ENG 
ESP Session S20 - Applied Math and Computational Methods and Analysis across the Americas
Talks
Friday, July 16, 12:00 ~ 12:30 UTC-3
On the implementation of mimetic anisotropic filtering with convolutional neural networks for glaucoma suspect detection
Lola Bautista
Universidad Industrial de Santander, Colombia - This email address is being protected from spambots. You need JavaScript enabled to view it.
Anisotropic filtering has been widely studied for edge detection in digital image processing. Special attention has been given to the Perona-Malik model in multiscale image analysis for image restoration. In a recent work [1] it was developed an implementation of such filtering through mimetic methods which discretise the gradient and divergence operators of the diffusion coefficient in the Perona-Malik model, which showed better effectiveness of glaucoma suspects detection when the filter was applied to the input images. In the recent years, convolutional neural networks (CNN) had become an important tool in image processing because their capabilities to learn the internal representation of images. In this work we present the comparison of two pre-trained CNNs using the GoogleNet architecture with a training set of 1084 images each, collected by the Centro de Prevención y Consultoría en Glaucoma, in order to estimate the influence of the mimetic anisotropic filtering before training. The first CNN was trained without the filter, and the second one was trained with the images after applying the mimetic anisotropic filter, reaching an accuracy of 90.68\%. It remains open the problem of calibrating the parameters of the filter, as well as the stopping criterion to avoid degradation of the image.
References [1] Jorge Villamizar et al. “Mimetic Finite Dierence Methods for Restoration of Fundus Images for Automatic Detection of Glaucoma Suspects.” In: Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization (2021). doi:10.1080/21681163.2021.1914733.
Joint work with Jorge Villamizar (Universidad Industrial de Santander, Colombia; Universidad de Los Andes, Venezuela, Biomedical Imaging, Vision and Learning Laboratory, Colombia), Juan Carrillo (Biomedical Imaging, Vision and Learning Laboratory, Colombia) and Juan Rueda (Centro de Prevención y Consultoría en Glaucoma, Colombia).
Friday, July 16, 12:30 ~ 13:00 UTC-3
A priori error estimates for a linear coupled elliptic problem using a mixed Hybrid High Order method
Rommel Bustinza
Universidad de Concepcion, Chile - This email address is being protected from spambots. You need JavaScript enabled to view it.
We analyze a linear coupled elliptic problem in a bounded domain, applying a mixed formulation of the Hybrid High Order (HHO) method. This approach gives approximation of the unknowns in the interior volume of each element and on the faces of its boundary, in the sense that the approximations of the exact solution are sought in the space of polynomials of total degree $k\,\geq\,0$ on the mesh elements and faces. Thus, we obtain a non-conforming discrete formulation, which is well posed, and after a condensation process, we can reduce it to another scheme defined on the skeleton induced by the mesh. This allows us to obtain a more compact system and reduce significantly the number of unknowns. We point out that we need to introduce an auxiliary unknown (Lagrange multiplier) in order to deal with the non homogeneous transmission / coupling conditions. We prove that the method is convergent in the energy norm, as well as in the $L^2-$norm for the potential, and a weighted $L^2-$norm for the Lagrange multiplier, for smooth enough exact solutions. Moreover, we can establish a kind of a super convergence result of an approximation of the potential, obtained by a post process. Finally, we include some numerical experiments that validate our theoretical results, even in situations not fully covered by the current analysis
Joint work with Jonathan Munguia (Universidad Nacional de Ingeniería, Perú).
Friday, July 16, 13:00 ~ 13:30 UTC-3
Multifrequency inverse obstacle scattering with unknown impedance boundary conditions
Carlos Borges
Department of Mathematics at the University of Central Florida, USA - This email address is being protected from spambots. You need JavaScript enabled to view it.
We consider the reconstruction of the shape and the impedance function of an obstacle from measurements of the scattered field at receivers outside the object. This inverse problem is reformulated as the optimization problem of finding band-limited shape and impedance functions which minimize the L2 distance between the computed value of the scattered field at the receivers and the data. The optimization problem is non-linear, non-convex, and ill-posed. Moreover, the objective function is computationally expensive to evaluate. The recursive linearization approach (RLA) proposed by Chen has been successful in addressing these issues in the context of recovering the sound speed of a domain or the shape of a sound-soft obstacle. We present an extension of the RLA for the recovery of both the shape and impedance functions. The RLA is a continuation method in frequency where a sequence of single frequency inverse problems is solved. At each higher frequency, one attempts to recover incrementally higher resolution features using a step assumed to be small enough to ensure that the initial guess obtained at the preceding frequency lies in the basin of attraction for Newton's method at the new frequency. We demonstrate the effectiveness of the method with several numerical examples. Surprisingly, we find that one can recover the shape with high accuracy even when the measurements are from sound-hard or sound-soft objects. While the method is effective in obtaining high quality reconstructions for complicated geometries and impedance functions, a number of interesting open questions remain. We present numerical experiments that suggest underlying mechanisms of success and failure, showing areas where improvements could help lead to robust and automatic tools.
Joint work with Manas Rachh (Center for Computational Mathematics, Flatiron Institute, New York, USA).
Friday, July 16, 13:30 ~ 14:00 UTC-3
Coarse virtual spaces for domain decomposition methods
Juan Gabriel Calvo
Universidad de Costa Rica, Costa Rica - This email address is being protected from spambots. You need JavaScript enabled to view it.
