Large-Scale Scientific Computing

This paper analyzes the discrete energy laws associated with first-order system least-squares (FOSLS) discretizations of time-dependent partial differential equations. Using the heat equation and the time-dependent Stokes’ equation as examples, we discuss how accurately a FOSLS finite-element formulation adheres to the underlying energy law associated with the physical system. Using regularity arguments involving the initial condition of the system, we are able to give bounds on the convergence of the discrete energy law to its expected value (zero in the examples presented here). Numerical experiments are performed, showing that the discrete energy laws hold with order $$\mathcal O\left( h^{2p}\right) $$Oh2p, where h is the mesh spacing and p is the order of the finite-element space. Thus, the energy law conformance is held with a higher order than the expected, $$\mathcal {O}\left( h^p\right) $$Ohp, convergence of the finite-element approximation. Finally, we introduce an abstract framework for analyzing the energy laws of general FOSLS discretizations.

We present and analyze a new stable multi-patch space-time Isogeometric Analyis (IgA) method for the numerical solution of parabolic diffusion problems. The discrete bilinear form is elliptic on the IgA space with respect to a mesh-dependent energy norm. This property together with a corresponding boundedness property, consistency and approximation results for the IgA spaces yields a priori discretization error estimates. We propose an efficient implementation technique via tensor product representation, and fast space-time parallel solvers. We present numerical results confirming the efficiency of the space-time solvers on massively parallel computers using more than 100.000 cores.

This work presents a survey on some of the recent results on numerical methods for controlled switching diffusions. Before presenting the numerical parts, the basics of switching diffusions are recalled. Finally, some numerical examples are presented for demonstration.

Time-harmonic formulations enable solution of time-dependent PDEs without use of normally slow time-stepping methods. Two efficient preconditioners for the discretized parabolic and eddy current electromagnetic optimal control problems, one on block diagonal form and one utilizing the two by two block structure of the resulting matrix, are presented with simplified analysis and numerical illustrations. Both methods result in tight eigenvalue bounds for the preconditioned matrix and very few iterations that hold uniformly with respect to the mesh, problem and method parameters, with the exception of the dependence on reluctivity for the block diagonal preconditioner.

The paper is concerned with reliable space-time IgA schemes for parabolic initial-boundary value problems. We deduce a posteriori error estimates and investigate their applicability to space-time IgA approximations. Since the derivation is based on purely functional arguments, the estimates do not contain mesh dependent constants and are valid for any approximation from the admissible (energy) class. In particular, they imply estimates for discrete norms associated with stabilised space-time IgA approximations. Finally, we illustrate the reliability and efficiency of presented error estimates for the approximate solutions recovered with IgA techniques on a model example.

This work is devoted to numerical studies on an algebraic multigrid preconditioned GMRES method for solving the linear algebraic equations arising from a space–time finite element discretization of the heat equation using h–adaptivity on tetrahedral meshes. The finite element discretization is based on a Galerkin–Petrov variational formulation using piecewise linear finite elements simultaneously in space and time. In this work, we focus on h–adaptivity relying on a residual based a posteriori error estimation, and study some important components in the algebraic multigrid method for solving the space–time finite element equations.

This work is devoted to the study of complex fluids composed by the mixture between isotropic (newtonian fluid) and nematic (liquid crystal) flows, taking into account how the liquid crystal molecules behave on the interface between both fluids (anchoring effects) and the influence of the shape of the liquid crystal molecules on the dynamics of the system (stretching effects).First, we present the PDE system to model Nematic-Isotropic mixtures, taking into account viscous, mixing, nematic, anchoring and stretching effects. Then, we provide a new linear unconditionally energy-stable splitting scheme. Moreover, we present numerical simulations to show the efficiency of the proposed numerical scheme and the influence of the different types of anchoring effects in the dynamics of the system.

The domain decomposition methods for time-dependent problems are based on special schemes of splitting into subdomains. To construct homogeneous numerical algorithms, overlapping subdomain methods are preferable. The domain decomposition is associated with corresponding additive representation of the problem operator. Such regionally-additive schemes are based on the general theory of additive operator-difference schemes. There are variants of decomposition operators differing by distinct types of data exchanges on interfaces.New classes of domain decomposition schemes for transient problems based on subdomains overlapping are constructed. The boundary value problem for the parabolic equation of second order is considered as a model problem. We propose a general approach to construct vector domain decomposition schemes for time-dependent systems of equations. Using a partition of unity for a computational domain we perform a transition to finding the individual components of the solution in the subdomains. General stability conditions are obtained for vector regionally-additive schemes with first and second order accuracy.

The purpose of this paper is an alternative proof of a strip estimate, used in Least-Squares methods for interface problems, as in [4] for a two-phase flow problem with incompressible flow in the subdomains. The Stokes flow problems in the subdomains are treated as first-order systems and a combination of $$H ({\text {div}})$$H(div)-conforming Raviart-Thomas and standard $$H^1$$H1-conforming elements were used for the discretization. The interface condition is built directly in the $$H ({\text {div}})$$H(div)-conforming space. Using the strip estimate, the homogeneous Least-Squares functional is shown to be equivalent to an appropriate norm allowing the use of standard finite element approximation estimates.

