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.