The construction of coarse spaces for irregular decompositions, as the ones obtained from mesh partitioners, usually involve functions that are discrete harmonic in the interior of the subdomains. In this talk we will discuss a variant used in the definition of coarse spaces for such irregular decompositions based on the virtual element method, that does not require discrete harmonic extensions and saves computational time. Theoretical results and numerical experiments that verify the results will be discussed.
Friday, July 16, 14:00 ~ 14:30 UTC-3
Application of Scientific computing techniques for studying chemical process simulation
Dany De Cecchis
Escuela Superior Politécnica del Litoral, Facultad de Ciencia Naturales y Matemáticas, Guayaquil, Ecuador - This email address is being protected from spambots. You need JavaScript enabled to view it.
The advent of Industry 4.0, the intelligent networking of machines and processes in the industry with the aid of information and communication technology, has incorporated more sophisticated tools for simulating and using scientific computing tools to obtain insights about the industrial process. In this talk, we introduce a framework to apply computational mathematics tools available in the Python ecosystem to chemical process simulations using high-resolution steady-state modular chemical process modelers, like PRO/II$^{\text{TM}}$. We start with the mechanism we use for connecting both software architectures, highlighting the benefits of taking advantage of an open-source and flexible platform as the modules developed in the Python ecosystem, together with a robust chemical process simulation as PRO/II$^{\text{TM}}$. The possibility of using different numerical and computational resources adds value for more complete and sophisticated simulations, supporting the decision-making process about operational windows. We outline some case studies of ongoing research.
Joint work with Santiago D. Salas (Escuela Superior Politécnica del Litoral, Ecuador), José A. Romagnoli (Louisiana State University, USA) and Daniela Galatro (University of Toronto, Canada).
Friday, July 16, 14:30 ~ 15:00 UTC-3
Additive Schwarz Preconditioners for a Localized Orthogonal Decomposition Method
José Garay
Louisiana State University, USA - This email address is being protected from spambots. You need JavaScript enabled to view it.
The solution of multiscale elliptic PDEs with non-separable scales and high contrast in the coefficients by standard Finite Element Methods (FEM) is typically prohibitively expensive since it requires the resolution of all characteristic lengths to produce an accurate solution. Numerical homogenization methods such as Localized Orthogonal Decomposition (LOD) methods provide access to feasible and reliable simulations of such multiscale problems. These methods are based on the idea of a generalized finite element space where the generalized basis functions are obtained by modifying standard coarse FEM basis functions to incorporate relevant microscopic information in a computationally feasible procedure. Using this enhanced basis one can solve a much smaller problem to produce an approximate solution whose accuracy is comparable to the solution obtained by the expensive standard FEM. We present a variant of LOD that uses domain decomposition techniques to compute the basis corrections and we also provide a two-level preconditioner for the resulting linear system.
Joint work with Susanne C. Brenner (Louisiana State University, United States) and Li-yeng Sung (Louisiana State University, United States).
Friday, July 16, 15:00 ~ 15:30 UTC-3
Modelling spatio-temporal data of dengue fever using generalized additive mixed models
Maritza Cabrera
CIEAM, Vicerrectoria de Investigación y Postgrado, Universidad Catolica del Maule, Chile - This email address is being protected from spambots. You need JavaScript enabled to view it.
Epidemiological studies have revealed a complex association between weather and dengue transmission. Our aim is the development of a Spatio-temporal modelling of dengue fever via a Generalized Additive mixed model (GAMM). The structure is based on unknown smoother functions for climatic and a set of non-climatic covariates. All the climatic covariates were found statistically significant with optimal lagged effect and the smoothed curves fairly captured the real dynamic on dengue fever. It was also found that critical levels of dengue cases were reached with temperature between 26 °C and 30 °C. The findings also revealed for the first time that the El Niño phenomenon fluctuating between 26.5 °C and 28.0 °C had the worse impact on dengue transmission. This study brings together a large dataset from different sources including Ministry of Health from Venezuela. It was also benefited from a remote satellite climatic data provided by the National Aeronautics and Space Administration (NASA).
Joint work with G. Taylor (University of Exeter Medical School, UK).
Friday, July 16, 15:30 ~ 16:00 UTC-3
On high-order conservative finite element methods for heterogeneous problems
Juan Galvis
Universidad Nacional de Colombia, Colombia - This email address is being protected from spambots. You need JavaScript enabled to view it.
We describe and analyze a volumetric and residual-based Lagrange multipliers saddle point reformulation of the standard high-order finite method, to impose conservation of mass constraints for simulating the pressure equation on two dimensional convex polygons, with sufficiently smooth solution and mobility phase. We establish high-order a priori error estimates with locally conservative fluxes and numerical results are presented that confirm the theoretical results. For the numerical test we consider Qr finite element for homogeneous problems and GMsFEM discretization for heterogeneous problems. This talk is based on the papers:1) Computers & Mathematics with Applications Volume 75, Issue 6, 15 2018, Pages 1852-1867, 2) Multiscale Model. Simul., 18(4), 1375–1408. 2020.
Joint work with Marcus Sarkis(Department of Mathematical Sciences, Worcester Polytechnic Institute Worcester) and Eduardo Abreu (University of Campinas, Department of Applied Mathematics).
Friday, July 16, 16:00 ~ 16:30 UTC-3
Numerics and nonlinear wave analysis of geochemical injection for multicomponent two phase flow in porous media
Amaury Alvarez Cruz
Federal University of Rio de Janeiro, Brazil - This email address is being protected from spambots. You need JavaScript enabled to view it.
