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Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines

Repositorio: BIRD: BCAM's Institutional Repository Data
Wozniak, M., Paszynski, M., Pardo, D., Dalcin, L., Calo, V.M.

This paper derives theoretical estimates of the computational cost for isogeometric multi-frontal direct solver executed on parallel distributed memory machines. We show theoretically that for the $C^{p-1}$ global continuity of the isogeometric solution, both the computational cost and the communication cost of a direct solver are of order $\mathcal{O}(log(N)p^2)$ for the one dimensional $(1D)$ case, $\mathcal{O}(Np^2)$ for the two dimensional $(2D)$ case, and $\mathcal{O}(N^{4/3}p^2)$ for the…



Direct solvers performance on h-adapted grids

Repositorio: BIRD: BCAM's Institutional Repository Data
Paszynski, M., Pardo, D., Calo, V.M.

We analyse the performance of direct solvers when applied to a system of linear equations arising from an $h$-adapted, $C^0$ finite element space. Theoretical estimates are derived for typical $h$-refinement patterns arising as a result of a point, edge, or face singularity as well as boundary layers. They are based on the elimination trees constructed specifically for the considered grids. Theoretical estimates are compared with experiments performed with MUMPS using the nested-dissection…



Fractional Laguerre spectral methods and their applications to fractional differential equations on unbounded domain

Repositorio: BIRD: BCAM's Institutional Repository Data
Aboelenen, T., Bakr, S.A., El-Hawary, H.M.

In this article, we first introduce a singular fractional Sturm-Liouville problem (SFSLP) on unbounded domain. The associated fractional differential operator is both Weyl and Caputo type. The properties of spectral data for fractional operator on unbounded domain have been investigated. Moreover, it has been shown that the eigenvalues of the singular problem are real-valued and the corresponding eigenfunctions are orthogonal. The analytical eigensolutions of SFSLP are obtained and defined as…



Stabilized dual-mixed method for the problem of linear elasticity with mixed boundary conditions

Repositorio: BIRD: BCAM's Institutional Repository Data
Gonzalez, M.

We extend the applicability of the augmented dual-mixed method introduced recently in Gatica (2007), Gatica et al. (2009) to the problem of linear elasticity with mixed boundary conditions. The method is based on the Hellinger-Reissner principle and the symmetry of the stress tensor is imposed in a weak sense. The Neumann boundary condition is prescribed in the finite element space. Then, suitable Galerkin least-squares type terms are added in order to obtain an augmented variational…



High-accuracy adaptive modeling of the energy distribution of a meniscus-shaped cell culture in a Petri dish

Repositorio: BIRD: BCAM's Institutional Repository Data
Gomez-Revuelto, I., Garcia-Castillo, L.E., Pardo, D.

Cylindrical Petri dishes embedded in a rectangular waveguide and exposed to a polarized electromagnetic wave are often used to grow cell cultures. To guarantee the success of these cultures, it is necessary to enforce that the specific absorption rate distribution is sufficiently high and uniform over the Petri dish. Accurate numerical simulations are needed to design such systems. These simulations constitute a challenge due to the strong discontinuity of electromagnetic material properties…



Multi-objective hierarchic memetic solver for inverse parametric problems

Repositorio: BIRD: BCAM's Institutional Repository Data
Gajda-Zagórska, E., Smolka, M., Schaefer, R., Pardo, D., Alvarez-Aramberri, J.

We propose a multi-objective approach for solving challenging inverse parametric problems. The objectives are misfits for several physical descriptions of a phenomenon under consideration, whereas their domain is a common set of admissible parameters. The resulting Pareto set, or parameters close to it, constitute various alternatives of minimizing individual misfits. A special type of selection applied to the memetic solution of the multi-objective problem narrows the set of alternatives to…



Semi-analytical response of acoustic logging measurements in frequency domain

Repositorio: BIRD: BCAM's Institutional Repository Data
Muga, I., Pardo, D., Matuszyk, P.J., Torres-Verdin, C.

This work proposes a semi-analytical method for simulation of the acoustic response of multipole eccentered sources in a fluid-filled borehole. Assuming a geometry that is invariant with respect to the azimuthal and vertical directions, the solution in frequency domain is expressed in terms of a Fourier series and a Fourier integral. The proposed semi-analytical method builds upon the idea of separating singularities from the smooth part of the integrand when performing the inverse Fourier…



The Modellers' Halting Foray into Ecological Theory: Or, What is This Thing Called 'Growth Rate'?

Repositorio: BIRD: BCAM's Institutional Repository Data
Deveau, M., Karsten, R., Teismann, H.

This discussion paper describes the attempt of an imagined group of non-ecologists ("Modellers" ) to determine the population growth rate from field data. The Modellers wrestle with the multiple definitions of the growth rate available in the literature and the fact that, in their modelling, it appears to be drastically model-dependent, which seems to throw into question the very concept itself. Specifically, they observe that six representative models used to capture the data produce…



Optimal quadrature rules for odd-degree spline spaces and their application to tensor-product-based isogeometric analysis

Repositorio: BIRD: BCAM's Institutional Repository Data
Barton, M., Calo, V.M.

We introduce optimal quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. Using the homotopy continuation concept (Barton and Calo, 2016) that transforms optimal quadrature rules from source spaces to target spaces, we derive optimal rules for splines defined on finite domains. Starting with the classical Gaussian quadrature for polynomials, which is an optimal rule for a discontinuous odd-degree space, we derive rules for…



Non-conforming curved finite element schemes for time-dependent elastic-acoustic coupled problems

Repositorio: BIRD: BCAM's Institutional Repository Data
Rodríguez-Rozas, A., Diaz, J.

High-order numerical methods for solving time-dependent acoustic-elastic coupled problems are introduced. These methods, based on Finite Element techniques, allow for a flexible coupling between the fluid and the solid domain by using non-conforming meshes and curved elements. Since characteristic waves travel at different speeds through different media, specific levels of granularity for the mesh discretization are required on each domain, making impractical a possible conforming coupling in…



Red refinements of simplices into congruent subsimplices

Repositorio: BIRD: BCAM's Institutional Repository Data
Korotov, S., Krizek, M.

We show that in dimensions higher than two, the popular "red refinement" technique, commonly used for simplicial mesh refinements and adaptivity in the finite element analysis and practice, never yields subsimplices which are all acute even for an acute father element as opposed to the two-dimensional case. In the three-dimensional case we prove that there exists only one tetrahedron that can be partitioned by red refinement into eight congruent subtetrahedra that are all similar to…



On nonobtuse refinements of tetrahedral finite element meshes

Repositorio: BIRD: BCAM's Institutional Repository Data
Korotov, S.

It is known that piecewise linear continuous finite element (FE) approximations on nonobtuse tetrahedral FE meshes guarantee the validity of discrete analogues of various maximum principles for a wide class of elliptic problems of the second order. Such analogues are often called discrete maximum principles (or DMPs in short). In this work we present several global and local refinement techniques which produce nonobtuse conforming (i.e. face-to-face) tetrahedral partitions of polyhedral domains…



On numerical regularity of the face-to-face longest-edge bisection algorithm for tetrahedral partitions

Repositorio: BIRD: BCAM's Institutional Repository Data
Hannukainen, A., Korotov, S., Krizek, M.

