Abstract: Logging-While-Drilling (LWD) devices are often used for geosteering applications. They interpret (invert) measurements in real time to determine the well trajectory. To perform the inversion, we require a forward solver with high performance since: (a) we often need to invert for thousands of logging positions in real time, and (b) we need to solve a considerable number of forward problems. In these applications, it is a common practice to approximate the domain with a sequence of 1D models. In a 1D model, the material properties vary only along one direction (z-direction). For such 1D models, we reduce the dimensionality of the problem using a Hankel transform. We can solve the resulting system of Ordinary Differential Equations (ODEs): (a) analytically, which leads to a so-called semi-analytic method after performing a numerical inverse Hankel transform, or (b) numerically. Semi-analytic methods are used vastly due to their high performance. However, they have major limitations, namely: • By today’s knowledge, the analytical solution of the aforementioned system of ODEs is available only for piecewise-constant resistivity values. • To perform geosteering, we need to invert the measurements with respect to some inversion variables using a gradient-based inversion method. For resistivity measurements, these inversion variables are often the constant resistivity values of each layer and the bed boundary positions. However, the analytical derivatives of cross-bedded formations and the analytical derivatives of the measurements with respect to the bed boundary positions have not been published to the best of our knowledge. The main contribution of this work is to overcome the above limitations by using an efficient multi-scale finite element method to solve the system of ODEs corresponding to each Hankel mode. To do so, we divide our computations into two parts, namely: • Computations which are independent of logging positions and consist of computing the multi-scale basis functions. Hence, we precompute them once, and we use them for all logging positions. • Computations which depend upon the logging positions. Using aforementioned method, we can: (a) consider arbitrary resistivity distributions which depend upon one direction, and (b) easily and rapidly compute the derivatives with respect to any inversion variable at almost no additional cost using an adjoint state method. Although the proposed method is slower than semi-analytic ones, it is highly efficient and more flexible when computing the derivatives. In addition, the proposed method is perfectly parallelizable with respect to Hankel modes and multi-scale basis functions.

Abstract: In this paper a novel hybridization of agent-based evolu- tionary system (EMAS) is presented. This method assumes utilization of PSO for upgrading certain agents living in the EMAS population, thus serving similar to local-search methods already used in EMAS (in memetic fashion). The gathered and presented results prove the applica- bility of this hybrid based on a selection of a number of 500 dimensional benchmark functions.

Abstract: In this paper, an agent-based data-driven model that focuses on path planning layer of origin/destination popularities and route choice is developed. This model improves on the existing mathematical modeling and pattern recognition approaches. The paths and origins/destinations are extracted from a video. The parameters are calibrated from density map generated from the video. We carried out validation on the path probabilities and densities, and showed that our model generates better results than the previous approaches. To demonstrate the usefulness of the approach, we also carried out a case study on capacity analysis of a building layout based on video data.

Abstract: Refined Isogeometric Analysis (rIGA) is a discretization method used to solve numerical problems governed by partial differential equations (PDEs). Starting from a highly continuous Isogeometric Analysis (IGA) discretization, rIGA reduces the continuity over certain hyperplanes that split the mesh into subdomains. This method maximizes the performance of direct solvers by reducing the continuity until C^0 over selected hyperplanes, which act as separators during the elimination of the degrees of freedom (DoF). By doing so, the solution time and best approximation error are simultaneously improved. In particular, D. Garcia et al. show that rIGA delivers a speedup factor with respect to IGA that is proportional to $p^2$ when solving Laplace based problems in 2D and 3D, with p being the polynomial degree. In this work, we extend rIGA method to solve multi-field problems. We consider incompressible fluid flow problems on bounded domains. They include the pressure and the vectorial velocity of the fluid. We use a spline-based generalization of the Raviart-Thomas finite element spaces to approximate the velocity field. We show that rIGA delivers a reduction in the computational cost when solving incompressible fluid flow problems that asymptotically reaches O(p^2), and it provides better accuracy than C^(p-1) IGA. For multi-field problems, however, we require larger problems to arrive at the asymptotic limit and reach the maximum possible savings since the system involves more equations. In our numerical 2D results, we observe a reduction factor in the computational cost of up to p^2. In 3D, the maximum reproducible problems are in the pre-asymptotic regime, and the maximum observed gain factors are of O(p).