Since there exists no general theory for the existence and uniqueness of solutions to systems of conservation laws, finding a numerical approximation to this solution is still a current challenge. In this work we propose a method to find approximated solutions of such systems by combining semi-analytical and numerical algorithms. We study a particular system arising from the analysis of the transport of chemical species, which poses a classical problem in Geochemical transport in porous media. Our analysis focuses on solving a Riemann problem of a system of four conservation laws of chemical species. Bifurcation and inflection surfaces lead us to propose a "more likely" solution that must appear in the numerical solution. Due to the structure of flux and accumulation functions, an n-dimensional analysis of the existence of waves on the system is possible in this case. Finite element methods and finite difference schemes such as Backward-Euler and Crank-Nicolson are used for solving the system of conservation laws. Coefficients of the system are obtained from chemical data. The analysis of the existence of generalized solutions is studied.
Joint work with I. S. Ledoino(Laboratório Nacional de Computação Científica), D. Marchesin (IMPA) and J. Bruining (Delft Institute).
Friday, July 16, 16:30 ~ 17:00 UTC-3
Error estimates for the Scaled Boundary Finite Element Method applied to harmonic problems
Sônia Gomes
Universidade Estadual de Campinas (Unicamp), Brazil - This email address is being protected from spambots. You need JavaScript enabled to view it.
The Scaled Boundary Finite Element Method (SBFEM) is a technique in which approximation spaces are constructed using a semi-analytical approach. They are based on partitions of the computational domain by polygonal/polyhedral subregions, where the shape functions approximate local Dirichlet problems with piecewise polynomial trace data. Using this operator adaptation approach, and by imposing a starlike scaling requirement on the subregions, the representation of local SBFEM shape functions in radial and surface directions are obtained from eigenvalues and eigenfunctions of an ODE system, whose coefficients are determined by the element geometry and the trace polynomial spaces. For harmonic model problems, we characterize SBFEM spaces in the context of Duffy’s approximations for which a gradient-orthogonality constraint is imposed. As a consequence, the scaled boundary functions are gradient-orthogonal to any function in Duffy’s spaces vanishing at the mesh skeleton, a discrete mimetic version of a well-known property valid for harmonic functions. This orthogonality result is applied to provide a priori SBFEM error estimates in terms of known finite element interpolant errors of the exact solution. Similarities with virtual harmonic approximations are also explored for the understanding of SBFEM convergence properties. Numerical experiments with 2D and 3D polytopal meshes confirm optimal SBFEM convergence rates for test problems with smooth solutions. Attention is also paid to the approximation of a point singular solution by using SBFEM close to the singularity and finite element approximations elsewhere, revealing optimal accuracy rates of standard regular contexts
Joint work with Karolinne O. Coelho (FEC-Unicamp, Campinas, SP, Brazil) and Philippe R. B. Devloo (FEC-Unicamp, Campinas, SP, Brazil).
Friday, July 16, 17:00 ~ 17:30 UTC-3
Neural Network as a New Method for Data Assimilation
Haroldo Fraga de Campos Velho
Instituto de Pesquisas Espaciais, Brazil - This email address is being protected from spambots. You need JavaScript enabled to view it.
Data assimilation is an essential issue for all operational centers with focus on numerical weather prediction, hydrology, ocean circulation, environmental forecasting, space weather, and ionospheric dynamics. Several methods has been proposed for data assimilation based on Kalman filter, variational schemes, and particle filter. However, such strategies has very high computational effort. Our investigation is to apply a self-configuring supervised artificial neural network to address the data assimilation process, with significant reduction of the CPU-time. Results will be shown for different models: shallow water 2D for ocean circulation simulation, global spectral 3D meteorological models (SPEED, and COAPS-FSU), and a regional meteorological model (WRF-NCAR).
Friday, July 16, 17:30 ~ 18:00 UTC-3
Local $L^2$ bounded commuting projections in finite element exterior calculus
Johnny Guzman
Brown University, USA - This email address is being protected from spambots. You need JavaScript enabled to view it.
Bounded, commuting projections are a chief tool in the analysis of finite element exterior calculus (FEEC). Such projections were originally constructed by Schoberl and Christiansen and Winther, to name a few. However, they were not local. More recently, in 2015 Falk and Winther constructed local and bounded commuting projection. They are defined for differential forms that are in $L^2$ and such that their exterior derivative is in $L^2$. Inspired by their work we construct a local and bounded commuting projection that is defined for differential forms that are in $L^2$.
Joint work with Douglas Arnold (University of Minnesota, USA).
Friday, July 16, 18:00 ~ 18:30 UTC-3
AN AGE STRUCTURED MODEL FOR THE INFESTATION OF MOSQUITOES
Roxana López-Cruz
Universidad Nacional Mayor de San Marcos, Peru - This email address is being protected from spambots. You need JavaScript enabled to view it.
The strategy of introduce bacteria in the mosquitoes population is very important for the biological control of vector in host-vector diseases. The introduction of bacteria in mosquitoes is called bacterial infestation, many researchers propose mathematical predictions for biological control of different host-vector diseases.
The mathematical model is considered through the infestation of a bacterium that inhibits the transmission of the virus that characterizes the diseases by indirect transmission. We divide the population of mosquitoes in aquatic and adult age and with epidemiological subdivision of infested and not infested will be taken into account.
We derive a criteria in the case that the susceptible subpopulation eventually win the competition with the infected subpopulation (the most desirable result).obtain the following result on global stabilty. The model is more sensible to parameters of infestation and average life time of the adult mosquito.