In this paper the spectral mimetic least-squares method is applied to a two-dimensional div-curl system. A test problem is solved on orthogonal and curvilinear meshes and both h- and p-convergence results are presented. The resulting solutions will be pointwise divergence-free for these test problems. For $$N>1$$N>1 optimal convergence rates on an orthogonal and a curvilinear mesh are observed. For $$N=1$$N=1 the method does not converge.

We present a spectral mimetic least-squares method on curvilinear grids, which conserves important invariants. The method is developed using differential forms where the topological part and the constitutive part have been separated. It is shown that the topological part is solved exactly, independent of the order of the spectral expansion. The method is applied to a model convection-diffusion problem, where we show that conservation of a potential is satisfied up to machine precision. The convective term is represented using the Lie derivative, by means of Cartans homotopy formula. The spectral mimetic least-squares method is compared to a standard spectral least-squares method. It is shown that both schemes lead to spectral convergence.

One of the most cited disadvantages of least-squares formulations is its lack of conservation. By a suitable choice of least-squares functional and the use of appropriate conforming finite dimensional function spaces, this drawback can be completely removed. Such a mimetic least-squares method is applied to a curl-curl system. Conservation properties will be proved and demonstrated by test results on two-dimensional curvilinear grids.

There is a growing interest in the phase-field approach to numerically handle the interface dynamics in multiphase flow phenomena because of its accuracy. The numerical solution of phase-field models has difficulties in dealing with non-self-adjoint operators and the resolution of high gradients within thin interface regions. We present an h-adaptive mesh refinement technique for the least-squares spectral element method for the phase-field models. $$C^1$$C1 Hermite polynomials are used to give global differentiability in the approximated solution, and a space-time coupled formulation and the element-by-element technique are implemented. Two benchmark problems are presented in order to compare two refinement criteria based on the gradient of the solution and the local residual.

In this article a mixed least-squares finite element method (LSFEM) for the time-dependent incompressible Navier-Stokes equations is proposed and investigated. The formulation is based on the incompressible Navier-Stokes equations consisting of the balance of momentum and the continuity equations. In order to obtain a first-order system the Cauchy stress tensor is introduced as an additional variable to the system of equations. From this stress-velocity-pressure approach a stress-velocity formulation is derived by adding a redundant residual to the functional without additional variables in order to strengthen specific physical relations, e.g. mass conservation. We account for implementation aspects of triangular mixed finite elements especially regarding the approximation used for H(div$$) \times H^1$$)×H1 and the discretization in time using the Newmark method. Finally, we present the flow past a cylinder benchmark problem in order to demonstrate the derived stress-velocity least-squares formulation.

Independent meshing of subdomains separated by an interface can lead to spatially non-coincident discrete interfaces. We present an optimization-based coupling method for such problems, which does not require a common mesh refinement of the interface, has optimal $$H^1$$H1 convergence rates, and passes a patch test. The method minimizes the mismatch of the state and normal stress extensions on discrete interfaces subject to the subdomain equations, while interface “fluxes” provide virtual Neumann controls.

In this work we present a computational capability featuring a hierarchy of models with different fidelities for the solution of electrokinetics problems at the micro-/nano-scale. A multifidelity approach allows the selection of the most appropriate model, in terms of accuracy and computational cost, for the particular application at hand. We demonstrate the proposed multifidelity approach by studying the mobility of a colloid in a micro-channel as a function of the colloid charge and of the size of the ions dissolved in the fluid.

We study questions of the difference approximation of optimal control problems (OCPs) described by the Dirichlet problem for semilinear elliptic equations with non-self-adjoint operators and an imperfect contact matching condition. The coefficients of the convective transport of a state equation and in the matching boundary condition are used as a control function. Finite difference approximations for OCPs are constructed, the approximation error is estimated with respect to the state and the cost functional. We prove weak convergence of the approximations with respect to control and regularize them using Tikhonov regularization.

We discuss error identities for two classes of free boundary problems generated by obstacles. The identities suggest true forms of the respective error measures which consist of two parts: standard energy norm and a certain nonlinear measure. The latter measure controls (in a weak sense) approximation of free boundaries. Numerical tests confirm sharpness of error identities and show that in different examples one or another part of the error measure may be dominant.

We consider an optimal control problem for an autonomous differential inclusion with free terminal time in the situation when there is a set M (“risk zone”) in the state space $$\mathbb {R}^n$$Rn which is unfavorable due to reasons of safety or instability of the system. Necessary optimality conditions in the form of Clarke’s Hamiltonian inclusion are developed when the risk zone M is an open set. The result involves a nonstandard stationarity condition for the Hamiltonian. As in the case of problems with state constraints, this allows one to get conditions guaranteeing nondegeneracy of the developed necessary optimality conditions.