Abstract: We focus on a fast explicit solver for solution of non-stationary problems using L2 projections with isogeometric finite element method. The algorithm has been implemented in Fortran 2008 with MPI and OpenMP frameworks. It enables for parallel multi-core hybrid memory simulations of different time-dependent problems in 3D. We have prepared the solwer framework in a way that enables for direct implementation of the selected Partial Differential Equations and corresponding boundary conditions. The presented package generates output suitable for interfacing with ParaView visualisation software. Finally new implementation is complementary to previously released GALOIS based shared memory code written in C++. Our library manages most of computations, while user has to provide subroutine with equations for Right Hand Side.

Abstract: Mistakes in pedestrian infrastructure design in modern cities decrease transfer comfort for people, impact greenery due to appearance of desire paths, and thus increase the amount of dust in the air because of open ground. These mistakes can be avoided if optimal path networks are created considering behavioral aspects of pedestrian traffic, which is a challenge. In this article, we introduce Ant Road Planner, a new method of computer simulation for estimation and creation of optimal path networks which not only considers pedestrians' behavior but also helps minimize the total length of the paths so that the area is used more efficiently. The method, which includes a modeling algorithm and its software implementation with a user-friendly web interface, makes it possible to predict pedestrian networks for new territories with high precision and detect problematic areas in existing networks. The algorithm was successfully tested on real territories and proved its potential as a decision making support system for urban planners.

Abstract: In time-domain goal-oriented adaptivity, it is essential to represent the error in the quantity of interest as an integral over the whole space-time domain. In that way, we can express the global error as a sum of local element contributions, and perform adaptivity. A space-time variational formulation provides such integral representation. Many authors employ implicit methods in time for performing goal-oriented adaptivity, like Backward Euler or Crank-Nicholson, as it is well known that these methods have variational structure. The Galerkin formulation of explicit methods in time for partial differential equations, however, remains elusive. In this work, we first construct a Petrov-Galerkin formulation for parabolic problems that is equivalent to the Forward Euler method in time (first order Runge-Kutta). Then, we derive an error representation and an explicit goal-oriented adaptive algorithm, enabling dynamic meshes in space. Some numerical results are provided for the 1D advection-diffusion equation to illustrate the proposed explicit algorithm. Finally, we provide an overview of how to build other Runge-Kutta methods using a variational formulation and follow a similar goal-oriented procedure.

Abstract: We focus on three-dimensional isogeometric analysis with tensor product C^k B-spline basis functions. We solve the computational problem with multi-frontal direct solver using the ordering obtained from the element partition trees. The trees have particular elements at the leaves, the entire mesh at the roof, and recursive partitions at internal nodes. The ordering obtained by browsing the tree in post-order, from leaves up to the root, results in a lower computational cost of the LU factorization than state-of-the art orderings obtained from the spare matrix analysis. We propose the algorithm that plots the map of FLOPS per mesh nodes using the trees, which in turn allows to identify the computationally expensive mesh nodes. Finally, we modify the algorithm of refined isogeometric analysis to introduce C0 separators at expensive mesh nodes, which reduces the cost of the solver by order of magnitude, while maintaining the numerical accuracy.

Abstract: To describe the diversity of opinions and dynamics of their changes in a society, there exist different approaches — from macroscopic laws of political processes to individual–based cognition and perception models. In this paper, we propose mesoscopic individual–based model of opinion dynamics which tackles the role of context by considering influence of different sources of information during life cycle of agents. The model combines several sub–models such as model of gen-eration and broadcasting of messages by mass media, model of daily activity, contact model based on multiplex network and model of information processing. To show the applicability of the approach, we present two scenarios illustrating the effect of the conflicting strategies of informational influence on a population and polarization of opinions about topical subject.

Abstract: In the paper, heuristic algorithm for tensor product approximation with B-spline basis functions of three-dimensional material data is presented. The algorithm has an application as a preconditioner for implicit dynamics simulations of a non-linear flow in heterogeneous media using alternating directions method. As the simulation use case non-stationary problem of liquid fossil fuels exploration with hydraulic fracturing is considered. Presented algorithm allows to approximate the permeability coefficient function as a tensor product what in turn allows for implicit simulations of the Laplasjan term in the partial differential equation. In the consequence the number of time steps of the non-stationary problem can be reduced, while the numerical accuracy is preserved.