Friday, July 16, 18:30 ~ 19:00 UTC-3
The MHM method for Linear Elasticity
Weslley da Silva Pereira
Laboratório Nacional de Computação Científica, Brazil - This email address is being protected from spambots. You need JavaScript enabled to view it.
The multiscale hybrid-mixed (MHM) method consists of a multi-level strategy to approximate the solution of boundary value problems with heterogeneous coefficients. One may find in the literature a couple of families of finite elements that can be used for the MHM methods in the context of linear elasticity. These finite elements rely on face degrees of freedom associated with a basis that is obtained from the solution of local Neumann elasticity problems. The local problems are independent of one another, and can therefore be solved in parallel trivially. Heterogeneities present in both the physical coefficients and source are considered at the finest-scale level, and the bases associated with the face degrees of freedom are responsible for bringing this information to the coarsest scale solution. In this talk, we present the MHM method for linear elasticity and some of its finite elements defined on coarse polytopal partitions. We show recent results on stability and convergence that mainly depend on local regularity assumptions. In particular, the multi-level error analysis demonstrates that the MHM method achieves convergence without changing the coarse partition. We show some numerical tests that assess theoretical results and verify the robustness of the method.
Joint work with Antônio Tadeu Gomes (Laboratório Nacional de Computação Científica, Brazil) and Frédéric Valentin (Laboratório Nacional de Computação Científica, Brazil).
Friday, July 16, 19:00 ~ 19:30 UTC-3
Effects of Charged Solute-Solvent Interaction on Reservoir Temperature during Subsurface CO2 and Produced Water Injection
Christopher Paolini
San Diego State University, USA - This email address is being protected from spambots. You need JavaScript enabled to view it.
A short-term side-effect of CO2 injection is a developing low-pH front that forms ahead of the bulk water injectant, due primarily to differences in solute diffusivity. Observations of bottom hole well temperature show a reduction in aqueous phase temperature with the arrival of a low pH front, followed by a gradual rise in temperature upon arrival of a high concentration of bicarbonate ion. We model aqueous-phase transient heat advection and diffusion with the volumetric energy generation rate computed from solute-solvent interaction using the Helgeson-Kirkham-Flowers (HKF) model, which is based on the Born Solvation model for computing specific molar heat capacity and enthalpy of charged electrolytes. A computed injectant water temperature profile is shown to agree with actual bottom-hole sampled temperature acquired from sensors. Accurate modeling of aqueous phase temperate during subsurface injection simulation is important for the accurate modeling of mineral dissolution and precipitation, as forward dissolution rates are governed by the temperature-dependent Arrhenius model.
Joint work with Jose Castillo, San Diego State University.
Friday, July 16, 19:30 ~ 20:00 UTC-3
Stabilizing radial basis functions techniques for a local boundary integral method
Luciano Ponzellini Marinelli
Universidad Nacional de Rosario, CIFASIS-CONICET-UNR, Argentina - This email address is being protected from spambots. You need JavaScript enabled to view it.
Radial basis functions (RBFs) have been gaining popularity recently in the development of methods for solving partial differential equations (PDEs) numerically. These functions have become an extremely effective tool for interpolation on scattered node sets in several dimensions.
One key issue with infinitely smooth RBFs is the choice of a suitable value for the shape parameter ($\varepsilon$) which controls the flatness of the function. It is observed that best accuracy is often achieved when $\varepsilon$ tends to zero. However, the system of discrete equations from interpolation matrices becomes ill-conditioned.
A few numerical algorithms have been presented that are able to stably compute an interpolant, even in the increasingly flat basis function limit like the RBF-QR method and the RBF-GA method.
We present these techniques in the context of boundary integral methods to improve the solution of PDEs with RBFs. These stable calculations open up new opportunities for applications and developments of local integral methods based on local RBF approximations.
Numerical results for small shape parameter that stabilize the error are presented. Accuracy and comparisons are also shown for elliptic PDEs.
Joint work with Nahuel Caruso (Universidad Nacional de Rosario, CIFASIS-CONICET-UNR, Argentina) and Margarita Portapila (Universidad Nacional de Rosario, CIFASIS-CONICET-UNR, Argentina).
Monday, July 19, 16:00 ~ 16:30 UTC-3
Forecast of some atmospheric variables using a monotonic convective scheme in the region of La Libertad-Perú
Obidio Rubio
Universidad Nacional de Trujillo, Perú - This email address is being protected from spambots. You need JavaScript enabled to view it.
We simulate the forecast of some atmospheric variables for the region of La Libertad-Peru, using the Brazilian Regional Atmospheric Modeling System BRAMS, taking into account that the topography of the region is varied, since its height above sea level varies from 3 msm to 4800 msnm, observes certain inestabilities in the simulation mainly when using a high resolution mesh, as in the case of 5km, due to this situation we try to improve stability by introducing a monotonic convective scheme of Walce, which has already been implemented in some variables such as the tracer scalars, by Freitas 2012(J. Adv. Model. Earth Syst., Vol. 3, M01001, 26 pp.) in some Brazilian tropical zones, obtaining better patterns and without generating spurious oscillations. Taking into account that they have not been tested in the case when the topography is varied as in the Peruvian case or in non-linear terms, in this case we use the method in the simulations of variables such as precipitation and aerosols, for this we use data from January and February 2021, as well as verifying that the scheme is high order and stable scheme.
