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We show how to construct a one-pass optimizing transformation by fusing a non-optimizing transformation with an optimization pass. We state the transformation in build form and the optimization pass in cata form, i.e., as a catamorphism; and we use cata/build fusion to combine them. We illustrate the method by fusing Plotkin's call-by-value and call-by-name CPS transformations with a reduction-free normalization function for the λ-calculus, thus obtaining two new one-pass CPS transformations. [ABSTRACT FROM AUTHOR]

Summary: This book constitutes the proceedings of the 12th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2015, held in Skövde, Sweden, in September 2015. The 18 revised full papers presented were carefully reviewed and selected from 38 submissions. They discuss theory and tools for modeling decisions, as well as applications that encompass decision making processes and information fusion techniques.

Sparse synthetic transmit aperture (STA) imaging systems are a good alternative to the conventional phased array systems. Unfortunately, the sparse STA imaging systems suffer from some limitations, which can be overcome with a proper design. In order to do so, a simulated annealing algorithm, combined with an effective approach can used for optimization of a sparse STA ultrasound imaging system. In this paper, three two-stage algorithms for optimization of both the positions of the transmit sub-apertures and the weights of the receive elements are considered and studied. The first stage of the optimization employs a simulated annealing algorithm that optimizes the locations of the transmit sub-aperture centers for a set of weighting functions. Three optimization criteria used at this stage of optimization are studied and compared. The first two criteria are conventional. The third criterion, proposed in this paper, combines the first two criteria. At the second stage of optimization, an appropriate weighting function for the receive elements is selected. The sparse STA system under study employs a 64-element array, where all elements are used in receive and six sub-apertures are used in transmit. Compared to a conventional phased array imaging system, this system acquires images of better quality 21 times faster than an equivalent phased array system. [ABSTRACT FROM AUTHOR]

This paper presents work on solving elliptic BVPs problems based on quasi-random walks, by using a subset of uniformly distributed sequences—completely uniformly distributed (c.u.d.) sequences. This approach is novel for solving elliptic boundary value problems. The enhanced uniformity of c.u.d. sequences leads to faster convergence. We demonstrate that c.u.d. sequences can be a viable alternative to pseudorandom numbers when solving elliptic boundary value problems. Analysis of a simple problem in this paper showed that c.u.d. sequences achieve better numerical results than pseudorandom numbers, but also have the potential to converge faster and so reduce the computational burden. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of tracking extended objects. Examples of extended objects are ships and a convoy of vehicles. Such kind of objects have particularities which pose challenges in front of methods considering the extended object as a single point. Measurements of the object extent can be used for estimating size parameters of the object, whose shape is modeled by an ellipse. This paper proposes a solution to the extended object tracking problem by mixture Kalman filtering. The system model is formulated in a conditional dynamic linear (CDL) form. Based on the specifics of the task, two latent indicator variables are proposed, characterising the mode of maneuvering and size type, respectively. The developed Mixture Kalman filter is validated and evaluated by computer simulation. [ABSTRACT FROM AUTHOR]

This paper propose a method for identification of complex engineering systems using wavelet transform. This transform is chosen because it can provide a well localization both in time and in frequency. The method is applied to an electrohydraulic system that drives a shaking table. The identification is made using real signals obtained from experimental tests. [ABSTRACT FROM AUTHOR]

The effect of soil-structure interaction (SSI) is an important consideration and cannot be neglected in the seismic design of structures on soft soil. Various methods have been developed to consider SSI effects and are currently being used. However, most of the approaches including a general finite element method cannot appropriately consider the properties and characteristics of the sites with complicated soil profiles. To overcome these difficulties, this paper presents soil-structure interaction analysis method, which can consider precisely complicated soil profiles by adopting an unaligned mesh generation approach. This approach has the advantages of rapid generation of structured internal meshes and leads to regular and precise stiffness matrix. The applicability of the proposed method is validated through several numerical examples and the influence of various properties and characteristics of soil sites on the response is investigated. [ABSTRACT FROM AUTHOR]