In this paper, we consider a population of a social network in which a fake news propagates and divides it into four categories: ignorants, spreaders, stiflers who accept the rumor, and stiflers who oppose the rumor. Starting from a SIR type model describing the propagation of e-rumor, we modify it by adding some external actions and control them in order to reduce the spread of a bad information. To carry out this investigation, we use known facts from optimal control theory. Numerical simulations illustrate the efficiency of the obtained control strategy.

We prove an extension of the Superposition Principle by Ambrosio-Gigli-Savaré in the context of a control problem. In particular, we link the solutions of a finite-dimensional control system, with dynamics given by a differential inclusion, to a solution of a continuity equation in the space of probability measures with admissible vector field. We prove also a compactness and an approximation result for admissible trajectories in the space of probability measures.

The problem of estimating reachable sets of nonlinear dynamical control systems with uncertainty in initial states is studied when it is assumed that only the bounding set for initial system positions is known and any additional statistical information is not available. We study the case when the system nonlinearity is generated from one side by bilinear terms in the matrix elements included in the state velocities and from the other side by quadratic functions in the right-hand part of system differential equations. Using results of the theory of trajectory tubes of control systems and techniques of differential inclusions theory and also results of ellipsoidal calculus we find set-valued estimates of reachable sets of such nonlinear uncertain control system.

The problems of reachability for linear control systems with joint integral constraints on the state and input functions have been studied in the literature on the theory of set-valued state estimation. In this paper we consider a reachability problem for a nonlinear affine-control system on a finite time interval. The constraints on the state and control variables are given by the joint integral inequality, which assumed to be quadratic in the control variables. Assuming the controllability of the linearized system, we prove that any admissible control, that steers the control system to the boundary of its reachable set, is a local solution to an optimal control problem with integral cost functional.

In this paper a class of infinite horizon optimal control problems with a mixed control-state isoperimetrical constraint, also interpreted as a budget constraint, is considered. Herein a linear both in the state and in the control dynamics is allowed. The problem setting includes a weighted Sobolev space as the state space. For this class of problems, we establish an existence theorem. The proved theoretical result is applied to a mixed control-state budget constrained advertisement model.

The paper investigates the stability of the solutions of linear-quadratic optimal control problems with bang-bang controls in terms of metric sub-regularity and bi-metric regularity. New sufficient conditions for these properties are obtained, which strengthen the known conditions for sub-regularity and extend the known conditions for bi-metric regularity to Bolza-type problems.

This paper focuses on minimizing further the communications in Monte Carlo methods for Linear Algebra and thus improving the overall performance. The focus is on producing set of small number of covering Markov chains which are much longer that the usually produced ones. This approach allows a very efficient communication pattern that enables to transmit the sampled portion of the matrix in parallel case. The approach is further applied to quasi-Monte Carlo. A comparison of the efficiency of the new approach in case of Sparse Approximate Matrix Inversion and hybrid Monte Carlo and quasi-Monte Carlo methods for solving Systems of Linear Algebraic Equations is carried out. Experimental results showing the efficiency of our approach on a set of test matrices are presented. The numerical experiments have been executed on the MareNostrum III supercomputer at the Barcelona Supercomputing Center (BSC) and on the Avitohol supercomputer at the Institute of Information and Communication Technologies (IICT).

The quasi-Monte Carlo algorithms utilize deterministic low-discrepancy sequences in order to increase the rate of convergence of stochastic simulation algorithms. Such kinds of algorithms are widely applicable and consume large share of the computational time on advanced HPC systems. The recent advances in HPC are increasingly rely on the use of accelerators and other similar devices that improve the energy efficiency and offer better performance for certain type of computations. The Xeon Phi coprocessors combine efficient vector floating point computations with familiar operational and development environment. One potentially difficult part of the conversion of a Monte Carlo algorithm into a quasi-Monte Carlo one is the generation of the low-discrepancy sequences. On such specialized equipment as the Xeon Phi, the value of memory increases due to the presence of a large number of computational cores. In order to allow quasi-Monte Carlo algorithms to make use of hybrid OpenMP+MPI programming, we implemented generation routines that save both memory space and memory bandwidth, with the aim to widen the applicability of quasi-Monte Carlo algorithms in environments with an extremely large number of computational elements. We present our implementation and compare it with regular Monte Carlo using a popular pseudorandom number generator, demonstrating the applicability and advantages of our approach.

The oncoming climate changes at the moment are the biggest challenge the mankind is faced with. They will exert influence on the ecosystems, on the all branches of the national economy, and on the quality of life. The climate changes and their consequences have a great number of regional features, which the global models cannot predict. That is why an operation plan for adaptation to climate changes has to be based on scientifically well-grounded assessments, giving an account of regional features in the climate changes and their consequences.The purpose of the current research is to develop a method that permits a set of validated models, tuned to the physical geographic and climate conditions of the region will be able reliably to predict the regional climate changes for different global climate scenarios. The comprehensive and detail computer simulations will be done for the present climate. Here an evaluation of the ERA-Interim-driven regional climate model RegCM v4.4 over Southeastern Europe is presented. The study documents the performance of 20 different model configurations in representing the basic spatial and temporal patterns of the SE European climate for the period 1999–2009. Model evaluation focuses on near-surface air temperature and precipitation, and uses the EOBS data set as observational reference.The study reveals that no particular model configuration can be judged as the best one, nevertheless seven ones indicate better performance for the precipitation during the summer.

