Abstract: The aim of this workshop is to integrate results of different domains of computer science, computational science and mathematics. We invite papers oriented toward simulations, either hard simulations by means of finite element or finite difference methods, or soft simulations by means of evolutionary computations, particle swarm optimization and other. The workshop is most interested in simulations performed by using agent-oriented systems or by utilizing adaptive algorithms, but simulations performed by other kind of systems are also welcome. Agent-oriented system seems to be the attractive tool useful for numerous domains of applications. Adaptive algorithms allow significant decrease of the computational cost by utilizing computational resources on most important aspect of the problem.

Abstract: We present a new discontinuous Petrov-Galerkin (DPG) method for continuous finite element (FE) approximations of linear boundary value problems of second order partial differential equations by using discontinuous, yet optimal, weight functions. The DPG method is based on the derivation of equivalent integral formulations by starting with element-by-element local residual functionals involving partial derivatives and Laplacian terms. Continuity of the normal inter-element fluxes across the element boundaries is subsequently weakly enforced in H-1/2 by applying Green's Identity or integration by parts. Correspondingly, the resulting integral formulations are posed in broken solution spaces in the sense that they are in H-Laplacian in each element (broken) yet globally only in H1 (continuous). The test functions have the same regularity locally on the element level but are in L2 globally and therefore discontinuous. As in recent DPG approaches [2], we introduce test functions that result in stable FE approximations with best approximation properties in terms of the energy norm that is induced by the bilinear form of the integral formulation. Since the bilinear form involves broken elementwise functionals, the best approximation property is here established in a broken Hilbert norm. Remarkably, the local contributions of test functions can be numerically solved on each element with high numerical accuracy and do not require the solution of global variational statements, as observed in recent DPG methods (e.g. see [1,2]). Optimal asymptotic convergence rates are obtained in the H1 norm and a broken H-LaPlacian type norm. In L2, optimal convergence is achieved for p greater than or equal to 2. We present 1D numerical verifications for the solution of second order reaction-diffusion as well as convection-diffusion problems. [1] L. Demkowicz, and J. Gopalakrishnan. ``Analysis of the DPG Method for the Poisson Equation'', SIAM Journal on Numerical Analysis, Vol. 49, No. 5, pp. 1788-1809, 2011. [2] L. Demkowicz, and J. Gopalakrishnan. `` A class of discontinuous Petrov-Galerkin methods. II. Optimal test functions'', Numerical Methods for Partial Differential Equations, Vol. 27, No. 1, pp. 70-105, 2011.

Abstract: Triaxial induction measurements provided by LWD tools generate crucial petrophysical data to determine several quantities of interest around the drilled formation under exploration, such as a map of resistivities. However, the corresponding forward modeling requires the simulation of a large-scale three-dimensional computational problem for each tool position. When the material properties are assumed to be homogeneous in one spatial direction, the problem dimensionality can be reduced to a so called 2.5 dimensional (2.5D) formulation. In this paper, we propose an a priori adaptive algorithm for properly selecting and interpolating Fourier modes in 2.5D simulations in order to speed up computer simulations. The proposed method first considers an adequate range of Fourier modes, and it then determines a subset of those which need to be estimated via solution of a Partial Differential Equation (PDE), while the remaining ones are simply interpolated in a logarithmic scale, without the need of solving any additional PDE. Numerical results validate our selection of Fourier modes, delivering superb results in real simulations when solving via PDE only for a very limited number of Fourier modes (below 50%).

Abstract: In the paper we consider the approach for solving the problem of extracting liquid fossil fuels respecting not only economical aspects but also the impact on natural environment. We model the process of extracting of the oil/gas by pumping the chemical fluid into the formation with the use of IGA-FEM solver as non-stationary flow of the non-linear fluid in heterogeneous media. The problem of extracting liquid fossil fuels is defined as a multiobjective one with two contradictory objectives: maximizing the amount of the oil/gas extracted and minimizing the contamination of the groundwater. The goal of the paper is to check the performance of a hybridized solver for multiobjective optimization of liquid fossil fuel extraction (LFFEP) integrating population-based heuristic (i.e.\ evolutionary multi-agent system and NSGA-II algorithm for approaching the Pareto frontier) with isogeometric finite element method IGA-FEM. The results of computational experiments illustrate how the considered techniques work for a particular test scenario.

Abstract: Following recently published socio-cognitively inspired ACO concept for global optimization, we try to verify the proposed idea by adapting the PSO in a similar way. The swarm is divided into species and the particles get inspired not only by the global and local optima, but share the knowledge about the optima with neighbourhood agents belonging to other species. After presenting the concept and motivation, the experimental results gathered for common benchmark functions tackled in 100 dimensions are shown and the efficacy of the proposed algorithm is discussed.