In designing tokamaks, the maintenance of vertical stability of plasma is one of the most important problems. For this purpose systems of passive and active feedbacks are applied. The role of passive system consisting of a vacuum vessel and passive stabilizer plates is to suppress fast MHD (magnetohydrodynamic) instabilities. The active feedback system is applied to control slow motions of plasma. The objective of this paper is to investigate three successive problems the solution of which will allow to determine the possibility to control plasma motions. The first problem is the vertical stability problem under the assumption of ideal conductivity of plasma and passive stabilizing elements. The problem is solved analytically and on the basis of the obtained solution a criterion of MHD-stability is formulated. The second problem is the vertical stability when finite conductivity of stabilizing elements is taken into account. The dispersion equation relative to instability growth rate is obtained and analyzed. For practical values of the parameters it is shown that there is a unique root with positive real part, which presents the growth rate of only unstable mode. The third problem is connected with the control of plasma vertical position with application of active feedback system. The problem of calculation of feedback control parameters is formulated as an optimization problem and its approximate solving method is suggested. [ABSTRACT FROM AUTHOR]

In recent years, the algorithms that extract information for target's behavior through mathematical transformation of the signals reflected from a target, find ever-widening practical application. In this paper, a new two-stage algorithm for target detection and target's radial velocity estimation that exploits the Hough transform is proposed. The effectiveness of the proposed algorithm is formulated in terms of both quality parameters - the probability of detection and the accuracy of velocity estimation. The quality parameters are estimated using the Monte Carlo simulation approach. [ABSTRACT FROM AUTHOR]

The integral equations studied here play very important role in the theory of parabolic initial-boundary value problems (heat conduction problems) and in various physical, technological and biological problems (epidemiology problems). This paper is concerned with the iterative-collocation method for solving these equations. We propose an iterative method with corrections based on the interpolation polynomial of spatial variable of the Lagrange type with given collocation points. The coefficients of these corrections can be determined by a system of Volterra integral equations. The convergence of the presented algorithm is proved and an error estimate is established. The presented theory is illustrated by numerical examples and a comparison is made with other methods. AMS Subject Classification: 65R20. [ABSTRACT FROM AUTHOR]

This paper introduces several approaches based on ant colony optimization for efficient scheduling the surveying activities of designing satellite surveying networks. These proposed approaches use a set of agents called ants that cooperate to iteratively construct potential observation schedules. Within the context of satellite surveying, a positioning network can be defined as a set of points which are coordinated by placing receivers on these point to determine sessions between them. The problem is to search for the best order in which these sessions can be observed to give the best possible schedule. The same problem arise in Mobile Phone Surveying networks. Several case studies have been used to experimentally assess the performance of the proposed approaches in terms of solution quality and computational effort. [ABSTRACT FROM AUTHOR]

In this paper, we consider a combined blending and distribution planning problem faced by a company that manages wheat supply chain. The distribution network consists of loading ports, and customers. Products are loaded on bulk vessels of various capacity levels for delivery to overseas customers. The purpose of this model is simultaneous planning of the assignment of an appropriate type and number of vessels to each customer order, the planning of quantities blended at ports, loaded from ports, and transported from loading ports to customers. We develop a mixed integer programming (MIP) model and provide a heuristic solution procedure for this distribution planning problem. An iterative fixing variable heuristic algorithm is used to assure that acceptable solutions are obtained quickly. The effectiveness of the proposed heuristic algorithm is evaluated by computational experiment. [ABSTRACT FROM AUTHOR]

In this paper we consider the problem of finding the solution of a differential game in relation with choosing an optimal tax policy rule. The paper extends the existing literature in two directions. First, instead of treating the tax base as given, in our formulation it is a control variable for the government. Secondly, we impose a phase constraint of mixed type for the considered problem of taxation. We present new conditions under which the solution of the differential game is found explicitly. The obtained optimal tax policy is time-consistent. [ABSTRACT FROM AUTHOR]

This paper is concerned with the relationship between the sum of roots with positive real parts (SORPRP) of an even polynomial and the polynomial spectral factor of the even polynomial. The SORPRP and its relationship to Gröbner bases are firstly reviewed. Then it is shown that the system of equations satisfied by the coefficients of the polynomial spectral factor is directly related to a Gröbner basis. It is then demonstrated by means of an $ {\mathcal{H}}_2 $ optimal control problem that the above fact can be used to facilitate guaranteed accuracy computation. [ABSTRACT FROM AUTHOR]

