simulation of RF liver ablation on an MRI scan data
View Description Hide DescriptionRadiofrequency (RF) ablation is a low invasive technique for treatment of liver tumors. An RFprobe is inserted in the patient's liver and a ground pad is applied to the skin. Then the tumor is heated with RF current. The heat causes the destruction of tumor cells. We use the finite element method (FEM) to simulate and analyze various aspects of the procedure. A 3D image of the patient's liver is obtained from a magnetic resonance imaging (MRI) scan. Then, the geometry for the RFprobe and the ground pad is added. Our focus is on the influence of the position of the ground pads on the ablation process. Our simulation is based on an unstructured mesh. The size of the mesh is large due to the complexity of the domain. We discretize and solve the problem on a parallel computer using MPI for the parallelization. The presented numerical tests are performed on IBM Blue Gene/P machine at BGSC. The parallel efficiency of the incorporated Boomer AMG solver is demonstrated as well.

A numerical approach to the nonconvex dynamic problem of pipelinesoil interaction under environmental effects
View Description Hide DescriptionA numerical approach for a problem arising in Civil and Environmental Engineering is presented. This problem concerns the dynamic soilpipeline interaction, when unilateral contact conditions due to tensionless and elastoplastic softening/fracturing behaviour of the soil as well as due to gapping caused by earthquake excitations are taken into account. Moreover, soilcapacity degradation due to environmental effects are taken into account. The mathematical formulation of this dynamic elastoplasticity problem leads to a system of partial differential equations with equality domain and inequality boundary conditions. The proposed numerical approach is based on a double discretization, in space and time, and on mathematical programming methods. First, in space the finite element method (FEM) is used for the simulation of the pipeline and the unilateral contact interface, in combination with the boundary element method (BEM) for the soil simulation. Concepts of the nonconvex analysis are used. Next, with the aid of Laplace transform, the equality problem conditions are transformed to convolutional ones involving as unknowns the unilateral quantities only. So the number of unknowns is significantly reduced. Then a marchingtime approach is applied and a nonconvex linear complementarity problem is solved in each timestep.

An efficient highly parallel implementation of a large air pollution model on an IBM blue gene supercomputer
View Description Hide DescriptionIn this paper we discuss the efficient distributedmemory parallelization strategy of the Unified Danish Eulerian Model (UNIDEM). We apply an improved decomposition strategy to the spatial domain in order to get more parallel tasks (based on the larger number of subdomains) with less communications between them (due to optimization of the overlapping area when the advectiondiffusion problem is solved numerically). This kind of rectangular block partitioning (with a squareshape trend) allows us not only to increase significantly the number of potential parallel tasks, but also to reduce the local memory requirements per task, which is critical for the distributedmemory implementation of the higherresolution/finergrid versions of UNIDEM on some parallel systems, and particularly on the IBM BlueGene/P platform  our target hardware. We will show by experiments that our new parallel implementation can use rather efficiently the resources of the powerful IBM BlueGene/P supercomputer, the largest in Bulgaria, up to its full capacity. It turned out to be extremely useful in the large and computationally expensive numerical experiments, carried out to calculate some initial data for sensitivity analysis of the Danish Eulerian model.
 CONTRIBUTED SESSIONS

 APPLIED ANALYSIS

State estimation for linear stochastic differential equations with uncertain disturbances via BSDE approach
View Description Hide DescriptionA backward stochastic differential equation (BSDE) is an Ito stochastic differential equation (SDE) for which a random terminal condition on the state has been specified. The paper deals with estimation problems for partly observed stochastic processes described by linear SDEs with uncertain disturbances. The disturbances and unknown initial states are supposed to be constrained by the inequality including mathematical expectation of the integral quadratic cost. We consider our equations as BSDEs, and construct at given instant the random information set of all possible states which are compatible with the measurements and the constraints. The center of this set represents the best estimation of the process' state. The evolutionary equations for the random information set and for the best estimation are given. Some examples and applications are considered.

Hausdorff continuous solutions of conservation laws
View Description Hide DescriptionWe present a framework for studying discontinuous solutions of the Cauchy problem for nonlinear conservation laws, in particular entropy solutions of scalar conservation laws. The space of generalized solutions is constructed as the completion of the space of continuously differentiable functions with respect to a suitable uniform convergence structure. Within this context the wellposedness of the problem follows in an easy and natural way. Furthermore, we show that the space of solutions is a subspace of the space of Hausdorff continuous interval valued functions which improves significantly on the current regularity results of the entropy solution.

On the axiomatization of scalespace theory
View Description Hide DescriptionScalespaces are a common method for analysis of images. It involves an operator depending on a parameter, called a scale, which acts in some space of real functions. Many different scalespaces have been defined and used in practice. The most popular example is the Gaussian ScaleSpace where the operator is defined as a convolution integral involving the Gaussian distribution function with the standard variation being the scale parameter. There have also been many attempts for axiomatization of scalespace theory. The novelty of our approach is that it does not assume integral representation of the scalespace operator. While the new theory is applicable to, and in fact represents and abstraction of the properties of all existing operators, most importantly that of causality, it uses as an essential example the operator and the respective scalespace provided by the Discrete Pulse Transform.

Dimensionless form for Goodwin's equation of business cycle
View Description Hide DescriptionWe have conducted numerically a comparative analysis of two models of the business cycle proposed by R. Goodwin, Econometrica, 19, 117 (1951): in form of the neutral differential equation with fixed delay and in form of the second order nonlinear ordinary differential equation. Both models demonstrate the possibility of oscillations of income (socalled Goodwin's oscillations). We have shown that for these models the excitation conditions for Goodwin's oscillations and the some its properties may be very different.