Monday, July 19, 16:30 ~ 17:00 UTC-3
Fractional Gradient Flows
Abner Salgado
Department of Mathematics, University of Tennessee, Knoxville, USA - This email address is being protected from spambots. You need JavaScript enabled to view it.
We consider a so-called fractional gradient flow: an evolution equation aimed at the minimization of a convex and l.s.c. energy, but where the evolution has memory effects. This memory is characterized by the fact that the negative of the (sub)gradient of the energy equals the so-called Caputo derivative of the state. We introduce a notion of "energy solutions" for which we refine the proofs of existence, uniqueness, and certain regularizing effects provided in [Li and Liu, SINUM 2019]. This is done by generalizing, to non-uniform time steps the "deconvolution" schemes of [Li and Liu, SINUM 2019], and developing a sort of "fractional minimizing movements" scheme.We provide an a priori error estimate that seems optimal in light of the regularizing effects proved above. We also develop an a posteriori error estimate, in the spirit of [Nochetto, Savare, Verdi, CPAM 2000] and show its reliability
Joint work with Wenbo Li (Department of Mathematics, University of Tennessee, Knoxville).
Monday, July 19, 17:00 ~ 17:30 UTC-3
Improving cooperation using fractional punishment in a compulsory public good game
Christian Schaerer
Polytechnic School, National University of Asuncion, Paraguay - This email address is being protected from spambots. You need JavaScript enabled to view it.
The effect of incentives in the evolution of cooperation has been studied using evolutionary game theory as a fundamental issue for improving and maintaining cooperation. Unfortunately, incentives have a cost. In this talk, based on an optional public good game model, I will present an approach to sanction, denoted as partial punishment, where a randomly selected set of the free riders is punished. The approach seeks to reduce the number of free riders while minimizing the cost of the sanctioning system. A parameter is used to establish the portion of free riders to be sanctioned with the purpose to control the population state evolution in the game. Adjusting this sanctioning parameter, the phase portrait of the system can be modified, and when it surpasses a threshold, full cooperation is achieved, i.e., the full cooperator state becomes a global attractor. It will discuss how fractional punishment can be used to adjust criteria for sanctioning to improve the cooperation and reduce the sanctioning cost.
Joint work with Rocio Botta (Polytechnic School, National University of Asuncion, Paraguay) and Gerardo Blanco (Polytechnic School, National University of Asuncion, Paraguay).
Monday, July 19, 17:30 ~ 18:00 UTC-3
A posteriori error estimation for a Multiscale Hybrid Mixed method
Denise de Siqueira
Federal University of Technology – Curitiba, PR, Brazil - This email address is being protected from spambots. You need JavaScript enabled to view it.
We present a computable and efficient procedure for a posteriori error estimation for a Multiscale Hybrid Mixed method denoted by (MHM-H(div)). This is a finite element strategy for the simulation of problems with strongly varying solutions and designed to efficiently capture the solutions large-scale behavior, without considering all the small-scale features. We consider a Darcy model problem where flow normal fluxes and piecewise constant pressure approximations in each macro element are solved by a global system (upscaling). Then, small details are recovered by local Newmann problems using mixed finite elements with enriched approximation spaces (downscaling). The general methodology for the error estimation is based on potential and flux reconstruction. As the flux variable given by the method is already equilibrated only the pressure reconstruction is required. The a posteriori error estimation has two main steps: smoothing of the computed pressure variable and solving local Dirichlet problems with hybridization. The performance of the estimators is investigated through several numerical convergence tests.
Joint work with Gustavo Alcalá Batistela (University of Campinas, Brazil), Phillipe R. B. Devloo (University of Campinas, Brazil) and Sônia Maria Gomes (University of Campinas, Brazil).
Monday, July 19, 18:00 ~ 18:30 UTC-3
Mathematical Modeling of Maintenance Operations in Natural Gas Pipelines
Jean Piero Suarez Solano
Universidad del Norte, Colombia - This email address is being protected from spambots. You need JavaScript enabled to view it.
This talk will present a one-dimensional transient mathematical model to estimate the position and speed of a pipeline inspection gauge during maintenance operations in natural gas pipelines, the discretization of the mathematical model by the method of characteristics, and modeling results in a single pipe.
Monday, July 19, 18:30 ~ 19:00 UTC-3
NO-SAS - Nonoverlapping Spectral Additive Schwarz Methods
Marcus Sarkis
Worcester Polytechnic Institute, USA , USA - This email address is being protected from spambots. You need JavaScript enabled to view it.
We design and analyze new preconditioners which combine features from both overlapping and non-overlapping additive Schwarz methods. These methods are designed for elliptic problems with highly heterogeneous coefficients. The methods are of the non-overlapping type without the need of Schur complements and the subdomain interactions are via the coarse space only. The coarse space is large however it can be solved very efficiently since the coarse matrix is a low-rank perturbation of a diagonal matrix, so Sherman–Morrison–Woodbury formula can be applied. The dimension of this perturbation is equal to the number of subdomains plus the number of local bad eigenvalues due to the heterogeneities of the coefficients inside the subdomains. We also characterize these bad eigenvalues with respect to the geometry of the coefficients (number of connected island/channels with large coefficients that touch the boundary of the subdomains. The NO-SAS methods are robust with respect any coefficient and has good parallelization properties. Numerical results are presented.
Joint work with Yu Yi ( WP, USAI) and Maksymilian Dryja (University of Warsaw, Poland).