In the paper we study discrete approximations of singularly perturbed system in a finite dimensional space. When the right-hand side is almost upper semicontinuous with convex compact values and one-sided Lipschitz we show that the distance between the solution set of the original and the solution set of the discrete system is $O\left(h^{\frac{1}{2}}\right)$. [ABSTRACT FROM AUTHOR]

This paper endeavors to show that genetic algorithms, namely Multipopulation genetic algorithms (MpGA), are of great utility in cases where complex cultivation process models have to be identified and, therefore, rational choices have to be made. A system of five ordinary differential equations is proposed to model biomass growth, glucose utilization and acetate formation. Parameter optimization is carried out using experimental data set from an E. coli cultivation. Several conventional algorithms for parameter identification (Gauss-Newton, Simplex Search and Steepest Descent) are compared to the MpGA. A general comment on this study is that traditional optimization methods are generally not universal and the most successful optimization algorithms on any particular domain, especially for the parameter optimization considered here. They have been fairly successful at solving problems of type which exhibit bad behavior like multimodal or nondifferentiable for more conventional based techniques. [ABSTRACT FROM AUTHOR]

Starting from the modelling requirements of the early design phase of the product development, the paper will show a possible strategy to overcome some limitations of current CAS/CAD systems. In fact, the styling stage involves both technical knowledge and fuzzy and dynamic aspects, which have to be taken into account for a proper management. The paper focuses on high-level modelling tools developed to deform surfaces with semantic (aesthetic) constraints, i.e. the crucial design elements for the stylist. Furthermore, the communication among the other actors of the design process is consequently facilitated. [ABSTRACT FROM AUTHOR]

In finance, the strong convergence properties of discretisations of stochastic differential equations (SDEs) are very important for the hedging and valuation of exotic options. In this paper we show how the use of the Milstein scheme can improve the convergence of the multilevel Monte Carlo method, so that the computational cost to achieve an accuracy of O(e) is reduced to O(ϵ−2) for a Lipschitz payoff. The Milstein scheme gives first order strong convergence for all one-dimensional systems (one Wiener process). However, for processes with two or more Wiener processes, such as correlated portfolios and stochastic volatility models, there is no exact solution for the iterated integrals of second order (Lévy area) and the Milstein scheme neglecting the Lévy area gives the same order of convergence as the Euler-Maruyama scheme. The purpose of this paper is to show that if certain conditions are satisfied, we can avoid the calculation of the Lévy area and obtain first convergence order by applying an orthogonal transformation. We demonstrate when the conditions of the two-dimensional problem permit this and give an exact solution for the orthogonal transformation. We present examples of pricing exotic options to demonstrate that the use of both the orthogonal Milstein scheme and the multilevel Monte Carlo give a substantial reduction in the computation cost. [ABSTRACT FROM AUTHOR]

This paper is meant to be the continuation of the previous work [1] where a coupled ODE/PDE method for the simulation of semiconductor devices was introduced. From a strictly mathematical viewpoint, analytical results on coupled PDE/ODE systems (as arising in integrated circuit simulation) can be found in [2]. In particular, in the present paper, we investigate numerically new algorithms of Domain Decomposition type for the simulation of circuits containing distributed devices (Sect. 2) as well as semiconductors in which some part is modeled with lumped parameters (Sect. 3). The results presented here have been investigated in the seminal work [3], while a more extended analysis is ongoing [4]. [ABSTRACT FROM AUTHOR]

Multiple Recursive Generators (MRGs) have become the most popular random number generators recently. They compute the next value iteratively from the previous k values using a k-th order recurrence equation which, in turn, corresponds to a k-th degree primitive polynomial under a prime modulus p. In general, when k and p are large, checking if a k-th degree polynomial is primitive under a prime modulus p is known to be a hard problem. A common approach is to check the conditions given in Alanen and Knuth [1964] and Knuth [1998]. However, as mentioned in Deng [2004], this approach has two obvious problems: (a) it requires the complete factorization of pk - 1, which can be difficult; (b) it does not provide any early exit strategy for non-primitive polynomials. To avoid (a), one can consider a prime order k and prime modulus p such that (pk - 1)/(p - 1) is also a prime number as considered in L'Ecuyer [1999] and Deng [2004]. To avoid (b), one can use a more efficient iterative irreducibility test proposed in Deng [2004]. In this paper, we survey several leading probabilistic and deterministic methods for the problems of primality testing and irreducibility testing. To test primality of a large number, it is known that probabilistic methods are much faster than deterministic methods. On the other hand, a probabilistic algorithm in fact has a very tiny probability of, say, 10-200 to commit a false positive error in the test result. Moreover, even when such an unlikely event had happened, for a speci.c choice of k and p, it can be argued that such an error has a negligible e.ect on the successful search of a primitive polynomial. We perform a computer search for large-order DX generators proposed in Deng and Xu [2003] and present many such generators in the paper for ready implementation. An extensive empirical study shows that these large-order DX generators have passed the stringent Crush battery of the TestU01 package. [ABSTRACT FROM AUTHOR]