The finite element method usually requires regular or strongly regular families of partitions in order to get guaranteed a priori or a posteriori error estimates. In this paper we examine the recently invented longest-edge bisection algorithm that always produces only face-to-face simplicial partitions. First, we prove that the regularity of the family of partitions generated by this algorithm is equivalent to its strong regularity in any dimension. Second, we present a number of 3d numerical…



Analysis of extreme wave events on the southern coast of Brazil

Repositorio: BIRD: BCAM's Institutional Repository Data
Guimaraes, P.V., Farina, L., Toldo, E.E.

Using the wave model SWAN (simulating waves nearshore), high waves on the southwestern Atlantic generated by extra-tropical cyclones are simulated from 2000 to 2010, and their impact on the Rio Grande do Sul (RS) coast is studied. The modeled waves are compared with buoy data and good agreement is found. The six extreme events in the period that presented significant wave heights above 5 m, on a particular point of interest, are investigated in detail. It is found that the cyclogenetic pattern…



A study of the apsidal angle and a proof of monotonicity in the logarithmic potential case

Repositorio: BIRD: BCAM's Institutional Repository Data
Castelli, R.

This paper concerns the behaviour of the apsidal angle for orbits of central force system with homogeneous potential of degree $-2 \le \alpha \le 1$ and logarithmic potential. We derive a formula for the apsidal angle as a fixed end-points integral and we study the derivative of the apsidal angle with respect to the angular momentum $\ell$. The monotonicity of the apsidal angle as function of $\ell$ is discussed and it is proved in the logarithmic potential case.



A hybrid method for inversion of 3D DC resistivity logging measurements

Repositorio: BIRD: BCAM's Institutional Repository Data
Gajda-Zagórska, E., Schaefer, R., Smolka, M., Paszynski, M., Pardo, D.

This paper focuses on the application of hp hierarchic genetic strategy (hp-HGS) for solution of a challenging problem, the inversion of 3D direct current (DC) resistivity logging measurements. The problem under consideration has been formulated as the global optimization one, for which the objective function (misfit between computed and reference data) exhibits multiple minima. In this paper, we consider the extension of the hp-HGS strategy, namely we couple the hp-HGS algorithm with a…



Fast smoothing parameter separation in multidimensional generalized P-splines: the SAP algorithm

Repositorio: BIRD: BCAM's Institutional Repository Data
Rodríguez-Álvarez, M.X., Lee, D.-J., Kneib, T., Durban, M., Eilers, P.H.C.

A new computational algorithm for estimating the smoothing parameters of a multidimensional penalized spline generalized linear model with anisotropic penalty is presented. This new proposal is based on the mixed model representation of a multidimensional P-spline, in which the smoothing parameter for each covariate is expressed in terms of variance components. On the basis of penalized quasi-likelihood methods, closed-form expressions for the estimates of the variance components are obtained.…



A decision tree to assess short-term mortality after an emergency department visit for an exacerbation of COPD: A cohort study

Repositorio: BIRD: BCAM's Institutional Repository Data
Esteban, C., Arostegui, I., Garcia-Gutierrez, S., Gonzalez, N., Lafuente, I., Bare, M., Fernandez-de-Larrea, N., Rivas, F., Quintana, J.M.

Background: Creating an easy-to-use instrument to identify predictors of short-term (30/60-day) mortality after an exacerbation of chronic obstructive pulmonary disease (eCOPD) could help clinicians choose specific measures of medical care to decrease mortality in these patients. The objective of this study was to develop and validate a classification and regression tree (CART) to predict short term mortality among patients evaluated in an emergency department (ED) for an eCOPD. Methods: We…



Flexible geostatistical modeling and risk assessment analysis of lead concentration levels of residential soil in the Coeur D'Alene River Basin

Repositorio: BIRD: BCAM's Institutional Repository Data
Lee, D.-J., Toscas, P.

Soil heavy metals pollution is an urgent problem worldwide. Understanding the spatial distribution of pollutants is critical for environmental management and decision-making. Children and adults are still routinely exposed to very high levels of heavy metals contaminants in some countries, particularly in regions with a long mining history. In this paper, we analyze lead concentration levels from residential soil samples in the Coeur D'Alene River Basin in the United States. The aim of…



Spatio-temporal functional data analysis for wireless sensor networks data

Repositorio: BIRD: BCAM's Institutional Repository Data
Lee, D.-J., Zhu, Z., Toscas, P.

A new methodology is proposed for the analysis, modeling, and forecasting of data collected from a wireless sensor network. Our approach is considered in the framework of a functional data-analysis paradigm where observed data is represented in a functional form. To reduce dimensionality, functional principal components analysis is applied to highlight important underlying characteristics and find patterns of variations. The principal scores are modeled with tensor product smooths that allow…



Effect of various dietary regimens on oral challenge with Mycobacterium avium subsp. paratuberculosis in a rabbit model

Repositorio: BIRD: BCAM's Institutional Repository Data
Arrazuria, R., Molina, E., Mateo-Abad, M., Arostegui, I., Garrido, J.M., Juste, R.A., Elguezabal, N.

Rabbits are susceptible to infection by Mycobacterium avium subspecies paratuberculosis (MAP) in both wildlife and experimental conditions. Under the hypotheses that nutrient balance might influence the establishment of infection, we designed an experiment where MAP intestinal colonization was assessed under three dietary regimens: high fiber, high protein, and regular diet in New Zealand white rabbits submitted to oral challenge with MAP.Lowest weight gain (F=5.17, p=0.024), higher tissue…



Fast algorithm for smoothing parameter selection in multidimensional P-splines

Repositorio: BIRD: BCAM's Institutional Repository Data
Rodríguez-Álvarez, M.X., Lee, D.-J., Kneib, T., Durban, M., Eilers, P.H.C.

A new computational algorithm for estimating the smoothing parameters of a multidimensional penalized spline generalized model with anisotropic penalty is presented. This new proposal is based on the mixed model representation of a multidimensional P-spline, in which the smoothing parameter for each covariate is expressed in terms of variance components. On the basis of penalized quasi-likelihood methods (PQL), closed-form expressions for the estimates of the variance components are obtained.…



Generalized restless bandits and the knapsack problem for perishable inventories

Repositorio: BIRD: BCAM's Institutional Repository Data
Graczova, D., Jacko, P.

In this paper we introduce the knapsack problem for perishable inventories concerning the optimal dynamic allocation of a collection of products to a limited knapsack. The motivation for designing such a problem comes from retail revenue management, where different products often have an associated lifetime during which they can only be sold, and the managers can regularly select some products to be allocated to a limited promotion space that is expected to attract more customers than the…



Optimal planning of slow-ramping power production in energy systems with renewables forecasts and limited storage

Repositorio: BIRD: BCAM's Institutional Repository Data
Richmond, N., Jacko, P., Makowski, A.M.