A well designed territory enhances customer coverage, increases sales, fosters fair performance and rewards systems and lower travel cost. This paper considers a real life case study to design a sales territory for a business sales plan. The business plan consists in assigning the optimal quantity of sellers to a territory including the scheduling and routing plans for each seller. The problem is formulated as a combination of assignment, scheduling and routing optimization problems. The solution approach considers a meta-heuristic using stochastic iterative projection method for large systems. Several real life instances of different sizes were tested with stochastic data to represent raise/fall in the customers demand as well as the appearance/loss of customers.

We consider diffusion problems with partially reflecting boundaries that can be formulated in terms of an elliptic equation. To solve boundary value problems with the Robin condition, we propose a Monte Carlo method based on a randomization of an integral representation. The algorithm behaviour is analysed in its application for solving a model problem.

Previously the authors have presented MLMC algorithms exploiting Multiscale Finite Elements and Reduced Bases as a basis for the coarser levels in the MLMC algorithm. In this paper a Renormalization based Multilevel Monte Carlo algorithm is discussed. The advantage of the renormalization as a basis for the coarse levels in MLMC is that it allows in a cheap way to create a reduced dimensional space with a variation which is very close to the variation at the finest level. This leads to especially efficient MLMC algorithms. Parallelization of the proposed algorithm is also considered and results from numerical experiments are presented.

The Intel Xeon Phi architecture is currently a popular choice for supercomputers, with many entries of the Top 500 list, using it either as main processors or as accelerators/coprocessors. In this paper, we explore the performance and scalability of the Intel Xeon Phi chips in the context of large sparse linear systems, commonly arising from the discretization of PDEs. At the first step, the PCG [1] is applied as a basic iterative solution method in the case of sparse SPD problems. The parallel multigrid (MG) implementation from Trilinos ML package is utilized as a preconditioner. A matrix free algebraic multilevel solver is used to reduce the memory requirements, thus allowing the cores to be more efficiently utilized. The second part of the paper is devoted to the fractional Laplacian, that is, we consider the equation $$-\varDelta ^\alpha {\mathbf {u}} = {\mathbf {f}}$$-Δαu=f, $$0<\alpha < 1$$0<α<1, . The related elliptic boundary value problem describes anomalous diffusion phenomena also referred to as super-diffusion. The implemented method approximates the solution of the nonlocal problem by a series of local elliptic problems. The currently available numerical methods for fractional diffusion Laplacian have computational complexity, comparable e.g., to the complexity of solving local elliptic problem in . The presented parallel results are for $$\varOmega =(0,1)^3$$Ω=(0,1)3, including meshes of very large scale. The numerical experiments are run on the Avitohol computer at the Institute of Information and Communication Technologies, IICT-BAS. The presented results show very good scalability when the CPU-cores and MIC work together for a certain number of compute nodes.

Training of feed-forward neural networks is a well-known and a vital optimization problem which is used to digital image lossy compression. Since the inter-pixel relationship in the picture is highly non-linear and unpredictive in the absence of a prior knowledge of the picture itself, it has shown that the neural networks combined with metaheuristics can be very efficient optimization method for image compression issues. In this paper, we propose an improved bat algorithm for training the input-output weights of the network which contains input-output layers of the equal sizes and a hidden layer of smaller size in-between. It has applied on five standard digital images. From the experimental analysis, it can be shown that the proposed method produces an acceptable quality of the compressed image as well as a good ratio of compression.

Our research was conducted in a project that aims to develop an intelligent freight broker agent for providing logistics brokerage services for the efficient allocation of transport resources (vehicles or trucks) to the transport applications. This agent coordinates transportation arrangements of customers (usually shippers and consignees) with resource providers or carriers, following the freight broker business model. The scheduling function of the freight broker agent was formulated as a special type of vehicle routing with pickup and delivery problem. This research is based on our recently proposed declarative model of the freight broker agent using constraint logic programming. This model allows the computation of the feasible transportation schedules. In this paper we augment this model with a declarative representation of optimal schedules and then we show how these optimal schedules can be computed using the ECLiPSe constraint logic programming system.

The possibility for application of Intercriteria Analysis over intuitionistic fuzzy data is discussed. An example in the area of mathematical logic is given as an illustration of the application of the Intercriteria Analysis.