It is well known that there are "nonclassical" situations where, in contrast to Lax's and Glimm's results, the Cauchy problem for a system of conservation laws does not possess a weak L∞-solution except for some particular initial data. To solve the Cauchy problem in this "nonclassical" situation, it is necessary to introduce new singular solutions called δ-shocks and singular shocks. The components of these solutions contain delta functions [ASh05], [B94], [DSh03]- [LW02], [S02]- [Sh04], [TZZ94]. The exact structure of such type solutions is given below in (2), (7) and Definition 1. The theory of δ-shocks and singular shocks has been intensively developed in the last 10 years. In particular, in numerous papers δ-shock type solutions of "zero-pressure gas dynamics" have been studied. Moreover, in the recent papers [PSh06], [Sh06] the theory of δ′-shocks was established, and a concept of δ(n)-shocks was introduced, n = 2, 3,. … They are new type singular solutions such that their components contain delta functions and their derivatives. [ABSTRACT FROM AUTHOR]

Many equations arising in continuum fluid dynamics do not, or at least are not known to, possess smooth solutions for general data. Therefore it is necessary to identify a larger class of "weak solutions" in order to develop a rigorous mathematical theory. Following the seminal paper of Leray [10] we introduce a class of weak solutions to the Navier-Stokes-Fourier system based on the concept of generalized derivatives (distributions). The main objective of the present paper is to illustrate the strength of the abstract theory reviewing several theoretical results on the asymptotic behavior of the weak solutions that are in good agreement with practical experiments as well as their numerical analysis.The main topics to be discussed include the following: [ABSTRACT FROM AUTHOR]

This paper studies the modified sensitivity analysis applied into an elastic-plastic finite element analysis of a 3D blank design in sheet metal forming. Originally the sensitivity method has successfully been applied to several arbitrary shapes. In the present paper the sensitivity coefficients are not considered constant during the analysis. The presented approach computes the new coefficients from the two last iterations. This method can produce an initial blank boundary shape that has any arbitrary flange shape. A cup with uniform flange has been studied in detail and results show a faster solution convergence than the published sensitivity method. Experimental tests were conducted to compare with the numerical simulations. The optimum blank shape obtained from the numerical simulations was used during the experimental trials. The results of experimental tests for both square and optimal blank are presented here. [ABSTRACT FROM AUTHOR]

In this paper, we use finite element methods to approximate the solutions of parameter-dependent geometric problems, and investigate the possibility of using symbolic methods as a preprocessing step. The main idea of our approach is to construct suitable finite element discretizations of the nonlinear elliptic equations leading to systems of algebraic equations, which can be subsequently solved by symbolic computation within the tolerance of computer algebra software. The prolongation of the preprocessed symbolic solution can serve as a starting value for a numerical iterative method on a finer grid. A motivation for this approach is that usual numerical iterations (e.g. via Newton-type or fixed-point iterations) may diverge if no appropriate initial values are available. Moreover, such a purely numerical approach will not find all solutions of the discretized problem if there are more than one. A final motivation for the use of symbolic methods is the fact that all discrete solutions can be obtained as functions of unknown parameters. In this paper, we focus on a special class of partial differential equations derived from geometric problems. A main challenge in this class is the fact that the polynomial structure of the nonlinearity is not explicit in the divergence form usually used for finite element discretization. As a consequence, the discrete form would always yield some non-polynomial terms. We therefore consider two different discretizations, namely a polynomial reformulation before discretization and a direct discretization of the divergence form with polynomial approximation of the discrete system. In order to perform a detailed analysis and convergence theory of the discretization methods we investigate some model problems related to mean-curvature type equations. [ABSTRACT FROM AUTHOR]