We address the cost-efficient operation of an energy production system under renewables uncertainty. We develop an MDP model for an idealized system with the following features: (1) perfectly predictable power demand, (2) a renewable power source subject to uncertain forecast, (3) limited energy storage, (4) an unlimited fast-ramping power source, and (5) a slow-ramping power source which requires (optimal) planning. A finite-horizon stochastic optimization problem is introduced to minimize the…



The economics of the cloud: Price competition and congestion

Repositorio: BIRD: BCAM's Institutional Repository Data
Anselmi, J., Ardagna, D., Lui, J.C.S., Wierman, A., Xu, Y., Yang, Z.

[No abstract available]



Generalized Nash equilibria for SaaS/PaaS Clouds

Repositorio: BIRD: BCAM's Institutional Repository Data
Anselmi, J., Ardagna, D., Passacantando, M.

Cloud computing is an emerging technology that allows to access computing resources on a pay-per-use basis. The main challenges in this area are the efficient performance management and the energy costs minimization. In this paper we model the service provisioning problem of Cloud Platform-as-a-Service systems as a Generalized Nash Equilibrium Problem and show that a potential function for the game exists. Moreover, we prove that the social optimum problem is convex and we derive some…



Efficiency of simulation in monotone hyper-stable queueing networks

Repositorio: BIRD: BCAM's Institutional Repository Data
Anselmi, J., Gaujal, B.

We consider Jackson queueing networks with finite buffer constraints (JQN) and analyze the efficiency of sampling from their stationary distribution. In the context of exact sampling, the monotonicity structure of JQNs ensures that such efficiency is of the order of the coupling time (or meeting time) of two extremal sample paths. In the context of approximate sampling, it is given by the mixing time. Under a condition on the drift of the stochastic process underlying a JQN, which we call hyper…



Ergodic transition in a simple model of the continuous double auction

Repositorio: BIRD: BCAM's Institutional Repository Data
Radivojevic, T., Anselmi, J., Scalas, E.

We study a phenomenological model for the continuous double auction, whose aggregate order process is equivalent to two independent M/M/1 queues. The continuous double auction defines a continuous-time random walk for trade prices. The conditions for ergodicity of the auction are derived and, as a consequence, three possible regimes in the behavior of prices and logarithmic returns are observed. In the ergodic regime, prices are unstable and one can observe a heteroskedastic behavior in the…



Nearly-optimal scheduling of users with Markovian time-varying transmission rates

Repositorio: BIRD: BCAM's Institutional Repository Data
Cecchi, F., Jacko, P.

We address the problem of developing a well-performing and implementable scheduler of users with wireless connections to the central controller, which arise in areas such as mobile data networks, heterogeneous networks, or vehicular communications systems. The main feature of such systems is that the quality of each user's channel is time-varying due to fading. The evolution of the channel over its quality states thus causes a time-varying transmission rate of each user. We consider…



Regularized optimization methods for convex MINLP problems

Repositorio: BIRD: BCAM's Institutional Repository Data
de Oliveira, W.

We propose regularized cutting-plane methods for solving mixed-integer nonlinear programming problems with nonsmooth convex objective and constraint functions. The given methods iteratively search for trial points in certain localizer sets, constructed by employing linearizations of the involved functions. New trial points can be chosen in several ways; for instance, by minimizing a regularized cutting-plane model if functions are costly. When dealing with hard-to-evaluate functions, the goal…



Decentralized proportional load balancing

Repositorio: BIRD: BCAM's Institutional Repository Data
Anselmi, J., Walton, N.S.

Load balancing is a powerful technique commonly used in communication and computer networks to improve system performance, robustness and fairness. In this paper, we consider a general model capturing the performance of communication and computer networks, and on top of it we propose a decentralized algorithm for balancing load among multiple network paths. The proposed algorithm is inspired by the modus operandi of the processor-sharing queue and on each network entry point operates as follows…



On the applicability of ant colony optimization to non-intrusive load monitoring in smart grids

Repositorio: BIRD: BCAM's Institutional Repository Data
Gonzalez-Pardo, A., Del Ser, J., Camacho, D.

Along with the proliferation of the Smart Grid, power load disaggregation is a research area that is lately gaining a lot of popularity due to the interest of energy distribution companies and customers in identifying consumption patterns towards improving the way the energy is produced and consumed (via e.g. demand side management strategies). Such data can be extracted by using smart meters, but the expensive cost of incorporating a monitoring device for each appliance jeopardizes…



An empirical study on collective intelligence algorithms for video games problem-solving

Repositorio: BIRD: BCAM's Institutional Repository Data
Gonzalez-Pardo, A., Palero, F., Camacho, D.

Computational intelligence (CI), such as evolutionary computation or swarm intelligence methods, is a set of bio-inspired algorithms that have been widely used to solve problems in areas like planning, scheduling or constraint satisfaction problems. Constrained satisfaction problems (CSP) have taken an important attention from the research community due to their applicability to real problems. Any CSP problem is usually modelled as a constrained graph where the edges represent a set of…



Path Planning for Single Unmanned Aerial Vehicle by Separately Evolving Waypoints

Repositorio: BIRD: BCAM's Institutional Repository Data
Yang, P., Tang, K., Lozano, J.A., Cao, X.

Evolutionary algorithm-based unmanned aerial vehicle (UAV) path planners have been extensively studied for their effectiveness and flexibility. However, they still suffer from a drawback that the high-quality waypoints in previous candidate paths can hardly be exploited for further evolution, since they regard all the waypoints of a path as an integrated individual. Due to this drawback, the previous planners usually fail when encountering lots of obstacles. In this paper, a new idea of…



Efficient approximation of probability distributions with k-order decomposable models

Repositorio: BIRD: BCAM's Institutional Repository Data
Pérez, A., Inza, I., Lozano, J.A.

During the last decades several learning algorithms have been proposed to learn probability distributions based on decomposable models. Some of these algorithms can be used to search for a maximum likelihood decomposable model with a given maximum clique size, k. Unfortunately, the problem of learning a maximum likelihood decomposable model given a maximum clique size is NP-hard for $k<2$. In this work, we propose the fractal tree family of algorithms which approximates this problem with a…



Theoretical Study of the Dissociative Adsorption of Methane on Ir(111): The Role of Steps and Surface Distortions at High Temperatures

Repositorio: BIRD: BCAM's Institutional Repository Data
Moiraghi, R., Lozano, A., Busnengo, H.F.

In this work we revisit the dissociative adsorption of methane on Ir(111) through density functional theory calculations. We focus on the role of surface defects entailing undercoordinated Ir atoms (e.g., steps), and thermally induced distortions of a defect-free terrace. Though both factors provoke a significant activation of the CH3⋯H bond cleavage, our results indicate that the latter (surface distortions) is more likely responsible for the low activation energy derived from experiments at…



Joint topology optimization, power control and spectrum allocation for intra-vehicular multi-hop sensor networks using dandelion-encoded heuristics

Repositorio: BIRD: BCAM's Institutional Repository Data
Del Ser, J., Bilbao, M.N., Perfecto, C., Gonzalez-Pardo, A., Campos-Cordobes, S.