We propose a new genetic algorithm with optimal recombination for the asymmetric instances of travelling salesman problem. The algorithm incorporates several new features that contribute to its effectiveness: 1. Optimal recombination problem is solved within crossover operator. 2. A new mutation operator performs a random jump within 3-opt or 4-opt neighborhood. 3. Greedy constructive heuristic of Zhang and 3-opt local search heuristic are used to generate the initial population. A computational experiment on TSPLIB instances shows that the proposed algorithm yields competitive results to other well-known memetic algorithms for asymmetric travelling salesman problem.

Every day optimization problems arise in our life and industry. Many of them require huge amount of calculations and need special type of algorithms to be solved. An important industrial problem is cutting stock problem (CSP). Cutting with less possible waste is significant in some industries. The aim of this work is to cut 2D items from rectangular stock, minimizing the waste. Even the simplified version of the problem, when the items are rectangular is NP hard. When the number of items increases, the computational time increases exponentially. It is impossible to find the optimal solution for a reasonable time. Only for very small problems the exact algorithms and traditional numerical methods can be applied. We propose a stochastic algorithm which solves the problem, when the items are irregular polygons.

In this paper an Ant Colony Optimization (ACO) algorithm for parameter identification of cultivation process models is proposed. In computational point of view it is a hard problem. To be solved problem with a high accuracy in reasonable time, metaheuristic techniques are used. The influence of ACO algorithm parameters, namely number of agents (ants) and number of iterations, to the quality of achieved solution is investigated. As a case study an E. coli fed-batch cultivation process is explored. Based on the parameter identification of E. coli MC4110 cultivation process model some conclusions for the optimal ACO parameter settings are done.

This study addresses application of population based optimization heuristics to the solution of packing problems as part of optimal cutting tasks in the field of operations research. Such problems are very common in the industrial material cutting. The problem has one, two or three dimensional variations. The focus of this paper is the two dimensional case of steel sheet cutting. A description of two dimensional plates is supplied as input for the algorithm. The output is in the form of coordinates of the plates in the steel sheet and angle of rotation for each plate. Population based global optimization heuristics are used for optimal packing. All experiments are done with open source libraries for 2D geometry and population based heuristics.

Assembly lines are of widely utilized mass production techniques emerged after the industrial revolution started in 18th century in England. Ever since, the changes in the global market and increasing interest in customized products forced companies to change their production systems in such a way that customer demands can be met in a more flexible environment. Assembly line balancing problem is an NP-hard class of combinatorial optimization problem for which exact solution techniques fail to solve large-scaled instances. This paper addresses to the problem of balancing mixed-model two-sided assembly lines, on which large-sized products (such as automobiles, trucks and buses) are assembled in an intermixed-sequence, with the aim of minimising two conflicting objectives (cycle time and number of workstations). A new ant colony optimization approach, called non-dominated sorting ant colony optimization (NSACO shortly), is proposed. Thus, the NSACO algorithm is used for the first time to solve an assembly line balancing problem. NSACO is described in details and a numerical example is solved to demonstrate its solution building mechanism. The results indicate that NSACO has a promising performance.

This work is devoted to development of threshold algorithms for one static probabilistic competitive facility location and design problem in the following formulation. New Company plans to enter the market and to locate new facilities with different design scenarios. Clients of each point choose to use the facilities of Company or its competitors depending on their attractiveness and distance. The aim of the new Company is to capture the greatest number of customers thus serving the largest share of the demand. This share for the Company is elastic and depends on clients’ decisions. We offer three types of threshold algorithms: Simulated annealing, Threshold improvement and Iterative improvement. Experimental tuning of parameters of algorithms was carried out. A comparative analysis of the algorithms, depending on the nature and value of the threshold on special test examples up to 300 locations is carried out. The results of numerical experiments are discussed.

InterCriteria Analysis is a recently developed approach for the evaluation of the correlation between multiple objects against multiple criteria. As such, it is expected to prove any existing correlations between the criteria themselves or even to discover any new. In this investigation different algorithms for InterCriteria relations calculation are explored to render the influence of the genetic algorithm (GA) parameters on the algorithm performance. GA is chosen as an optimization technique as they are among the most widely used out of the biologically inspired approaches for global search. GA is here applied to parameter identification of a S. cerevisiae fed-batch fermentation process model.

In the modern world of billions connected things and exponentially growing data, search in multidimensional spaces and optimisation of multidimensional tasks will become a daily need for variety of technologies and scientific fields. Resolving multidimensional tasks with thousands parameters and more require time, energy and other resources and seems to be an embarrassing challenge for modern computational systems in terms of software abilities and hardware capacity. Presented study focuses on evaluation and comparison of thousands dimensional heterogeneous real-value numerical optimisation tests on two enhanced performance computer systems. The aim is to extend the knowledge on multidimensional search and identification of acceptable solutions with non-zero probability on heterogeneous tasks. It aims also to study computational limitations, energy consumptions and time. Use of energy and time are measured and analysed. Experimental results are presented and can be used for further research and evaluation of other methods.