Monday, July 19, 19:00 ~ 19:30 UTC-3
One- and Two-level Asynchronous Optimized Schwarz Methods for the solution of PDEs
Daniel Szyld
Temple University, Philadelphia, USA - This email address is being protected from spambots. You need JavaScript enabled to view it.
Asynchronous methods refer to parallel iterative procedures where each process performs its task without waiting for other processes to be completed, i.e., with whatever information it has locally available and with no synchronizations with other processes. For the numerical solution of a general partial differential equation on a domain, Schwarz iterative methods use a decomposition of the domain into two or more (possibly overlapping) subdomains. In essence one is introducing new artificial boundary conditions on the interfaces between these subdomains. In the classical formulation, these artificial boundary conditions are of Dirichlet type. Given an initial approximation, the method progresses by solving for the PDE restricted to each subdomain using as boundary data on the artificial interfaces the values of the solution on the neighboring subdomain from the previous step. This procedure is inherently parallel, since the (approximate) solutions on each subdomain can be performed by a different processor. In the case of optimized Schwarz, the boundary conditions on the artificial interfaces are of Robin or mixed type. In this way one can optimize the Robin parameter(s) and obtain a very fast method.Instead of using this method as a preconditioner, we use it as a solver, thus avoiding the pitfall of synchronization required by the inner products. In this talk, an asynchronous version of the optimized Schwarz method is presented for the solution of differential equations on a parallel computational environment. A coarse grid correction is added and one obtains a scalable method. Several theorems show convergence for particular situations.Numerical results are presented on large three-dimensional problems illustrating the efficiency of the proposed asynchronous parallel implementation of the method. The main application shown is the calculation of the gravitational potential in the area around the Chicxulub crater, in Yucatan, where an asteroid is believed to have landed 66 million years ago contributing to the extinction of the dinosaurs.
Monday, July 19, 19:30 ~ 20:00 UTC-3
A SIR epidemic model accounting for population mobility
Daniel Gregorio Alfaro Vigo
Universidade Federal do Rio de Janeiro, Brazil - This email address is being protected from spambots. You need JavaScript enabled to view it.
In this work, we propose a susceptible-infectious-recovered (SIR) model for the spreading of an infectious disease in a population. Our modeling uses a novel approach in order to take into account the influence of spatial heterogeneity and population mobility on disease transmission. The proposed model consist of a coupled system of three parabolic and one elliptic equations. We prove the existence and uniqueness of weak solutions of the proposed model. We also give a complete characterization of the (disease free) steady state solutions and introduce the corresponding basic reproduction number. We present several numerical examples to illustrate our theoretical results, using Galerkin/Finite Element Method for spatial discretization and finite difference time-integration schemes such as Backward-Euler and Crank-Nicolson.
Joint work with Amaury Alvarez Cruz (Universidade Federal do Rio de Janeiro).
Posters
NONLINEAR OSCILLATIONS OF VECTOR FIELDS WITH APPLICATIONS IN PHYSICS
Tahmineh Azizi
Kansas State University, United States - This email address is being protected from spambots. You need JavaScript enabled to view it.
A dynamical system describes the evolution of a system over time using a set of mathematical laws. Also, it can be used to predict the interactions between different components of a system. There are two main methods to model the dynamical behaviors of a system, continuous time modeling, discrete-time modeling. When the time between two measurements is negligible, the continuous time modeling governs the evolution of the system, however, when there is a gap between two measurements, discrete-time system modeling comes to play. Ordinary differential equations are the tool to model a continuous system and iterated maps represent the discrete generations. Investigating local dynamics of equilibrium points of nonlinear systems plays an important role in studying the behavior of dynamical systems. There are many different definitions for stable and unstable solutions in the literature. The main goal to develop stability definitions is exploring the responses or output of a system to perturbation as time approaches infinity. Due to the wide range of application of local dynamical system theory in physics, biology, economics and social science, it still attracts many researchers to play with its definitions to find out the answers for their questions. In this study, we look at local dynamical behavior of famous dynamical systems, Hénon-Heiles system, Duffing oscillator and Van der Pol equation and analyze them.
On the Adaptive Switching controller for avoiding stagnation on restarting $GMRES$
Juan Carlos Cabral
Scientific Computing and Applied Mathematics Group of the Polytechnic School/National University of, Paraguay - This email address is being protected from spambots. You need JavaScript enabled to view it.
The Restarted Generalized Minimal Residual method, denotes as GMRES($m$), is normally used for the solution of large, sparse, and nonsymmetric linear systems. In practice, it has the drawback of eventually presenting at certain re-starting cycles a stagnation or a slowdown rate of convergence. In this work, we are going to discuss strategies for avoiding stagnation and how a combination of them can exploit better their individual properties. The combination is implemented as a switching controller that changes the structure of the GMRES($m$) when stagnation is detected. The switching controller chooses conveniently from several techniques, how to augment the Krylov subspace for enriching it. Moreover, the controller varies the restarting parameter to modify the dimension of the Krylov subspace is needed. This strategy makes the adaptive switching controller competitive from the point of view of avoiding the stagnation and acceleration of the convergence respect to the number of iterations and the computational time. We are going to present computational experiments to show the advantages and the main issues raised from the perspective of the adaptive switching controller. For instance, when to perform the switching, what information is more important at each stage, and when to modify the restart parameter.
Joint work with Christian E. Schaerer (National University of Asuncion).
Stress and stretch alveolar sac simulation and the effect on respiratory gases concentrations in the lung
Luis Jhony Caucha Morales
Universidad Nacional de Tumbes, Perú - This email address is being protected from spambots. You need JavaScript enabled to view it.