In the last years the interest in multi-hop communications has gained momentum within the research community due to the challenging characteristics of the intra-vehicular radio environment and the stringent robustness imposed on critical sensors within the vehicle. As opposed to point-to-point network topologies, multi-hop networking allows for an enhanced communication reliability at the cost of an additional processing overhead. In this context this manuscript poses a novel bi-objective…



Fitting the data from embryo implantation prediction: Learning from label proportions

Repositorio: BIRD: BCAM's Institutional Repository Data
Hernández-González, J., Inza, I., Crisol-Ortíz, L., Guembe, M.A., Iñarra, M.J., Lozano, J.A.

Machine learning techniques have been previously used to assist clinicians to select embryos for human-assisted reproduction. This work aims to show how an appropriate modeling of the problem can contribute to improve machine learning techniques for embryo selection. In this study, a dataset of 330 consecutive cycles (and associated embryos) carried out by the Unit of Assisted Reproduction of the Hospital Donostia (Spain) throughout 18 months has been analyzed. The problem of the embryo…



Mechanism of hydrogen production via water splitting on 3C-SiC's different surfaces: A first-principles study

Repositorio: BIRD: BCAM's Institutional Repository Data
Du, J., Wen, B., Melnik, R.

The reaction mechanism of producing hydrogen via water splitting on the different surfaces of cubic silicon carbide (3C-SiC), the adsorption energy and the activation energy have been studied here by using density functional theory. The results indicated that the adsorption behavior of water molecule could take place on 3C-SiC's different surfaces and it leads to the surface reconstruction. Besides, the water splitting reaction is found to be a thermally activated process, and the first…



Shoaling of nonlinear steady waves: maximum height and angle of breaking

Repositorio: BIRD: BCAM's Institutional Repository Data
Romero, S., Farina, L.

A Fourier approximation method is used for modeling and simu- lation of fully nonlinear steady waves. The set of resulting nonlinear equations are solved by Newton’s method. The shoaling of waves is simulated based on comparisons with experimental data. The wave heights and the angles of breaking are analysed until the limit of inadequacy of the numerical method. The results appear quite close to those criteria predicted by the theory of com- pletely nonlinear surface waves and contribute to…



Wealth distribution and the Lorenz curve: a finitary approach

Repositorio: BIRD: BCAM's Institutional Repository Data
Scalas, E., Radivojevic, T., Garibaldi, U.

We use three stochastic games for the wealth of economic agents which may be at work in a real economy and we derive their statistical equilibrium distributions. Based on a heuristic argument, we assume that the expected observed wealth distribution is a mixture of these three distributions. We compare the Lorenz curves obtained from this conjecture with the empirical curves for a set of countries.



A differential equation with state-dependent delay from cell population biology

Repositorio: BIRD: BCAM's Institutional Repository Data
Getto, P., Waurick, M.

We analyze a differential equation, describing the maturation of a stem cell population, with a state-dependent delay, which is implicitly defined via the solution of an ODE. We elaborate smoothness conditions for the model ingredients, in particular vital rates, that guarantee the existence of a local semiflow and allow to specify the linear variational equation. The proofs are based on theoretical results of Hartung et al. combined with implicit function arguments in infinite dimensions.…



Non-Markovian models of the growth of a polymer chain

Repositorio: BIRD: BCAM's Institutional Repository Data
Sokolovski, D., Rusconi, S., Akhmatskaya, E., Asua, J.M.

Using simple exactly solvable models, we show that event-dependent time delays may lead to significant non-Poisson effects in the statistics of polymer chain growth. The results are confirmed by stochastic simulation of various growth scenarios. Our interest in mathematical aspects of non-Markovian growth arises from recent successful application of delayed probability density functions in stochastic modelling of controlled radical polymerization.



Complex angular momentum theory of state-to-state integral cross sections: Resonance effects in the $F + HD \to HF(v' = 3) + D$ reaction

Repositorio: BIRD: BCAM's Institutional Repository Data
Sokolovski, D., Akhmatskaya, E., Echeverria-Arrondo, C., de Fazio, D.

State-to-state reactive integral cross sections (ICSs) are often affected by quantum mechanical resonances, especially near a reactive threshold. An ICS is usually obtained by summing partial waves at a given value of energy. For this reason, the knowledge of pole positions and residues in the complex energy plane is not sufficient for a quantitative description of the patterns produced by resonance. Such description is available in terms of the poles of an S-matrix element in the complex plane…



Numerical simulation of extreme wave runup during storm events in Tramandaí­ Beach, Rio Grande do Sul, Brazil

Repositorio: BIRD: BCAM's Institutional Repository Data
Guimaraes, P.V., Farina, L., Toldo, E., Diaz-Hernandez, G., Akhmatskaya, E.

We present a high resolution analysis of the interaction of irregular waves with natural and urban structures leading to extreme wave runup. Horizontal runup data, instantaneous flooding maps, and wave propagation beyond the coastline are numerically predicted. The novel methodology combining the Wave Watch III, SWAN and SWASH models to achieve accurate and computationally feasible simulation of waves at different time and spatial scales, from the formation process at deep water up to the total…



Relative frequencies of constrained events in stochastic processes: An analytical approach

Repositorio: BIRD: BCAM's Institutional Repository Data
Rusconi, S., Akhmatskaya, E., Sokolovski, D., Ballard, N., de La Cal, J.C.

The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They relies on knowledge of interevent probability density functions (PDFs) and on information about dependencies between all possible events. Analytical representations of a PDF are difficult to specify in advance, in many real life applications. Knowing the shapes of PDFs, and using experimental data, different optimization schemes can…



The airfoil equation on near disjoint intervals: Approximate models and polynomial solutions

Repositorio: BIRD: BCAM's Institutional Repository Data
Farina, L., Ferreira, M.R.S., Peron, V.

The airfoil equation is considered over two disjoint intervals. Assuming the distance between the intervals is small an approximate solution is found and relationships between this approximation and the solution of the classical airfoil equation are obtained. Numerical results show the convergence of the solution of the original problem to the approximation. Polynomial solutions for an approximate model are obtained and a spectral method for the generalized airfoil equation on near disjoint…



On the Perturbation Methods for Vibration Analysis of Linear Time-Varying Systems

Repositorio: BIRD: BCAM's Institutional Repository Data
Yang, X.-D., Liu, M., Zhang, W., Qian, Y.J., Melnik, R.

Some perturbation methods in the studying vibrations of the linear time-varying (LTV) system are discussed. Three classical perturbation methods, namely, averaging method, harmonic balance method, and multiple scales method with linear scales, have been used from a new perspective based on analytical approximations to the corresponding LTV ordinary differential equations. The deploying beam model has been taken as an example to validate the explicit approximate solutions obtained by these…



Vortex filament equation for a regular polygon

Repositorio: BIRD: BCAM's Institutional Repository Data
De la Hoz, F., Vega, L.

In this paper, we study the evolution of the vortex filament equation,$$ X_t = X_s \wedge X_{ss},$$with $X(s, 0)$ being a regular planar polygon. Using algebraic techniques, supported by full numerical simulations, we give strong evidence that $X(s, t)$ is also a polygon at any rational time; moreover, it can be fully characterized, up to a rigid movement, by a generalized quadratic Gau$\beta$ sum. We also study the fractal behaviour of $X(0, t)$, relating it with the so-called Riemann's…



A Mean-field model for spin dynamics in multilayered ferromagnetic media

Repositorio: BIRD: BCAM's Institutional Repository Data
Chen, J., García-Cervera, C.J., Yang, X.