Adhesive capsulitis is a musculoskeletal condition of the shoulder characterized by pain and gradual loss of the global shoulder motion. Proper diagnosis of adhesive capsulitis is extremely important for designing a coordinated exercise program and reliable monitoring progress during treatment. In this investigation we present a successful example of Generalized Nets (GN) application in orthopedics and propose a novel approach to timely detection of adhesive capsulitis. The developed GN-model provides a framework that can be used by primary care practitioners to guide diagnostic processes for patients suspected to have adhesive capsulitis and might assist in optimizing patient outcomes and more effective treatment. The method proposed in this investigation accurately identifies the various steps during the diagnosing processes and significantly improve the health care level. Obtained so far results could be used to assist in the decision making in the diagnostic processes.

The aim of this paper is to propose a model for an adaptive multi-agent system based on wasp-like behaviour for dynamic allocation of puzzles and quests in the virtual learning game SOTIRIOS. This is a digital learning game integrated inside a First Person Shooter designed by the second author of this paper. The learning process is based on many puzzles hidden in the game flow. The multi-agent system is necessary to integrate a multiplayer mode into the game. The agents use wasp task allocation behaviour, combined with a model of wasp dominance hierarchy in order to create a unique multiplayer learning system, where each user has a different learning curve, based on his results. The wasp behaviour is required to create a balanced multiplayer mode and to optimize the results of teams within the game.

When Evolutionary Algorithms (EAs) are used for Artificial Neural Networks (ANNs) training, the most valuable advantage is the potential for this training to be done in parallel or even using distributed computing. With the capabilities of modern mobile devices, for example their use for distributed computations, they can be used much more extensively for scientific calculations. It is well known that distributed computing systems are limited by their communication bandwidth, because of network latency. In such environment some EAs are pretty suitable for distributed implementation. This is because of their high level of parallelism and relatively less intensive network communication needs. Subset of distributed computing is volunteer computing where users donate some of the computing power provided by devices under their control. This research proposes Android Live Wallpaper volunteer computing implementation of a system used for financial time series prediction. The forecasting module is organized as ANN, which is trained by hybrid combination of Backpropagation and EAs.

The objective is to analyze the neutron diffusion benchmark developed by the Atomic Energy Research community for verification of best-estimate neutronics codes. The 3D benchmark of Schulz models a VVER-1000 core in steady state. The assemblies are homogeneous, represented by given diffusion theory parameters. There are seven material compositions including four enrichments, burnable absorber, control rods and a reflector. The finite element method on tetrahedron computational grids is used to solve the three-dimensional neutron problem. The software has been developed using the engineering and scientific library FEniCS. The matrix spectral problem is solved using a scalable and flexible toolkit SLEPc. The solution accuracy of the benchmark is analyzed by condensing the computational grid and varying the degree of the finite elements.

The expected reduction of the precipitation over many regions in a non-stationary climate is a major concern for Europe. Climate change has the potential to increase drought risk by subjecting areas with all natural, social and economic consequences. Thus it is of great interest to analyze future drought severity projected from the climate models in order to elaborate effective mitigation strategies. In the presented work the tendencies of the total precipitation for two 30-year time periods, 2021–2050 and 2071–2100, simulated at the National Institute of Meteorology and Hydrology (NIMH-BAS) in the frame of the CECILIA project with ALADIN Climate model are used. Intending to find the precipitation sums in these periods, the tendencies are superposed over the averages for the World Meteorological Organization (WMO) reference period 1961–1990, obtained from the E-OBS gridded data set. The Standardized Precipitation Index (SPI) is selected to quantify the drought conditions and is calculated for three time-scales: SPI-3 for each season, SPI-6 for the cold and warm halves of the year and SPI-12 for the whole year. The study suggests that the magnitude of the prevailing negative tendency over the domain, which is better expressed in the second 30-year period, leads only to insignificant change of the resulting SPI distribution patterns.

We implement implicit-explicit (IMEX) linear multistep time-discretization to HOC difference schemes for weakly coupled nonlinear parabolic systems with desirable time-step restrictions and positivity preservation of the numerical solution. Numerical experiments are performed with IMEX-BDF1 (backward difference method of order one), IMEX-BDF2 (backward difference method of order two) and CN-LF (Crank-Nicolson Leap Frog) to check the properties of the methods.

Shallow landslides triggered by weather conditions are a major hazard in most mountainous and hilly regions of Europe. An efficient system for the evaluation of landslide hazard level from weather forecast data allows the possibility to develop fast alert systems and well-organized crisis management plans. A system of this kind should estimate the effect of weather on the slope stability and translate this estimation in a easy to use hazard map. So, its main components are a model for the dynamics of soil moisture, a model for the slope stability analysis, and a proper information system able to manage the corresponding data flow. The system presented in this paper has been developed during the LANDSLIDE project and it is available at web site http://93.123.110.111/landslide/.

