Browsing by Author "Pereira, L. Felipe"
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Item A Multiscale Direct Solver for the Approximation of Flows in High Contrast Porous Media(Elsevier B.V.) Akbari, H.; Engsig-Karup, A. P.; Ginting, V.; Pereira, L. Felipe; Pereira, L. FelipeWe consider a non-overlapping domain decomposition approach to approximate the solution of elliptic boundary value problems with high contrast in their coefficients. We propose a method such that initially local solutions subject to Robin boundary conditions in each primal subdomain are constructed with (locally conservative) finite element or finite volume methods. Then, a novel approach is introduced to obtain a (discontinuous) global solution in terms of linear combination of the local subdomain solutions. In the proposed algorithm the computation of local solutions for unions of subdomains are localized at nearest-neighbor subdomain boundaries, thus avoiding the solution of global interface problems. We remove discontinuities in a smoothing step that is defined on a staggered grid or dual subdomains. The resulting algorithm is naturally parallelizable and can be employed as a parallel direct solver, offering great potential for the numerical solution of large problems. In fact, subdomains can be considered small enough to fit well in GPUs and the proposed procedure can handle adaptive (in space) simulations effectively. Numerical simulations are presented and discussed. We demonstrate the effectiveness of the proposed approach with two and three dimensional high contrast and channelized coefficients, that lead to challenging approximation problems. The new procedure, although designed for parallel processing, is also of value for serial calculations. ©2019 Elsevier B.V.Item Modeling and Sensitivity Analysis for Trace Gas Sensors(2022-12-01T06:00:00.000Z) Mozumder, Ali Ahammed; Minkoff, Susan E.; Zweck, John; King, Lindsay J.; Cao, Yan; Pereira, L. FelipeTrace gas sensors can detect very low concentrations of gases such as methane and sulfur dioxide. An important class of trace gas sensors are quartz-enhanced photoacoustic spectroscopy (QEPAS) sensors, which employ a quartz tuning fork (QTF) and modulated laser to detect trace gases. Existing models of QEPAS sensors employ one-way coupling from the fluid to the structure that requires prior experimental measurements of the damping of the QTF due to its motion in the viscous fluid. We study an improved two-way coupled model that is based on a Helmholtz system of thermo- visco-acoustic equations in the fluid, together with a system of equations for the temperature and the displacement of the structure. These two subsystems are coupled across the fluid-structure interface via several conditions. With this model, the user specifies the geometry of the structure and the viscous and thermal parameters of the fluid, and the model outputs an effective damping parameter and a signal strength that is proportional to the concentration of the trace gas. We derive analytic solutions of the two-way coupled model in the special case that the QTF is replaced by an annular structure. This simplification of the geometry allows the pressure, temperature of the fluid, and the displacement of the structure to be expressed in terms of Bessel functions. These solutions show reasonable agreement between the one-way and two-way coupled models at higher ambient pressures. However, at low ambient pressure the one-way coupled model does not adequately capture thermo-viscous effects. For the two-way coupled model, excellent agreement is obtained between the analytical results and simulations performed using a finite element formulation of the model. Computational models for trace gas sensors involve a large number of parameters. If one wants to quantify uncertainty of the output quantities of interest (for example, pressure, temperature or displacement of the tuning fork tines) then one must estimate statistical distributions that describe these quantities. However, statistical studies require that one runs the physical simulator for hundreds or thousands of different input parameter values. This process is computationally prohibitive unless one can first identify which parameters influence the model output. We use the active sub- space method to identify a subset of parameters that is influential for the output. The application of the active subspace method to the pressure-temperature subsystem in the special case of cylindrical symmetry identifies one influential parameter for the fluid temperature and three for the pressure from the five dimensional parameter space. Similarly, for the two-way coupled model with annular geometry the active subspace method reduces the 13 dimensional parameter space to a 5 dimensional subspace by identifying 4 influential parameters for the fluid temperature and 5 influential parameters for the remaining quantities of interest. Finally, for the one-way coupled model with tuning fork geometry, the active subspace method identifies 5 influential parameters for the fluid pressure, temperature, and displacement of the QTF reducing a 10 dimensional parameter space to a 5 dimensional subspace. These results also show an excellent agreement with the results obtained using kernel density estimation and a simple sensitivity study.Item Multiscale Sampling for Subsurface Characterization(2021-07-21) Ali, Alsadig