In this paper, we develop a mean-field model for describing the dynamics of spintransfer torque in multilayered ferromagnetic media. Specifically, we use the techniques of Wigner transform and moment closure to connect the underlying physics at different scales and reach a macroscopic model for the dynamics of spin coupled with the magnetization within the material. This provides a further understanding of the linear response model proposed by Zhang, Levy, and Fert [Phys. Rev. Lett., 88 (2002…



An atomistic/continuum coupling method using enriched bases

Repositorio: BIRD: BCAM's Institutional Repository Data
Chen, J., García-Cervera, C.J., Li, X.

A common observation from an atomistic to continuum coupling method is that the error is often generated and concentrated near the interface, where the two models are combined. In this paper, a new method is proposed to suppress the error at the interface, and as a consequence, the overall accuracy is improved. The method is motivated by formulating the molecular mechanics model as a two-stage minimization problem. In particular, it is demonstrated that the error at the interface can be…



Relativistic Hardy Inequalities in Magnetic Fields

Repositorio: BIRD: BCAM's Institutional Repository Data
Fanelli, L., Vega, L., Visciglia, N.

We deal with Dirac operators with external homogeneous magnetic fields. Hardy-type inequalities related to these operators are investigated: for a suitable class of transversal magnetic fields, we prove a Hardy inequality with the same best constant as in the free case. This leaves naturally open an interesting question whether there exist magnetic fields for which a Hardy inequality with a better constant than the usual one, in connection with the well known diamagnetic phenomenon arising in…



The Vortex Filament Equation as a Pseudorandom Generator

Repositorio: BIRD: BCAM's Institutional Repository Data
De la Hoz, F., Vega, L.

In this paper, we consider the evolution of the so-called vortex filament equation (VFE), $$ X_t = X_s \wedge X_{ss},$$ taking a planar regular polygon of M sides as initial datum. We study VFE from a completely novel point of view: that of an evolution equation which yields a very good generator of pseudorandom numbers in a completely natural way. This essential randomness of VFE is in agreement with the randomness of the physical phenomena upon which it is based.



The dynamics of vortex filaments with corners

Repositorio: BIRD: BCAM's Institutional Repository Data
Vega, L.

This paper focuses on surveying some recent results obtained by the author together with V. Banica on the evolution of a vortex filament with one corner according to the so-called binormal flow. The case of a regular polygon studied in collaboration with F. de la Hoz is also considered.



The initial value problem for the binormal flow with rough data

Repositorio: BIRD: BCAM's Institutional Repository Data
Banica, V., Vega, L.

In this article we consider the initial value problem of the binormal flow with initial data given by curves that are regular except at one point where they have a corner. We prove that under suitable conditions on the initial data a unique regular solution exists for strictly positive and strictly negative times. Moreover, this solution satisfies a weak version of the equation for all times and can be seen as a perturbation of a suitably chosen self-similar solution. Conversely, we also prove…



Shell interactions for Dirac operators: On the point spectrum and the confinement

Repositorio: BIRD: BCAM's Institutional Repository Data
Arrizabalaga, N., Mas, A., Vega, L.

Spectral properties and the confinement phenomenon for the coupling $H + V$ are studied, where $H =-i\alpha \cdot \nabla + m\beta$ is the free Dirac operator in $\mathbb{R}^3$ and $V$ is a measure-valued potential. The potentials V under consideration are given in terms of surface measures on the boundary of bounded regular domains in $\mathbb{R}^3$. A criterion for the existence of point spectrum is given, with applications to electrostatic shell potentials. In the case of the sphere, an…



An Isoperimetric-Type Inequality for Electrostatic Shell Interactions for Dirac Operators

Repositorio: BIRD: BCAM's Institutional Repository Data
Arrizabalaga, N., Mas, A., Vega, L.

In this article we investigate spectral properties of the coupling $H + V_{\lambda}$, where $H =-i\alpha \cdot \nabla + m\beta$ is the free Dirac operator in $\mathbb{R}^3$, $m>0$ and $V_{\lambda}$ is an electrostatic shell potential (which depends on a parameter $\lambda \in \mathbb{R}$) located on the boundary of a smooth domain in $\mathbb{R}^3$. Our main result is an isoperimetric-type inequality for the admissible range of $\lambda$'s for which the coupling $H + V_{\lambda}$…



Spectral asymptotics of the Dirichlet Laplacian in a conical layer

Repositorio: BIRD: BCAM's Institutional Repository Data
Dauge, M., Ourmières-Bonafos, T., Raymond, N.

The spectrum of the Dirichlet Laplacian on conical layers is analysed through two aspects: the infiniteness of the discrete eigenvalues and their expansions in the small aperture limit. On the one hand, we prove that, for any aperture, the eigenvalues accumulate below the threshold of the essential spectrum: For a small distance from the essential spectrum, the number of eigenvalues farther from the threshold than this distance behaves like the logarithm of the distance. On the other hand, in…



Mean-field dynamics of the spin-magnetization coupling in ferromagnetic materials: Application to current-driven domain wall motions

Repositorio: BIRD: BCAM's Institutional Repository Data
Chen, J., García-Cervera, C.J., Yang, X.

In this paper, we present a mean-field model of the spin-magnetization coupling in ferromagnetic materials. The model includes non-isotropic diffusion for spin dynamics, which is crucial in capturing strong spin-magnetization coupling. The derivation is based on a moment closure of the quantum spinor dynamics coupled to magnetization dynamics via the Landau-Lifchitz-Gilbert equation and the spin-transfer torque. The method is general and systematic, and can be used to study spin-orbit coupling…



Time-resolved adaptive FEM simulation of the DLR-F11 aircraft model at high Reynolds number

Repositorio: BIRD: BCAM's Institutional Repository Data
Hoffman, J., Jansson, J., Jansson, N., de Abreu, R.V.

We present a time-resolved, adaptive finite element method for aerodynamics, together with the results from the HiLiftPW-2 workshop, where this method is used to compute the ow past a DLR-F11 aircraft model at realistic Reynolds number. The mesh is automatically constructed by the method as part of the computation, and no explicit turbulence model is used. The effect of unresolved turbulent boundary layers is modeled by a simple parametrization of the wall shear stress in terms of the skin…



LBM-HPC - An open-source tool for fluid simulations. Case study: Unified parallel C (UPC-PGAS)

Repositorio: BIRD: BCAM's Institutional Repository Data
Valero-Lara, P., Jansson, J.

The main motivation of this work is the evaluation of the Unified Parallel C (UPC) model, for Boltzmann-fluid simulations. UPC is one of the current models in the so-called Partitioned Global Address Space paradigm. This paradigm attempts to increase the simplicity of codes and achieve a better efficiency and scalability. Two different UPC-based implementations, explicit and implicit, are presented and evaluated. We compare the fundamental features of our UPC implementations with other parallel…



A Non-uniform Staggered Cartesian Grid approach for Lattice-Boltzmann method

Repositorio: BIRD: BCAM's Institutional Repository Data
Valero-Lara, P., Jansson, J.