The study of pathologies of the lung is very important, the specialist improves the experiments to know the behavior of respiratory gases in the lung. We are interesting to simulate the effect of the gas concentrations in the alveolar sac, when the alveolar sac is subjected to stress and stretch during a respiratory cycle. Using the Navier-Stokes and convection-diffusion equations and classical boundary conditions in combinations with Nitsche’s method, we simulate the gas transport in an alveolar sac and quantified the stress, stretch in the wall, and the accumulations of CO2 for different volumes. For a numerical solution, we apply finite element methods and anisotropic LPS (Local projection stabilization). During inspiration, the CO2 concentrations take values from 0.056 to 0.06, and with Neumann condition for expiration is already uniformly around 0.06 the value prescribed in the boundary for exchange from blood. In conclusion, the boundary conditions for the CO2 concentrations have a strong influence on all alveolar sac and the amount of CO2 in the alveolar sac depends of capillaries numbers in the wall and it is not affected with forced maneuver. Keywords: Gases exchange, Navier-Stokes, Nitsche method
Joint work with Obidio Rubio (Mathematics, Universidad Nacional de Trujillo, Perú.).
Second-order fractional differential equations: a numerical approach.
Monzón Gabriel
Universidad Nacional de General Sarmiento, Argentina - This email address is being protected from spambots. You need JavaScript enabled to view it.
A finite difference type scheme is proposed for second-order fractional differential equations. Such a scheme is based on the numerical rules to approximate the Caputo fractional derivative and the Riemann-Liouville integral operator given in [ODIBAT Z., {\it Approximations of fractional integral and Caputo fractional derivatives}, Appl. Math. Comput., 178, pp. 527-533 (2006)].
Some simple and elementary examples are given to illustrate the aplicability of the proposed method.
Diagnosis of diseases in plants using Gaussian Mixture Models and Probabilistic Saliency.
Lili Guadarrama Bustos
CIMAT, Mexico - This email address is being protected from spambots. You need JavaScript enabled to view it.
A simple and robust approach is presented for plant disease diagnosis by means of a neural network through images of plants even in uncontrolled environments, identifying and quantifying the colors associated with the diseases for the purpose of estimating the portion of the plant that has presence of diseased tissue. In order to improve the performance of the neural network, Gaussian Mixture Models and Probabilistic Saliency are used to accurately segment the plant from the background of an image.
Joint work with Carlos Paredes (Centro de Investigación en Óptica) and Omar Mercado (CIMAT).
Solution of the radiation problem using isogeometric analysis
Victoria Hernandez Mederos
Instituto de Cibernética Matemática y Física (ICIMAF), Cuba - This email address is being protected from spambots. You need JavaScript enabled to view it.
We discuss the numerical solution of the 2D Helmoltz equation with mixed boundary conditions, defining the so called radiation problem. This problem depends on a constant parameter k, the wavenumber. For relative small values of k, the radiation problem can be handled with low order Finite Element Method (FEM). But in modern medical and industrial applications the values of k can be of order of thousands, and several numerical difficulties appear. To overcome these difficulties we solve the radiation problem using the isogeometric method, a kind of generalization of the classic FEM based on B-splines functions. Our numerical experiments show that isogeometric approach is superior than the classic FEM reducing significatively the pollution error, especially for high values of k.
Joint work with Eduardo Moreno Hernandez (ICIMAF, Cuba), Jorge Estrada Sarlabous (ICIMAF, Cuba), Isidro Abello Ugalde (Universidad de La Habana, Cuba) and Domenico Lahaye ( DIAM TU Delf, The Netherlands).
Approximation of non-homogeneous partial differential equations using the Scaled Boundary Finite Element Method
Karolinne O. Coelho
State University of Campinas, Brazil - This email address is being protected from spambots. You need JavaScript enabled to view it.
The Scaled Boundary Finite Element Method (SBFEM) is a semi-analytical technique in which finite element spaces are constructed based on the approximation of local Dirichlet problems with piecewise polynomial trace data. The basis functions are Duffy's approximations with a gradient-orthogonality constraint imposed to solve homogeneous partial differential equations (PDEs) - a mimetic version of harmonic functions. Since the method was originally proposed for homogeneous PDEs, loss of convergence is observed in formulations where a source term is present. Therefore, this study aims to develop a formulation to approximate non-homogeneous partial differential equations based on orthogonal bubble functions. Due to the orthogonality property, the approximation of non-homogeneous PDE using the SBFEM can be decoupled into boundary and domain problems and be solved separately. Three examples show the accuracy and optimal rates of convergence for a parabolic PDE (a heat flow) and Elasticity problems.
Joint work with Philippe R. B. Devloo (University of Campinas).
Contact integrator for nonholonomic mechanical systems
Inocencio Ortiz
Polytechnic School - National University of Asunción, Paraguay - This email address is being protected from spambots. You need JavaScript enabled to view it.
We propose a numerical scheme for time-integration of nonholonomic mechanical systems, both conservative and non-conservative. The method is obtained by discretizing both the constraint equations and the Herglotz variational principle, which encodes the dynamics of the system. We validate the method by numerical simulations to contrast it against standard methods known in the literature.
Joint work with Elías Maciel (Polytechnic School - National University of Asunción) and Christian Schaerer (Polytechnic School - National University of Asunción).