We present a study of the winter wave climate of the Western Black Sea with a focus on the annual maximums and the mean seasonal wave heights. We did a numerical simulation of the wave parameters in the Black Sea by the wave model SWAN for a period of 110 years. The input wind fields are from the atmospheric reanalysis ERA-CLIM. We also performed a hindcast for the period 1980–2015 using winds from the CFSR reanalysis. Extended winter (December–March) was studied. We also studied the characteristics of the pressure gradients in a larger region attempting to quantify this way the interaction of Mediterranean lows with blocking highs. No significant long term changes were found for any of the characteristics of the mean and extreme wave climate.

Some extensive numerical simulations of the atmospheric composition fields in the city of Sofia have been recently performed. An ensemble, comprehensive enough as to provide statistically reliable assessment of the atmospheric composition climate of Sofia—typical and extreme features of the special/temporal behavior, annual means and seasonal variations, etc. has been constructed. The simulations were carried out using the American Environment Protection Agency (US EPA) Models-3 system. As the National Centers for Environmental Prediction (NCEP) Global Analysis Data with 1 degree resolution was used as meteorological background, the system nesting capabilities were applied for downscaling the simulations to a 1 km resolution over Sofia. The national emission inventory was used as an emission input for Bulgaria, while outside the country the emissions were taken from the Netherlands Organization for Applied Scientific research (TNO) inventory. Special pre-processing procedures are created for introducing temporal profiles and speciation of the emissions. The biogenic emissions of Volatile Organic Compound (VOC) are estimated by the model Sparse Matrix Operator Kernel Emissions (SMOKE). The air pollution pattern is formed as a result of interaction of different processes, so knowing the contribution of each for different meteorological conditions and given emission spatial configuration and temporal behavior could be interesting. Different characteristics of the numerically obtained concentration fields of pollutants as well as of determining the contribution of different types of pollutants and pollution sources will be demonstrated in the present paper.

Export of softwood sawn timber requires development of sawmill technology for better wood recovery. Therefore, problem of optimization of raw material cutting to obtain the maximum volume of high-quality sawn timber is of urgent priority. In this work we consider the elasticity equations that describe stress-strain state of timber. For numerical solution we approximate our system using finite element method. As the model problem we consider the deformations of the sawn timber under grown stresses depending on cutting patterns to define their board grade, which is linked with warp value. Wood parameters and inner stress model correspond to dahurian larch wood, which accounts for great part of timber export of Yakutia. The numerical simulation of the 3D problem is presented.

Many phenomena in the nature may be considered in the frame of the incompressible fluid flows. Such flows are described by the Navier-Stokes equations. As usually we have deal with the flows with large gradients of hydrodynamic parameters (flows with a free surface, stratified fluid flows, separated flows, etc.). For direct numerical simulation of such flows finite difference schemes should possess by the following properties: high order of accuracy, minimum scheme viscosity, dispersion and monotonicity. The Splitting on the physical factors Method for Incompressible Fluid flows (SMIF) with hybrid explicit finite difference scheme based on Modified Central Difference Scheme (MCDS) and Modified Upwind Difference Scheme (MUDS) with special switch condition depending on the velocity sign and the signs of the first and second differences of transferred functions has been developed. This method has been successfully applied for the flows with a free surface including regimes with broken surface wave, for 3D separated homogeneous and stratified fluid flows around a sphere and a circular cylinder including transitional regimes. The air, heat and mass transfer in the clean rooms for the pharmaceutical industry is considered. The parallelization of the algorithm has been made and applied on the massive parallel computers with a distributed memory. Some examples of calculated problems will be discussed.

We present the reasonableness of the extension of a two-level domain decomposition method to a multilevel method as a preconditioner for interpolation with radial basis functions (RBF) on distributed memory systems. The arising subproblems are efficiently solved using the FGP algorithm, a method that is well-suited for shared memory settings.

In silico studies of biological molecules face the problem of sampling quality due to the systems size (in atom numbers), the time scale of the investigated processes and the admissible computational time step. Advances in hardware alone are incapable of resolving this problem and the efforts are oriented towards sampling techniques enhancements, multilevel system representations and development of multistage and multiscale methods through synergistic protocols from complementary approaches. We combine a mean field approach with all atom molecular dynamics (MD), to develop a multistage algorithm that can model protein folding and dynamics over very long time periods with atomic-level precision. We compare the quality of conformation-space sampling for villin headpiece (PDB ID 2F4K) with a 125 $$\upmu $$μs long folding simulation performed on the dedicated supercomputer ANTON.

A computational approach is presented for the seismic response of existing Cultural Heritage industrial reinforced concrete (RC) structures, which have been degraded due to extreme actions (environmental, seismic etc.) and are to be seismically upgraded by using cable elements (tension-ties). Emphasis is given to shear effects, which are common for old RC buildings not designed according to new (after 2000) seismic codes concerning Civil Engineering praxis. The unilateral behavior of the cable-elements and the non-linear behavior of the RC structural elements are strictly taken into account and result to inequality constitutive conditions. For the numerical treatment of the system of partial differential relations (PDE), a double discretization, in space by the Finite Element Method and in time by a direct incremental approach, is used. So, in each time-step, a non-convex linear complementarity problem is solved. The decision for the optimal cable-strengthening scheme under seismic sequences is obtained on the basis of computed damage indices, as shown in a numerical example.