We propose a numerical approach based on the Lattice-Boltzmann method (LBM) for dealing with mesh refinement of Non-uniform Staggered Cartesian Grid. We explain, in detail, the strategy for mapping LBM over such geometries. The main benefit of this approach, compared to others, consists of solving all fluid units only once per time-step, and also reducing considerably the complexity of the communication and memory management between different refined levels. Also, it exhibits a better matching…



Towards a parameter-free method for high Reynolds number turbulent flow simulation based on adaptive finite element approximation

Repositorio: BIRD: BCAM's Institutional Repository Data
Hoffman, J., Jansson, J., Jansson, N., de Abreu, R.V.

This article is a review of our work towards a parameter-free method for simulation of turbulent flow at high Reynolds numbers. In a series of papers we have developed a model for turbulent flow in the form of weak solutions of the Navier-Stokes equations, approximated by an adaptive finite element method, where: (i) viscous dissipation is assumed to be dominated by turbulent dissipation proportional to the residual of the equations, and (ii) skin friction at solid walls is assumed to be…



Accelerating fluid-solid simulations (Lattice-Boltzmann & Immersed-Boundary) on heterogeneous architectures

Repositorio: BIRD: BCAM's Institutional Repository Data
Valero-Lara, P., Igual, F.D., Prieto-Matias, M., Pinelli, A., Favier, J.

We propose a numerical approach based on the Lattice-Boltzmann (LBM) and Immersed Boundary (IB) methods to tackle the problem of the interaction of solids with an incompressible fluid flow, and its implementation on heterogeneous platforms based on data-parallel accelerators such as NVIDIA GPUs and the Intel Xeon Phi. We explain in detail the parallelization of these methods and describe a number of optimizations, mainly focusing on improving memory management and reducing the cost of host-…



Adaptive simulation of unsteady flow past the submerged part of a floating wind turbine platform

Repositorio: BIRD: BCAM's Institutional Repository Data
Jansson, J., Nava, V., Sanchez, M., Aguirre, G., de Abreu, R.V., Hoffman, J., Villate, J.L.

Offshore floating platforms for wind turbines represent challenging concepts for designers trying to combine an optimal compromise between cost effectiveness and performance. Modelling of the hydrodynamic behaviour of the structure is still the subject of wide debate in the technical communities. The assessment of the hydrodynamics of the support structure is not an easy task as the floaters consist of an assembly of columns, braces and pontoons, commonly also with heave plates: Each of these…



Multi-domain grid refinement for lattice-Boltzmann simulations on heterogeneous platforms

Repositorio: BIRD: BCAM's Institutional Repository Data
Valero-Lara, P., Jansson, J.

The main contribution of the present work consists of several parallel approaches for grid refinement based on a multi-domain decomposition for lattice-Boltzmann simulations. The proposed method for discretizing the fluid incorporates different regular Cartesian grids with no homogeneous spatial domains, which are in need to be communicated each other. Three different parallel approaches are proposed, homogeneous Multicore, homogeneous GPU, and heterogeneous Multicore-GPU. Although, the…



FEniCS-HPC: Automated predictive high-performance finite element computing with applications in aerodynamics

Repositorio: BIRD: BCAM's Institutional Repository Data
Hoffman, J., Jansson, J., Jansson, N.

Developing multiphysics finite element methods (FEM) and scalable HPC implementations can be very challenging in terms of software complexity and performance, even more so with the addition of goal-oriented adaptive mesh refinement. To manage the complexity we in this work present general adaptive stabilized methods with automated implementation in the FEniCS-HPC automated open source software framework. This allows taking the weak form of a partial differential equation (PDE) as input in near-…



Many-task computing on many-core architectures

Repositorio: BIRD: BCAM's Institutional Repository Data
Valero-Lara, P., Nookala, P., Pelayo, F.L., Jansson, J., Dimitropoulos, S., Raicu, I.

Many-Task Computing (MTC) is a common scenario for multiple parallel systems, such as cluster, grids, cloud and supercomputers, but it is not so popular in shared memory parallel processors. In this sense and given the spectacular growth in performance and in number of cores integrated in many-core architectures, the study of MTC on such architectures is becoming more and more relevant. In this paper, authors present what are those programming mechanisms to take advantages of such massively…



Aerodynamic study of a tricycle wheel subsystem for drag reduction

Repositorio: BIRD: BCAM's Institutional Repository Data
Driant, T., Remaki, L., Fellouah, H., Moreau, S., Desrochers, A.

This paper deals with a computational fluid dynamics (CFD) and experimental drag analysis on an isolated rotating wheel subsystem (including its accessories: tire, suspension, A-arms, and fender) of a motor tricycle vehicle with two wheels in front. The main goal of the present work is to study the effect of the fender on the wheel subsystem drag and its optimization. The Star CCM+ commercial code was used for the numerical simulations. Different flow conditions were simulated and some results…



Discontinuous high-order finite-volume/finite-element method for inviscid compressible flows

Repositorio: BIRD: BCAM's Institutional Repository Data
Ramezani, A., Stipcich, G., Remaki, L.

The discontinuous, hybrid control-volume/finite-element method merges the desirable conservative properties and intuitive physical formulation of the finite-volume technique, with the capability of local arbitrary high-order accuracy distinctive of the discontinuous finite-element method. This relatively novel scheme has been previously applied to the solution of advection-diffusion problems and the shallow-water equations, and is in the present work extended to the Euler equations. The…



Efficient Rotating Frame Simulation in Turbomachinery

Repositorio: BIRD: BCAM's Institutional Repository Data
Remaki, L., Ramezani, A., Blanco, J.M., Antolin, J.I.

This paper deals with the simulation of steady flows in tur- bomachinery. Two approaches are proposed, the first one is the classical multiple-rotating frame method (MRF) by multi- zone approach where the different zones are separated by non- overlapping interfaces and solved independently. Since each zone is loaded separately, a transferring system should be prop- erly implemented at the interface boundaries. Two techniques are considered, in the first one the conservative variables are in-…



Spray Drag Effect of Fluidized Sand for a Supersonic Vehicle

Repositorio: BIRD: BCAM's Institutional Repository Data
Remaki, L., Hassan, O., Evans, B.J., Morgan, K.

This paper deals with fluidized sand simulation in order to estimate the impact of sand particle motion on the BLOODHOUND SuperSonic Car (SSC) drag forces, such phenomenon is known as a spray drag effect. A gas-particle model is used to simulate the sand particles that rise from the ground because of the strong shockwave-desert surface interaction. A finite volume scheme is used to discretise the continuous model with a special treatment of the solid phase equations. An indefinitely…



BBIPED: BCAM-Baltogar Industrial Platform for Engineering Design

Repositorio: BIRD: BCAM's Institutional Repository Data
Alonso-Montes, C., Garcia, I., Ramezani, A., Remaki, L.