TM5 is a global chemistry Transport Model. It allows two-way nested zooming which leads to possibility to run the model on relatively very fine space grid (1° ×1°) over selected regions (Europe is most often used in up to now experiments but North America, Africa and Asia can be treated separately or in combinations). The boundary conditions for the zoomed subdomains are provided consistently from the global model. The TM5 model is a good tool for studying some effects due to the grid refinement on global atmospheric chemistry issues (intercontinental transport of air pollutants, etc.). The huge increase in the number of the multi-processor platforms and their differences leads to a need of different approaches in order to meet the requirements for the optimality of the computer runs. The paper is devoted to an implementation of a parallel version of the TM5 model on a cluster of SUN Workstations and to the developing of a new parallel algorithm. It is based on the decomposition, in some sense, of the computational domain supposing that the zoomed regions are more than one. If it is assumed that the number of zoomed regions is N and the number of the processors available is p. The processors are divided in N/p groups and each group is responsible for the whole computational domain and one of the zoomed regions. Some communications are needed in order to impose the inner boundary conditions. The new algorithm has better parallel feathers than the old one which is used in the inner level. Some results concerning the CPU time, speed up and efficiency can be found. Subject classifications: 65Y05. [ABSTRACT FROM AUTHOR]

The goal of the paper is to review and compare two of the most popular methods for modeling the dendritic solidification in 2D, that tracks the interface between phases implicitly, e.g. the phase-field method and the level set method. We apply these methods to simulate the dendritic crystallization of a pure melt. Numerical experiments for different anisotropic strengths are presented. The two methods compare favorably and the obtained tip velocities and tip shapes are in good agreement with the microscopic solvability theory. [ABSTRACT FROM AUTHOR]

To simulate turbulent Rayleigh-Bénard convection in cylindrical domains an explicit/semi-implicit finite volume method with fourth order approximations in space was developed. Using this method and cylindrical staggered grids of about 11 million nodes clustered in vicinity of the boundary we performed simulations of turbulent Rayleigh-Bénard convection in wide cylindrical containers of the aspect ratios Γ = 5 and 10 and the Rayleigh number from 105 to 108. In the present paper the method, its numerical stability and mesh generation algorithm are discussed. [ABSTRACT FROM AUTHOR]

Order adaptive algorithm for real time holography applications is presented in this paper. The algorithm is based on Master-Worker parallel computation paradigm. Definite integrals required for visualization of fringes are computed using a novel order adaptive quadrature rule with an external detector defining the order of integration in real time mode. The proposed integration technique can be effectively applied in hybrid numerical-experimental techniques for analysis of micro-mechanical components. [ABSTRACT FROM AUTHOR]

The paper deals with a numerical approach for the dynamic soil-pile interaction, considered as an inequality problem of structural engineering. So, the unilateral contact conditions due to tensionless and elastoplastic softening/fracturing behavior of the soil as well as due to gapping caused by earthquake excitations are taken into account. Moreover, second-order geometric effects for the pile behavior due to preexisting compressive loads and environmental soil effects causing instabilization are taken also into account. The numerical approach is based on a double discretization and on mathematical programming. 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. Next, with the aid of Laplace transform, the problem conditions are transformed to convolutional ones involving as unknowns the unilateral quantities only. So the number of unknowns is significantly reduced. Then a marching-time approach is applied and finally a nonconvex linear complementarity problem is solved in each time-step. [ABSTRACT FROM AUTHOR]

The paper presents Large Eddy Simulations of plane channel flow at a friction Reynolds number of 180 and 395 with a block-structured Finite Volume method. Local grid refinement near the solid wall is employed in order to reduce the computational cost of such simulations or other simulations of wall-bounded flows. Different subgrid-scale models are employed and different expressions for the length scale in these models are investigated. It turns out that the numerical discretization has an non-negligible impact on the computed fluctuations. [ABSTRACT FROM AUTHOR]