Abstract: In swarm robotics, it is necessary to develop methods and strategies that guide the collective execution of tasks by the robots. The design of such tasks can be done considering it as a collection of simpler behaviors, called subtasks. In this paper, the Wave Swarm is presented as a general strategy to manage the sequence of subtasks that compose the collective navigation , which is an important task in swarm robotics. The proposed strategy is based mainly on the execution of wave algorithms. The swarm is viewed as a distributed system, wherein the communication is achieved by message passing among robot’s neighborhood. Message propagation delimits the start and end of each subtask. Simulations are performed to demonstrate that controlled navigation of robot swarms/clusters is achieved with three subtasks, which are recruitment, alignment and movement.

Abstract: The growing share of LED light sources in outdoor lighting enables developing street lighting solutions characterized by high energy efficiency. It is accomplished by replacing high intensity discharging lamps with LEDs and implementing various control strategies. It was also shown that a well tailored lighting design may significantly decrease the power usage. To apply this method in large projects, however, the computationally efficient approach is necessary. In this article we propose the method of energy efficiency optimization relying on a multi-agent system framework which enables scalable computations capable of handling large-scale projects. The case of a real-life optimization is also presented in the paper.

Abstract: We study the features of a new mixed integration scheme dedicated for solving the nonstationary variational problems. The scheme is composed of the FEM approximation with respect to the space variable coupled with a 3-layered time integration scheme with a linearized right-hand side operator. It was applied in solving the Cahn-Hilliard parabolic equation with a nonlinear, fourth-order elliptic part. The second order of the approximation along the time variable was proven. Moreover, the good scalability of the software based on this scheme was confirmed during simulations. We verify the proposed time integration scheme by monitoring the Ginzberg-Landau free energy. The numerical simulations are performed using parallel multifrontal direct solver executed over STAMPEDE Linux cluster. Its scalability was compared to the results of the three direct solvers, including MUMPS, SuperLU and PaSTiX.

Abstract: This paper deals with a concept of memetic search in agent-based evolutionary computation. In the presented approach, local search is applied during mutation of an agent. Using memetic algorithms causes increased demand on the computing power as the number of fitness function calls increases, therefore careful planning of the fitness computing (through the proposed local search mechanism based on caching parts of the fitness function) leads to significant lowering of this demand. Moreover, applying local search with care, can lead to gradual improvement of the whole population. In the paper the results obtained for selected high-dimensional (5000 dimensions) benchmark functions are presented. Results obtained by the evolutionary and memetic multi-agent systems are compared with classic evolutionary algorithm.

Abstract: A major concern in multi-agent coordination is how to select algorithms that can lead agents to learn together to achieve certain goals. Much of the research on multi-agent learning relates to reinforcement learning (RL) techniques. One element of RL is the interaction model, which describes how agents should interact with each other and with the environment. Discrete, continuous and objective-oriented interaction models can improve convergence among agents. This paper proposes an approach based on the integration of multi-agent coordination models designed for reward-sharing policies. By taking the best features from each model, better agent coordination is achieved. Our experimental results show that this approach improves convergence among agents even in large state-spaces and yields better results than classical RL approaches.

Abstract: Around the world, invasive Argentine ants have formed “supercolonies”: societies of societies where separate colonies share one identity and behave as one colony, but can they be maintained long enough to transform into the next major evolutionary transition? Here we argue no, and use an agent-based, spatially-explicit model of Argentine ant supercolonies to demonstrate how the extreme supercolony structure of invasive Argentine ants will collapse over time. Our model explains supercolonies as ethnocentric collections of ant colonies, making social decisions based on cuticular hydrocarbon (CHC) markers demarcating in-group from out-group. When simulated, we observe supercolonies as fragile assemblages, where the shared identity that constitutes supercolonies depends on consistent warfare, and fades over time in invasive habitats where supercolonies face no competitors. With unicoloniality in ants being a rare and phylogenetically scattered trait, they appear to be only a temporary evolutionary phenomenon. Our model explains why. It is because the consistency of “self” cannot be maintained at the scale of supercolonies, and therefore the next major evolutionary transition must be found elsewhere.