Abdallah Hassan; Pereira, L. Felipe; Rahunanthan, ArunasalamIn this work we are interested in the (ill-posed) inverse problem for absolute permeability characterization that arises in predictive modeling of porous media flows. We consider a Bayesian framework combined with a preconditioned Markov Chain Monte Carlo (MCMC) for the solution of the inverse problems. Reduction of uncertainty can be accomplished by incorporating measurements at sparse locations (static data) in the prior distribution. The first contribution of this work is a new method to condition Gaussian fields (the log of permeability fields) to available measurements. A truncated Karhunen-Lo`eve expansion (KLE) is used for dimension reduction. In the proposed method the imposition of static data is made through the projection of a sample (expressed as a vector of independent, identically distributed normal random variables) onto the nullspace of a data matrix, that is defined in terms of the KLE. Through numerical experiments for a model second-order elliptic equation we show the importance of conditioning in accelerating MCMC convergence. The second contribution of this dissertation is the introduction of a new multiscale sampling strategy. This is a new algorithm to decompose the stochastic space in orthogonal complement subspaces, through a one-to-one mapping onto a non-overlapping domain decomposition of the region of interest. The localization of the search is performed by Gibbs sampling: we apply a KL expansion locally, at the subdomain level. The effectiveness of the proposed framework is tested also in the solution of inverse problems related to elliptic partial differential equations. We use multi-chain studies in a multi-GPU cluster to show that the new algorithm clearly improves the convergence rate of the preconditioned MCMC method. We propose a new method to speed up MCMC studies of subsurface flow problems as the third contribution of this dissertation. We formulate a multiscale perturbation method for uncertainty quantification problems. The new procedure is presented for (linear) contaminant transport problems in the subsurface. The method, however, may be applicable to non-linear problems, such as two-phase immiscible displacements in petroleum reservoirs.Item Stabilization of Nonholonomic Euler–poincaré Mechanical Systems With Broken Symmetry by Controlled Lagrangians(2022-12-01T06:00:00.000Z) Garcia, Jorge Silva; Ohsawa, Tomoki; Stelling, Allison; Dragovic, Vladimir; Ramakrishna, Viswanath; Pereira, L. FelipeWe extend the method of Controlled Lagrangians to nonholonomic Euler–Poincaré mechanical systems with broken symmetry by considering the problem of stabilizing what we call a pendulum skate, a simple model of a figure skater developed by Gzenda and Putkaradze. By exploiting the symmetry of the system as well as taking care of the part of the symmetry broken by the gravity, the equations of motion are given as nonholonomic Euler–Poincaré equation with advected parameters. After that, we discovered the general form of the equilibrium points and presented the classification of two special ones, designated as sliding and spinning. Of our main interest is the stability of the sliding and spinning equilibria of the system. We show that the former is unstable and the latter is stable only under certain conditions. We use the method of Controlled Lagrangians to find a control to stabilize the sliding equilibrium and also show how to achieve the stabilization for the general equilibrium point.Item Synthesis of Functionalized Polycaprolactones for Drug Delivery Applications(2021-08-01T05:00:00.000Z) Calubaquib, Erika Joy; Stefan, Mihaela C.; Pereira, L. Felipe; Biewer, Michael C.; Meloni, Gabriele; Pantano, PaulPolycaprolactones (PCLs) have been used in various applications due to their biodegradability, biocompatibility, and favorable mechanical properties. The ability to attach multiple functionalities in the PCL backbone can provide many possibilities to tune the polymer’s physicochemical properties. Among the applications, extensive efforts have been dedicated to developing PCLs as carriers of bioactive compounds; however, some limitations still encountered are low payload, instability, and uncontrolled release of the cargo. In this work, micellar drug delivery systems obtained from the self-assembly of amphiphilic block copolymers comprising of benzyloxy- and oligo(ethylene glycol)-substituted PCLs were designed to load the doxorubicin anticancer drug and a quercetin cardioprotective polyphenol. The co-loading approach provided a way to enhance the loading capacity of the micelle for both cargoes. The utilization of various lengths of oligo(ethylene glycol) side-chains permitted tuning of the polymer’s thermoresponsive behavior to modulate the release of the cargo. These micelles exhibited a low critical micelle concentration, which is necessary for tolerating severe dilutions. Many copolymers have been explored for drug delivery; however, amphiphilic homopolymers can also be an alternative due to their more straightforward synthesis. Most reported amphiphilic homopolymers have a nonbiodegradable backbone, exhibits pH-dependent assembly, and are charged. Herein, non-ionic amphiphilic PCL homopolymers readily self-assembled to form micelles. The potential of using these micelles as drug carriers were explored by loading a eugenol anti-inflammatory molecule.