Modeling, control, and simulation of Mendelian and maternal inheritance, with application to the biological control of dengue vectors
Pastor E. Pérez Estigarribia
Facultad Politécnica - Universidad Nacional de Asunción, Paraguay - This email address is being protected from spambots. You need JavaScript enabled to view it.
The fight against arboviruses such as dengue consists largely in controlling mosquito vector populations. The modeling and simulation of simultaneous control strategies can provide key insights to avoid costly field trials. We are here interested in a biological control method based on the intentional infection of the wild mosquito population by the bacterium Wolbachia, which has the property to reduce greatly their competence as a vector of various arboviruses. We provide and study a mathematical model for mixtures of Wolbachia infected and uninfected populations, including a combination of attributes of autosomal inheritance for insecticide resistance and maternal inheritance for Wolbachia. A feedback control law for the release of specific genotypes of mosquitoes infected with Wolbachia is given and analyzed. Finally, computational simulations are presented, which illustrate the influence that some factors should have on the release campaigns of genotype-specific mosquitoes infected with Wolbachia.
Joint work with Pastor E Pérez-Estigarribia (Polytechnic School, National University of Asunción, P.O. Box 2111 SL, San Lorenzo, Paraguay. Electronic address: This email address is being protected from spambots. You need JavaScript enabled to view it.), Pierre-Alexandre Bliman (Sorbonne Université, Université Paris-Diderot SPC, Inria, CNRS, Laboratoire Jacques-Louis Lions, équipe Mamba, 75005 Paris, France. Electronic address: This email address is being protected from spambots. You need JavaScript enabled to view it.) and Christian E. Schaerer (Polytechnic School, National University of Asunción, P.O. Box 2111 SL, San Lorenzo, Paraguay. Electronic address: This email address is being protected from spambots. You need JavaScript enabled to view it.).
Modeling and simulation of adaptive resistance evolution
Pastor E. Pérez Estigarribia
Facultad Politécnica - Universidad Nacional de Asunción, Paraguay - This email address is being protected from spambots. You need JavaScript enabled to view it.
Resistance to insecticides (larvicides and / or adulticides) is considered today one of the greatest threats to the control of vector mosquitoes, since its appearance drastically reduces the efficiency of chemical control campaigns and can also disrupt the application of other control methods, such as biological and genetic control. In this work we use a general population model continuous in time with two life phases under selective pressure, simplified through slow manifold theory to simulate various evolution scenarios in mosquito populations, including directional and non-directional (i.e. overdominance and subdominance) selection. In addition, it is illustrated how the level of allelic dominance and the reversibility in the evolution of resistance can increase the effectiveness of chemical control.
Joint work with Pastor E Pérez-Estigarribia (Polytechnic School, National University of Asunción, P.O. Box 2111 SL, San Lorenzo, Paraguay. Electronic address: This email address is being protected from spambots. You need JavaScript enabled to view it.), Pierre-Alexandre Bliman (Sorbonne Université, Université Paris-Diderot SPC, Inria, CNRS, Laboratoire Jacques-Louis Lions, équipe Mamba, 75005 Paris, France. Electronic address: This email address is being protected from spambots. You need JavaScript enabled to view it.) and Christian E Schaerer (Polytechnic School, National University of Asunción, P.O. Box 2111 SL, San Lorenzo, Paraguay. Electronic address: This email address is being protected from spambots. You need JavaScript enabled to view it.).
The evaluation of two-fluid model for suspended sediment transport using Direct Numerical Simulation
Hyun Ho Shin
Universidad Nacional de Asunción, Paraguay - This email address is being protected from spambots. You need JavaScript enabled to view it.
The sediment transport in a horizontal open channel flow can be represented as two-phase flow, where the water flow is considered as a continuous (liquid) phase, and the sediment particles as a dispersed (solid) phase. Among the two-phase flow modeling, two approaches can be considered: (i) point-particle Direct Numerical Simulation (DNS), and (ii) two-fluid models. In the point-particle DNS, the continuous-phase is modeled by incompressible Navier-Stokes equations where all the turbulence length and time-scales are solved detailly, and each particle considered as a point-source is tracked individually. On the other hand, in two-fluid models, both phases are considered as the interpenetrable fluids represented by two sets of averaged equations for mass and momentum. As the particle concentration of the suspended sediment is very dilute, it is commonly accepted that the one-way coupling situation is a good approximation, i.e., the fluid-particle interactions influence only on the dispersed-phase, and the continuous-phase is not affected by the presence of the particles.
Although, the two-fluid models are more adequate for the engineering applications, the point-particle DNS is used for the fundamental investigation to study the dynamics of the phenomena. In this context, the point-particle DNS can be useful in the subside for the development of two-fluid models for the engineering flows in sediment transport. In this work, the point-particle DNS is used for the evaluations of two-fluid models. The averaged equation for the particle momentum is developed in the context of point-particle one-way coupling, and then, the balances of different fluid-particle interactions are evaluated. We show that in the absence of gravity, the interplay between the stress-gradient force and the turbophoretic effects is dominant. On the other hand, when gravity force acts in the wall-normal direction, the dominant forces are gravity and drag. In two-fluid models, both stress-gradient and turbophoresis can be modelled in terms of fluid Reynolds stresses, and for the drag force, it has to be included a model for the drift velocity.
Joint work with Luis M., Portela (Delft University of Technology, The Netherlands), Christian E., Schaerer (Universidad Nacional de Asunción, Paraguay) and Norberto, Mangiavacchi (Universidade do Estado do Rio de Janeiro, Brasil).