Currently, commercial software for computational fluid dynamics offers a good set of features to deal with traditional designs. Within a competitive market industrial innovation is a key factor that must be faced by companies. However, the design of solutions to deal with industrial challenges cannot be done within commercial software due to the lack of flexibility. Open source initiatives are a good option but the learning curve is high, specially for industrial engineers profiles. In this…



Identification of defects originated during the filling of cast pieces through particles modelling

Repositorio: BIRD: BCAM's Institutional Repository Data
Blanco, J.M., Carranza, P., Pintos, R., Arriaga, P., Remaki, L.

In casting processes, strong recirculation zones may trap air, gases and strip particles of sand off the mold affecting seriously the quality of the cast pieces. Especially during the filling of molten pieces with large surfaces, several faults were detected which are responsible of considerable economic losses in such casting processes. The aim of this work is focused on the correct identification of these physical phenomena, through Computational Fluid Dynamics (CFD). A fully experimental…



High order discontinuous finite-volume/finite-element method for CFD applications

Repositorio: BIRD: BCAM's Institutional Repository Data
Ramezani, A., Stipcich, G.

The proposed method naturally merges the desirable conservative properties and intuitive physical formulation of the widely used finite-volume (FV) technique, with the capability of local arbitrary high-order accuracy and high-resolution which is distinctive in the discontinuous finite-element (FE) framework. This relatively novel scheme, the discontinuous hybrid control-volume/finite-element method (DCVFEM), has been already applied to the solution of advection-diffusion problems and shallow-…



Unstructured, curved elements for the two-dimensional high order discontinuous control-volume/finite-element method

Repositorio: BIRD: BCAM's Institutional Repository Data
Stipcich, G., Piller, M.

Quadrilateral and triangular elements with curved edges are developed in the framework of spectral, discontinuous, hybrid control-volume/finite-element method for elliptic problems. In order to accommodate hybrid meshes, encompassing both triangular and quadrilateral elements, one single mapping is used. The scheme is applied to two-dimensional problems with discontinuous, anisotropic diffusion coefficients, and the exponential convergence of the method is verified in the presence of curved…



Lagged and instantaneous dynamical influences related to brain structural connectivity

Repositorio: BIRD: BCAM's Institutional Repository Data
Alonso, C., Diez, I., Remaki, L., Escudero, I., Mateos, B., Rosseel, Y., Marinazzo, D., Stramaglia, S., Cortes, J.M.

Contemporary neuroimaging methods can shed light on the basis of human neural and cognitive specializations, with important implications for neuroscience and medicine. Indeed, different MRI acquisitions provide different brain networks at the macroscale; whilst diffusion-weighted MRI (dMRI) provides a structural connectivity (SC) coincident with the bundles of parallel fibers between brain areas, functional MRI (fMRI) accounts for the variations in the blood-oxygenation-level-dependent T2*…



Numerical investigation of the aerodynamic performance for a wells-type turbine in a wave energy converter

Repositorio: BIRD: BCAM's Institutional Repository Data
Stipcich, G., Ramezani, A., Nava, V., Touzon, I., Sanchez-Lara, M., Remaki, L.

Ocean waves constitute an extensive energy resource, whose extraction has been the subject of intense research activity in the last three decades. Among the different variants of Wave Energy Converters, the principle of the Oscillating Water Column (OWC) is one of the most promising ones. An OWC comprises two key elements: A collector chamber, which transfers the wave oscillations' energy to the air within the chamber by back and forth displacement, and a power take off system, which…



Low cost a posteriori error estimators for an augmented mixed FEM in linear elasticity. Dedicated to Professor Rodolfo Rodríguez on the occasion of his 60th birthday.

Repositorio: BIRD: BCAM's Institutional Repository Data
Barrios, T.P., Behrens, E.M., Gonzalez, M.

We consider an augmented mixed finite element method applied to the linear elasticity problem and derive a posteriori error estimators that are simpler and easier to implement than the ones available in the literature. In the case of homogeneous Dirichlet boundary conditions, the new a posteriori error estimator is reliable and locally efficient, whereas for non-homogeneous Dirichlet boundary conditions, we derive an a posteriori error estimator that is reliable and satisfies a quasi-efficiency…



Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers

Repositorio: BIRD: BCAM's Institutional Repository Data
Wozniak, M., Kuznik, K., Paszynski, M., Calo, V.M., Pardo, D.

In this paper we present computational cost estimates for parallel shared memory isogeometric multi-frontal solvers. The estimates show that the ideal isogeometric shared memory parallel direct solver scales as $\mathcal{O}( p^2log(N/p))$ for one dimensional problems, $\mathcal{O}(Np^2)$ for two dimensional problems, and $\mathcal{O}(N^{4/3}p^2)$ for three dimensional problems, where $N$ is the number of degrees of freedom, and p is the polynomial order of approximation. The computational costs…



Fast simulation of through-casing resistivity measurements using semi-analytical asymptotic models. Part 1: Accuracy study

Repositorio: BIRD: BCAM's Institutional Repository Data
Erdozain, A., Peron, V., Pardo, D.

When trying to obtain a better characterization of the Earth's subsurface, it is common to use borehole through-casing resistivity measurements. It is also common for the wells to be surrounded by a metal casing to protect the well and avoid possible collapses. The presence of this metal case highly complicates the numeric simulation of the problem due to the high conductivity of the casing compared to the conductivity of the rock formations. Here we present an application of some…



Unified modeling language description of the object-oriented multi-scale adaptive finite element method for step-and-flash imprint lithography simulations

Repositorio: BIRD: BCAM's Institutional Repository Data
Paszynski, M., Gurgul, P., Sieniek, M., Pardo, D.

In the first part of the paper we present the multi-scale simulation of the Step-and-Flash Imprint Lithography (SFIL), a modern patterning process. The simulation utilizes the hp adaptive Finite Element Method (hp-FEM) coupled with Molecular Statics (MS) model. Thus, we consider the multi-scale problem, with molecular statics applied in the areas of the mesh where the highest accuracy is required, and the continuous linear elasticity with thermal expansion coefficient applied in the remaining…



Quantities of interest for surface based resistivity geophysical measurements

Repositorio: BIRD: BCAM's Institutional Repository Data
Alvarez-Aramberri, J., Bakr, S.A., Pardo, D., Barucq, H.

The objective of traditional goal-oriented strategies is to construct an optimal mesh that minimizes the problem size needed to achieve a user prescribed tolerance error for a given quantity of interest (QoI). Typical geophysical resistivity measurement acquisition systems can easily record electromagnetic (EM) fields. However, depending upon the application, EM fields are sometimes loosely related to the quantity that is to be inverted (conductivity or resistivity), and therefore they become…



A posteriori error analysis of a stabilized mixed FEM for convectuion-diffusion problems

Repositorio: BIRD: BCAM's Institutional Repository Data
Gonzalez, M., Jansson, J., Korotov, S.

We present an augmented dual-mixed variational formulation for a linear convection-diffusion equation with homogeneous Dirichlet boundary conditions. The approach is based on the addition of suitable least squares type terms. We prove that for appropriate values of the stabilization parameters, that depend on the diffusion coefficient and the magnitude of the convective velocity, the new variational formulation and the corresponding Galerkin scheme are well-posed, and a Céa estimate holds. In…



One-dimensional chaos in a system with dry friction: analytical approach

Repositorio: BIRD: BCAM's Institutional Repository Data
Begun, N., Kryzhevich, S.