Large-scale environmental models are powerful tools, designed to meet the increasing demand in various environmental studies. The atmosphere is the most dynamic component of the environment, where the pollutants and other chemical species actively interact with each other, and can quickly be moved in a very long distance. Therefore the advanced modeling is usually done in a large computational domain. Moreover, all relevant physical, chemical and photochemical processes should be taken into account, which heavily depend on the meteorological conditions. All this makes the air pollution modeling a huge and rather difficult computational task, requiring a large amount of computational power. The most powerful supercomputers have been used for the development and test runs of such a model, the Danish Eulerin Model (DEM). Distributed parallel computing via MPI is one of the most efficient techniques in achieving good performance and getting results in real time. The quickly advancing GRID computing technology is another powerful tool that can be used to reach higher level of performance of such a huge model. Both techniques and their inherent problems are discussed in this paper. Results of numerical experiments are presented and analysed and some conclusions are drown, based on the experiments. [ABSTRACT FROM AUTHOR]

In this paper we give a short overview of some traditional operator splitting methods. Then we introduce two new methods, namely the additive splitting and the iterated splitting. We analyze these methods and compare them to the traditional ones. [ABSTRACT FROM AUTHOR]

In this paper we investigate connection between semi-integer orthogonal polynomials and Szegő's class of polynomials, orthogonal on the unit circle. We find a representation of the semi-integer orthogonal polynomials in terms of Szegő's polynomials orthogonal on the unit circle for certain class of weight functions. [ABSTRACT FROM AUTHOR]

The paper proposes an approach for self-verified solving of linear systems involving rational dependencies between interval parameters. A general inclusion method is combined with an interval arithmetic technique providing inner and outer bounds for the range of monotone rational functions. The arithmetic on proper and improper intervals is used as an intermediate computational tool for eliminating the dependency problem in range computation and for obtaining inner estimations by outwardly rounded interval arithmetic. Supporting software tools with result verification, developed in the environment of CAS Mathematica, are reported. [ABSTRACT FROM AUTHOR]

Hausdorff continuous (H-continuous) functions appear naturally in many areas of mathematics such as Approximation Theory [11], Real Analysis [1], [8], Interval Analysis, [2], etc. From numerical point of view it is significant that the solutions of large classes of nonlinear partial differential equations can be assimilated through H-continuous functions [7]. In particular, discontinuous viscosity solutions are better represented through Hausdorff continuous functions [6]. Hence the need to develop numerical procedures for computations with H-continuous functions. It was shown recently, that the operations addition and multiplication by scalars of the usual continuous functions on $\Omega\subseteq\mathbb{R}^n$ can be extended to H-continuous functions in such a way that the set ℍ(Ω) of all Hausdorff continuous functions is a linear space [4]. In fact ℍ(Ω) is the largest linear space involving interval functions. Furthermore, multiplication can also be extended [5], so that ℍ(Ω) is a commutative algebra. Approximation of ℍ(Ω) by a subspace were discussed in [3]. In the present paper we consider numerical computations with H-continuous functions using ultra-arithmetical approach [9], namely, by constructing a functoid of H-continuous functions. For simplicity we consider $\Omega\subseteq\mathbb{R}$. In the next section we recall the definition of the algebraic operations on ℍ(Ω). The concept of functoid is defined in Section 3. In Section 4 we construct a functoid comprising a finite dimensional subspace of ℍ(Ω) with a Fourier base extended by a set of H-continuous functions. Application of the functoid to the numerical solution of the wave equation is discussed in Section 5. [ABSTRACT FROM AUTHOR]

The paper presents a method for designing 2-D linear-phase FIR filters with an equiripple magnitude response. The filter design problem is transformed into an equivalent nonlinear optimization problem. In order to improve the speed of convergence, a two-step solution procedure of the considered problem is proposed. In the first step, a genetic algorithm is applied. The final point from the genetic algorithm is used as the starting point for a local optimization method. The proposed technique is applied to the design of 2-D FIR linear-phase filters with different symmetries. Design examples are included. [ABSTRACT FROM AUTHOR]

This paper presents a solution methodology to tackle a new realistic vehicle routing problem that incorporates heterogeneous fleet, multiple commodities and multiple vehicle compartments. The objective is to find minimum cost routes for a fleet of heterogeneous vehicles without violating capacity, loading and time window constraints. The solution methodology hybridizes in a reactive fashion systematic diversification mechanisms of Greedy Randomized Adaptive Search Procedures with Variable Neighborhood Search for intensification local search. Computational results reported justify the applicability of the methodology. [ABSTRACT FROM AUTHOR]