Stationary localized waves are considered in the frame moving to the right. The original ill–posed problem has a non–unique solution. To cope with this issue, the bifurcation problem is reformulated into a problem for identification of an unknown coefficient from over-posed boundary data in which the trivial solution is excluded. This approach to solving the modified fifth order Kawahara equation is original allowing identification of the non–trivial solutions. The numerical solutions are compared with known analytical solution. The convergence of the difference scheme is illustrated with numerical examples.

A variational data assimilation algorithm is studied numerically. In situ concentration measurement data are assimilated into transport and transformation model of atmospheric chemistry. The algorithm is based on decomposition and splitting methods with solution of variational data assimilation problems for separate splitting stages. A direct algorithm without iterations is used for the linear transport stage. An iterative gradient algorithm is applied for data assimilation at the non-linear chemical transformation stage. In a realistic numerical experiment, the contributions of data assimilation algorithms for the different splitting stages are compared.

Human interferon gamma (hIFN-$$\gamma $$γ) is an important signalling molecule, which plays a key role in the formation and modulation of immune response. The controversial conclusions concerning the function of hIFN-$$\gamma $$γ C-termini as well as the lack of structural information about this domain motivated us to perform molecular dynamics simulations in order to model the structure of the hIFN-$$\gamma $$γ C-terminal part. The simulations were carried out with the CHARMM22 force field, starting from a fully extended conformation of the C-termini. They showed unambiguously that the C-termini tend to approach the globular part of the protein, so that the whole hIFN-$$\gamma $$γ molecule adopts a more compact conformation. The energetic favourability of the more compact conformations of the whole cytokine was also confirmed by means of free energy perturbation simulations.

UNI-DEM is a large-scale environmental model described by a non-linear system of partial differential equations (PDEs) and used in many studies of air pollution levels in different European countries. The discretization of UNI-DEM leads to a long series of huge computational tasks, because it is necessary to run the discretized model with many different scenarios during long time-periods of many consecutive years. Therefore, both the storage requirements and the computational work are enormous. We had to resolve four difficult problems in the efforts to perform successfully the required simulations. More precisely, we had to do the following:(a)to implement fast numerical methods,(b)to select suitable splitting procedures,(c)to exploit efficiently the cache memories of the available high-speed computers(d)to parallelize the computer codes.We use several runs over sixteen consecutive years and with fourteen scenarios. Our main purpose will be to show the long-range transport of potentially dangerous air pollutants to Bulgaria.

We focus on the extension of the MLD2P4 package of parallel Algebraic MultiGrid (AMG) preconditioners, with the objective of improving its robustness and efficiency when dealing with sparse linear systems arising from anisotropic PDE problems on general meshes. We present a parallel implementation of a new coarsening algorithm for symmetric positive definite matrices, which is based on a weighted matching approach. We discuss preliminary results obtained by combining this coarsening strategy with the AMG components available in MLD2P4, on linear systems arising from applications considered in the Horizon 2020 Project “Energy oriented Centre of Excellence for computing applications” (EoCoE).

Multi-phase flow in porous media is relevant for many applications, e.g. geothermal energy production, groundwater remediation, CO$$_2$$2 sequestration, enhanced oil recovery or nuclear waste storage. The arising non-linear partial differential equations are highly non-linear and thus often solved in a fully implicit way. We present a Schur complement reduction method relying on algebraic multigrid methods for solving the arising linear systems. This method is compared to a classical Constrained Pressure Residual (CPR-AMG) approach. It turns out that the new method is competitive to the classical approach with the advantage that it relies only on scalable algebraic multigrid (AMG) and not on incomplete LU (ILU) preconditioning. Scaling results are presented for both methods on the Jülich high performance computer JUQUEEN.

In this paper, we consider a class of non-linear models in mathematical finance, where the volatility depends on the second spatial derivative of the option value. We study the convergence and realization of the constructed, on a fitted non-uniform meshes, implicit difference schemes. We implement various Picard and Newton iterative processes. Numerical experiments are discussed.

This paper is an initial study of subdivision schemes in connection with blending technics such as Expo Rational B-splines, see [1]. The study is done on curves, but surfaces are a natural next step. It turns out that blending two second degree polynomial curves, which interpolates three points, generate a 4-point subdivision scheme for Catmull Rom Splines, see [2]. It can be shown that different subdivision schemes can be developed from a blending spline construction using different types of local curves and/or blending functions. We will show examples, as circular arcs, and discuss some problems and properties.

In this research we study a problem of identifying of the right-hand side in a parabolic equation dependent on spatial variables in multidimensional domain. For numerical solution of the set inverse initial-boundary problem we use a conjugate gradient method with purely implicit time approximation. The results of the computational experiment performed on model problems with quasi-real solutions, including those with noise in input data are being discussed.