We introduce a new analytical method, which allows to find chaotic regimes in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered. The corresponding mathematical model is being studied. We show that the considered dynamical system is a skew product over a piecewise smooth mapping of a segment (the so-called base map). For this base map we demonstrate existence of a domain of parameters where a chaotic dynamics can be observed.…



Fourier finite element modeling of light emission in waveguides: 2.5-dimensional FEM approach

Repositorio: BIRD: BCAM's Institutional Repository Data
Ou, Y., Pardo, D., Chen, Y.

We present a Fourier finite element modeling of light emission of dipolar emitters coupled to infinitely long waveguides. Due to the translational symmetry, the three-dimensional (3D) coupled waveguide-emitter system can be decomposed into a series of independent 2D problems (2.5D), which reduces the computational cost. Moreover, the reduced 2D problems can be extremely accurate, compared to its 3D counterpart. Our method can precisely quantify the total emission rates, as well as the fraction…



An Agent-Oriented Hierarchic Strategy for Solving Inverse Problems

Repositorio: BIRD: BCAM's Institutional Repository Data
Smolka, M., Schaefer, R., Paszynski, M., Pardo, D., Alvarez-Aramberri, J.

The paper discusses the complex, agent-oriented hierarchic memetic strategy (HMS) dedicated to solving inverse parametric problems. The strategy goes beyond the idea of two-phase global optimization algorithms. The global search performed by a tree of dependent demes is dynamically alternated with local, steepest descent searches. The strategy offers exceptionally low computational costs, mainly because the direct solver accuracy (performed by the hp-adaptive finite element method) is…



Goal-oriented adaptivity using unconventional error representations for the 1D Helmholtz equation

Repositorio: BIRD: BCAM's Institutional Repository Data
Darrigrand, V., Pardo, D., Muga, I.

In this work, the error of a given output functional is represented using bilinear forms that are different from those given by the adjoint problem. These representations can be employed to design novel h, p, and hp energy-norm and goal-oriented adaptive algorithms. Numerical results in 1D show that, for wave propagation problems, the advantages of this new representation are notorious when selecting the Laplace equation as the dual problem. Specifically, the computed upper bounds of the new…



A posteriori error analysis of an augmented mixed finite element method for Darcy flow

Repositorio: BIRD: BCAM's Institutional Repository Data
Barrios, T.P., Cascón, J.M., Gonzalez, M.

We develop an a posteriori error analysis of residual type of a stabilized mixed finite element method for Darcy flow. The stabilized formulation is obtained by adding to the standard dual-mixed approach suitable residual type terms arising from Darcy's law and the mass conservation equation. We derive sufficient conditions on the stabilization parameters that guarantee that the augmented variational formulation and the corresponding Galerkin scheme are well-posed. Then, we obtain a simple…



Hypersingular integral equations over a disc: Convergence of a spectral method and connection with Tranter's method

Repositorio: BIRD: BCAM's Institutional Repository Data
Farina, L., Martin, P.A., Peron, V.

Two-dimensional hypersingular equations over a disc are considered. A spectral method is developed, using Fourier series in the azimuthal direction and orthogonal polynomials in the radial direction. The method is proved to be convergent. Then, Tranter's method is discussed. This method was devised in the 1950s to solve certain pairs of dual integral equations. It is shown that this method is also convergent because it leads to the same algebraic system as the spectral method.



Automatic Red-Channel underwater image restoration

Repositorio: BIRD: BCAM's Institutional Repository Data
Galdran, A., Pardo, D., Picón, A., Alvarez-Gila, A.

Underwater images typically exhibit color distortion and low contrast as a result of the exponential decay that light suffers as it travels. Moreover, colors associated to different wavelengths have different attenuation rates, being the red wavelength the one that attenuates the fastest. To restore underwater images, we propose a Red Channel method, where colors associated to short wavelengths are recovered, as expected for underwater images, leading to a recovery of the lost contrast. The Red…



Some discrete maximum principles arising for nonlinear elliptic finite element problems

Repositorio: BIRD: BCAM's Institutional Repository Data
Karátson, J., Korotov, S.

The discrete maximum principle (DMP) is an important measure of the qualitative reliability of the applied numerical scheme for elliptic problems. This paper starts with formulating simple sufficient conditions for the matrix case and for nonlinear forms in Banach spaces. Then a DMP is derived for finite element solutions for certain nonlinear partial differential equations: we address nonlinear elliptic problems with mixed boundary conditions and interface conditions, allowing possibly…



On the maximum angle condition for the conforming longest-edge n-section algorithm for large values of n

Repositorio: BIRD: BCAM's Institutional Repository Data
Korotov, S., Plaza A, Suárez, J.P.

In this note we introduce the conforming longest-edge $n$-section algorithm and show that for $n \ge 4$ it produces a family of triangulations which does not satisfy the maximum angle condition.



Parameterization of Invariant Manifolds for Periodic Orbits I: Efficient Numerics via the Floquet Normal Form

Repositorio: BIRD: BCAM's Institutional Repository Data
Castelli, R., Lessard, J.-P., James, J.D.M.

We present an efficient numerical method for computing Fourier-Taylor expansions of (un)stable manifolds associated with hyperbolic periodic orbits. Three features of the method are that (1) we obtain accurate representation of the invariant manifold as well as the dynamics on the manifold, (2) it admits natural a posteriori error analysis, and (3) it does not require numerically integrating the vector field. Our approach is based on the parameterization method for invariant manifolds, and…



Rigorous numerics for NLS: Bound states, spectra, and controllability

Repositorio: BIRD: BCAM's Institutional Repository Data
Castelli, R., Teismann, H.

In this paper it is demonstrated how rigorous numerics may be applied to the one-dimensional nonlinear Schrödinger equation (NLS); specifically, to determining bound-state solutions and establishing certain spectral properties of the linearization. Since the results are rigorous, they can be used to complete a recent analytical proof (Beauchard et al., 2015) of the local exact controllability of NLS.



A Secondary Field Based hp-Finite Element Method for the Simulation of Magnetotelluric Measurements

Repositorio: BIRD: BCAM's Institutional Repository Data
Alvarez-Aramberri, J., Pardo, D., Barucq, E.

In some geophysical problems, it is sometimes possible to divide the subsurface resistivity distribution as a one dimensional (1D) contribution plus some two dimensional (2D) inhomogeneities. Assuming this scenario, we split the electromagnetic fields into their primary and secondary components, the former corresponding to the 1D contribution, and the latter to the 2D inhomogeneities. While the primary field is solved via an analytical solution, for the secondary field we employ a multi-goal…



Enhanced variational image dehazing

Repositorio: BIRD: BCAM's Institutional Repository Data
Galdran, A., Vazquez-Corral, J., Pardo, D., Bertalmio, M.

Images obtained under adverse weather conditions, such as haze or fog, typically exhibit low contrast and faded colors, which may severely limit the visibility within the scene. Unveiling the image structure under the haze layer and recovering vivid colors out of a single image remains a challenging task, since the degradation is depth-dependent and conventional methods are unable to overcome this problem. In this work, we extend a well-known perception-inspired variational framework for single…