This paper gives brief information about a new electronic course for enhanced learning in making optimal decisions using the Multi-Attribute Decision Making paradigm. Emphasis is put on the construction of the exams of this electronic course. In order to provide ready to use tests for students' exams, an algorithm based on a Monte Carlo method was conceived. This algorithm and its benefits are presented. [ABSTRACT FROM AUTHOR]

This paper is addressed to the numerical solving of the rendering equation in realistic image creation. The rendering equation is integral equation describing the light propagation in a scene accordingly to a given illumination model. The used illumination model determines the kernel of the equation under consideration. Nowadays, widely used are the Monte Carlo methods for solving the rendering equation in order to create photorealistic images. In this work we consider the Monte Carlo solving of the rendering equation in the context of the parallel sampling scheme for hemisphere. Our aim is to apply this sampling scheme to stratified Monte Carlo integration method for parallel solving of the rendering equation. The domain for integration of the rendering equation is a hemisphere. We divide the hemispherical domain into a number of equal sub-domains of orthogonal spherical triangles. This domain partitioning allows to solve the rendering equation in parallel. It is known that the Neumann series represent the solution of the integral equation as a infinity sum of integrals. We approximate this sum with a desired truncation error (systematic error) receiving the fixed number of iteration. Then the rendering equation is solved iteratively using Monte Carlo approach. At each iteration we solve multi-dimensional integrals using uniform hemisphere partitioning scheme. An estimate of the rate of convergence is obtained using the stratified Monte Carlo method. This domain partitioning allows easy parallel realization and leads to convergence improvement of the Monte Carlo method. The high performance and Grid computing of the corresponding Monte Carlo scheme are discussed. [ABSTRACT FROM AUTHOR]

Exact error estimates for evaluating multi-dimensional integrals are considered. An estimate is called exact if the rates of convergence for the low- and upper-bound estimate coincide. The algorithm with such an exact rate is called optimal. Such an algorithm has an unimprovable rate of convergence. The problem of existing exact estimates and optimal algorithms is discussed for some functional spaces that define the regularity of the integrand. Important for practical computations data classes are considered: classes of functions with bounded derivatives and Hölder type conditions. The aim of the paper is to analyze the performance of two optimal classes of algorithms: deterministic and randomized for computing multi-dimensional integrals. It is also shown how the smoothness of the integrand can be exploited to construct better randomized algorithms. [ABSTRACT FROM AUTHOR]

The paper deals with a finite element solution of transient thermo-elasticity problems. In this context, it is especially devoted to the parallel computing of nonstationary heat equations, when the linear systems arising in each time step are solved by the overlapping domain decomposition method. The numerical tests are performed by OpenMP and/or MPI solvers on a large benchmark problem derived from geoenvironmental model KBS. [ABSTRACT FROM AUTHOR]

It is well-known that iterative methods of optimal order complexity with respect to the size of the system can be set up by utilizing preconditioners based on various multilevel extensions of two-level finite element methods (FEM), as was first shown in [5]. Thereby, the constant γ in the so-called Cauchy-Bunyakowski-Schwarz (CBS) inequality, which is associated with the angle between the two subspaces obtained from a (recursive) two-level splitting of the finite element space, plays a key role in the derivation of optimal convergence rate estimates. In this paper a generalization of an algebraic preconditioning algorithm for second-order elliptic boundary value problems is presented, where the domain is discretized using linear Crouzeix-Raviart finite elements and the two-level splitting is defined by differentiation and aggregation (DA). It is shown that the uniform estimate on the constant γ (as presented in [6]) can be improved if a minimum angle condition, which is an integral part in any mesh generator, is assumed to hold in the triangulation. The improved values of γ can then be exploited in the set up of more problem-adapted multilevel preconditioners with faster convergence rates. [ABSTRACT FROM AUTHOR]

The paper deals with an efficient solution technique to large-scale discretized shape and topology optimization problems. The efficiency relies on multigrid preconditioning. In case of shape optimization, we apply a geometric multigrid preconditioner to eliminate the underlying state equation while the outer optimization loop is the sequential quadratic programming, which is done in the multilevel fashion as well. In case of topology optimization, we can only use the steepest-descent optimization method, since the topology Hessian is dense and large-scale. We also discuss a Newton-Lagrange technique, which leads to a sequential solution of large-scale, but sparse saddle-point systems, that are solved by an augmented Lagrangian method with a multigrid preconditioning. At the end, we present a sequential coupling of the topology and shape optimization. Numerical results are given for a geometry optimization in 2-dimensional nonlinear magnetostatics. [ABSTRACT FROM AUTHOR]