Abstract: In this paper we present a multi-criteria optimization of element partition trees and resulting orderings for multi-frontal solver algorithms executed for two dimensional h adaptive finite element method. In particular, the problem of optimal ordering of elimination of rows in the sparse matrices resulting from adaptive finite element method computations is reduced to the problem of finding of optimal element partition trees. Given a two dimensional h refined mesh, we find all optimal element partition trees by using the dynamic programming approach. An element partition tree defines a prescribed order of elimination of degrees of freedom over the mesh. We utilize three different metrics to estimate the quality of the element partition tree. As the first criterion we consider the number of floating point operations (FLOPs) performed by the multi -frontal solver. As the second criterion we consider the number of memory transfers (MEMOPS) performed by the multifrontal solver algorithm. As the third criterion we consider memory usage ( NONZEROS) of the multi-frontal direct solver. We show the optimization results for FLOPs vs MEMOPS as well as for the execution time estimated as FLOPs+100*MEMOPS vs NONZEROS. We obtain Pareto fronts with multiple optimal trees, for each mesh, and for each refinement level. We generate a library of optimal elimination trees for small grids with local singularities. We also propose an algorithm that for a given large mesh with multiple local singularities finds separators that partition the mesh into multiple sub -grids, each one with local singularity. We compute Schur complements over the local singularities using the optimal trees from the library, and later we submit the sequence of Schur complements into the iterative solver ILUPCG.

Abstract: Goal-oriented adaptive algorithms have been widely employed during the last three decades to produce optimal grids in order to solve challenging engineering problems. In this work, we extend the error representation using unconventional dual problems for goal-oriented adaptivity in the context of frequency-domain wave-propagation problems to the case of time-domain problems. To do that, we express the entire problem in weak form in order to formulate the adjoint problem and apply the goal-oriented adaptivity. We have also chosen specific spaces of trial and test functions that allow us to express a classical Method of Lines in terms of a Galerkin scheme. Some numerical results are provided in on espatial dimension which show that the upper bounds of the new error representation are sharper than the classical ones and, therefore, this new error representation can be used to design better goal-oriented adaptive processes.

Abstract: The paper presents an extension of the hypergraph grammar model of the hp-adaptive finite element method algorithm with rectangular elements to the case of non-stationary problems. In our approach the finite element mesh is represented by hypergraphs, the mesh transformations are modelled by means of hypergraph grammar rules. The extension concerns the construction of the elimination tree during the generation of the mesh and mesh adaptation process. Each operation on the mesh (generation of the mesh as well as h-adaptation of the mesh) is followed by the corresponding operation on the elimination tree. The constructed elimination tree allows the solver for reutilization of the matrices computed in the previous step of Finite Element Method. Based on the constructed elimination tree the solver can efficiently solve non-stationary problems.

Abstract: The magnetotelluric (MT) method is a passive electromagnetic (EM) exploration technique governed by Maxwell's equations aiming at estimating the resistivity distribution of the subsurface on scales varying from few meters to hundreds of kilometers. Natural EM sources induce electric currents in the Earth, and these currents generate secondary fields. By measuring simultaneously the horizontal components of these fields on the Earth's surface, it is possible to obtain information about the electrical properties of the subsurface. The dimensionality analysis of MT data is a hot and ongoing research topic in the area. In particular, the work of Weaver et al. (2000) has to be highlighted. There, he presented a dimensionality study based on the rotational invariants of the MT tensor. We also emphasize the more recent work of Martí et al. (2009), who implemented a software (based on these invariants) able to describe in a robust way the dimensionality of the problem when real measurements are employed. The dimension of the formation is not clear in some scenarios. When employing traditional inversion techniques, the dimension (the full 2D (or 3D) problem) is usually fixed in forward simulations and inversion. However, a proper study of the dimensionality of the problem may indicate some areas where the problem is fully 2D (or 3D), while others where a 1D (or 2D) consideration of the problem may be sufficient. Following this idea, we propose an initial step towards an algorithm that takes advantage of this scenario via an adaptivity in the spatial variable. Thus, we first consider a full 1D inverse problem, with an exact (and fast) forward solution, and after that, we introduce this 1D inverse problem solution into the 2D inverse problem. Numerical results show savings in the inversion process of the 75% in some scenarios.

Abstract: In this paper we compare three different strategies for dealing with local singularities with two dimensional isogeometric finite element method. The first strategy employs local h refinements with T-spline basis functions. The second strategy is a modification of the first one, also using local h refinements and T-splines, but with some additional refinements intended to localize the support of the T-spline basis functions. The third strategy utilizes C^0 separators and B-splines. We compare the strategies by means of their computational cost from the point of view of multi-frontal direct solvers. We also compare the computational costs of our strategies with classical FEM using second order polynomials and C^0 separators between elements. We analyse the computational costs theoretically and as well compare the number of floating point operations (FLOPs) executed by the multi-frontal direct solver MUMPS. We show that third strategy outperforms both IGA-FEM and classical FEM.