In the present paper we concentrate on algebraic two-level and multilevel preconditioners for symmetric positive definite problems arising from discretization by Rannacher-Turek non-conforming rotated bilinear finite elements on quadrilaterals. An important point to make is that in this case the finite element spaces corresponding to two successive levels of mesh refinement are not nested (in general). To handle this, a proper two-level basis is required in order to fit the general framework for the construction of two-level preconditioners for conforming finite elements and to generalize the methods to the multilevel case. The proposed variants of hierarchical two-level basis are first introduced in a rather general setting. Then, the involved parameters are studied and optimized. As will be shown, the obtained bounds - in particular - give rise to optimal order AMLI methods of additive type. The presented numerical tests fully confirm the theoretical estimates. [ABSTRACT FROM AUTHOR]

It is important to incorporate all available observations when large-scale mathematical models arising in different fields of science and engineering are used to study various physical and chemical processes. Variational data assimilation techniques can be used in the attempts to utilize efficiently observations in a large-scale model. Variational data assimilation techniques are based on a combination of three very important components numerical methods for solving differential equations,splitting procedures and optimization algorithms. It is crucial to select an optimal (or, at least, a good) combination of these three components, because models which are very expensive computationally become much more expensive (the computing time being often increased by a factor greater than 100) when a variational data assimilation technique is applied. Therefore, it is important to study the interplay between the three components of the variational data assimilation techniques as well as to apply powerful parallel computers in the computations. Some results obtained in the search for a good combination will be reported. Parallel techniques described in [1] are used in the runs related to this paper. Modules from a particular large-scale mathematical model, the Unified Danish Eulerian Model (UNI-DEM), are used in the experiments. The mathematical background of UNI-DEM is discussed in [1], [24] The ideas are rather general and can easily be applied in connection with other mathematical models. [ABSTRACT FROM AUTHOR]

This paper investigates the utility of the Hilbert-Huang transform for the analysis of aeroelastic flight data. The recently-developed Hilbert-Huang algorithm addresses the limitations of the classical Hilbert transform through a process known as empirical mode decomposition. Using this approach, the data is filtered into a series of intrinsic mode functions, each of which admits a well-behaved Hilbert transform. In this manner, the Hilbert-Huang algorithm affords time-frequency analysis of a large class of signals. The purpose of this paper is to demonstrate the potential applications of the Hilbert-Huang algorithm for the analysis of aeroelastic systems. Applications for correlations between system input and output, and amongst output sensors, are discussed to characterize the time-varying amplitude and frequency correlations present in the various components of multiple data channels. Examples are given using aeroelastic flight test data from the F/A-18 Active Aeroelastic Wing aircraft and Aerostructures Test Wing. [ABSTRACT FROM AUTHOR]

This paper presents a study of tunneling in saturated poro-elastoplastic soils by means of two and three-dimensional coupled numerical analyses. To perform 2D simulations of the excavation stage, we employ an approach proposed in a previous paper as an extension to the saturated case of the so-called "convergence-confinement" method. To validate the plane procedure, the comparison with results of several 3D simulations of the excavation of shallow pervious tunnels is considered. By means of the hydro-mechanically coupled formulation employed in these comparisons, we investigate the face-advance rate influence on soil response to excavation. The proposed 2D method shows to be able to reproduce with satisfying approximation the effects of tunnel-face advancement on in-plane components of displacements and water flow. [ABSTRACT FROM AUTHOR]

The prior objective of the present paper is to predict the formation of desiccation cracks in a mineral liner for landfills. Therefore, a coupled pore water diffusion and stress analysis is made using the finite element method and the numerical program ABAQUS. For this analysis, test results of hydraulic soil relations and tensile behaviour of the investigated cohesive soil are needed. Also the inelastic mechanical properties must be given and implemented in the used numerical model. The present paper shows these test results, the used plasticity model and the geometry, loading and results of the numerical model. [ABSTRACT FROM AUTHOR]