Fernando A. Rochinha

Higher-order gradient post-processings for second-order elliptic problems

Abstract Global, element-by-element and macroelement post-processing recovery techniques based on least-square residuals of equilibrium equation and irrotationality condition are proposed for second-order elliptic problems. Improved accuracy for the flux finite element approximations is obtained with low computational cost and easy implementation. Error estimates are derived and numerical experiments are reported confirming the higher-order rates of convergence predicted in the analysis.

A structural defect identification approach based on a continuum damage model

Abstract This paper introduces a structural identification technique built on finite element (FE) model updating. The FE model is parameterized by a structural parameter that continuously describes the damage in the structure, and besides, an evolution equation of this damage parameter is presented. The model updating is accomplished by determining the subset of this damage parameters that minimizes a global error derived from the dynamic residue vectors, which is obtained by introducing the experimental modal properties into the original model eigenproblem. A mode-shape projection technique is used in order to achieve compatibility between the dimension of the experimental and analytical models. The adjusted model maintains basic properties of the analytical model as the sparsity and the symmetry, which plays an important role in model updating-based damage identification. The verification and assessment of the current structural defect identification is performed on a analytically derived bidimensional truss structure and on a cantilever bidimensional Euler–Bernouilli beam through a virtual test simulator. This simulator is used to realistically simulate the corrupting effects of noise, filtering, digital sampling and truncation of the modal spectrum. The eigensystem realization algorithm along with the common-based normalized system identification were utilized to obtain the required natural frequencies and mode shapes.

A GENETIC ALGORITHM APPLIED TO COMPOSITE ELASTIC PARAMETERS IDENTIFICATION

The aim of this work is to present a technique to identify elastic parameters of composite materials. The identification is based on model updating involving an optimization process in which the objective function is defined as the difference between analytical natural frequencies and their experimental counterparts. Such analytical natural frequencies are obtained by means of the finite element method while the experimental ones are obtained by standard modal tests. The optimization problem is solved by a genetic algorithm (GA), which does not require the cost function gradient avoiding the expensive eigenvectors computation presents in gradient methods. The proposed technique is assessed by a number of different tests.

Consistent discontinuous finite elements in elastodynamics

Finite element discontinuities with respect to time have recently been extremely used in elastodynamic problems due to their natural utilization in combination with adaptive methods and their efficiency in discontinuity capturing techniques for non-smooth problems. In this work, we present some theoretical aspects and numerical results concerning the use of spatial discontinuities in a consistent finite element method for the same class of problems. We first review some formulations for the elastostatic problem and prove two Korn-like inequalities which are very useful for the derivation of convergence rates in Sobolev norms. Next, we present formulations for the dynamic case along with comments on their properties and estimates of convergence rates for smooth solutions, followed by numerical investigations of a typically non-smooth problem involving classical and emerging variational formulations. We also show some numerical experiments with finite element spaces enriched by discontinuous functions other than piecewise Lagrangian polynomials.

Numerical and Experimental Approach for Identifying Elastic Parameters in Sandwich Plates

This article deals with the identification of elastic parameters (engineering constants) in sandwich honeycomb orthotropic rectangular plates. A non-destructive method is introduced to identify the elastic parameters through the experimental measurements of natural frequencies of a plate undergoing free vibrations. Four elastic constant are identified. The estimation of the elastic parameter problem is solved by minimizing the differences between the measured and the calculated natural frequencies. The numerical method to calculate the natural frequencies involves the formulation of Rayleigh-Ritz using a series of characteristic orthogonal polynomials to properly model the free edge boundary conditions. The analysis of the results indicates the efficiency of the method.

Discontinuous finite element formulations applied to cracked elastic domains

The solutions of boundary value problems defined on cracked domains are usually non-smooth in the surroundings of the crack. In this work, we formulate the elasticity problem of a body with such geometric characteristic in a number of equivalent variational alternatives and show that we can take advantage of the theory of discontinuous finite elements in order to approximate its solution in an interesting way at little higher programming cost in comparison with the classical Galerkin method. The idea consists in splitting the global domain into a number of regions in which local mesh refinements are undertaken independently, producing irregular meshes with non-matching elements that are suitable to be used in discontinuous finite element methods. This strategy seems to be attractive to be employed in situations that we know in advance where the critical regions of the domain are located as well as in adaptive techniques.

Data-centric iteration in dynamic workflows

Dynamic workflows are scientific workflows to support computational science simulations, typically using dynamic processes based on runtime scientific data analyses. They require the ability of adapting the workflow, at runtime, based on user input and dynamic steering. Supporting data-centric iteration is an important step towards dynamic workflows because user interaction with workflows is iterative. However, current support for iteration in scientific workflows is static and does not allow for changing data at runtime. In this paper, we propose a solution based on algebraic operators and a dynamic execution model to enable workflow adaptation based on user input and dynamic steering. We introduce the concept of iteration lineage that makes provenance data management consistent with dynamic iterative workflow changes. Lineage enables scientists to interact with workflow data and configuration at runtime through an API that triggers steering. We evaluate our approach using a novel and real large-scale workflow for uncertainty quantification on a 640-core cluster. The results show impressive execution time savings from 2.5 to 24 days, compared to non-iterative workflow execution. We verify that the maximum overhead introduced by our iterative model is less than 5% of execution time. Also, our proposed steering algorithms are very efficient and run in less than 1 millisecond, in the worst-case scenario. Algebraic operators support data-centric iteration in dynamic workflows.Runtime data lineage, a concept inspired by provenance enables dynamic loops.Two algorithms support runtime adaptation of the workflow based on user input.Real-life experiment for Uncertainty Quantification in the Oil & Gas domain.A novel iterative workflow for Uncertainty Quantification is steered by users.

Monitoring hydraulic fractures: state estimation using an extended Kalman filter

There is considerable interest in using remote elastostatic deformations to identify the evolving geometry of underground fractures that are forced to propagate by the injection of high pressure viscous fluids. These so-called hydraulic fractures are used to increase the permeability in oil and gas reservoirs as well as to pre-fracture ore-bodies for enhanced mineral extraction. The undesirable intrusion of these hydraulic fractures into environmentally sensitive areas or into regions in mines which might pose safety hazards has stimulated the search for techniques to enable the evolving hydraulic fracture geometries to be monitored. Previous approaches to this problem have involved the inversion of the elastostatic data at isolated time steps in the time series provided by tiltmeter measurements of the displacement gradient field at selected points in the elastic medium. At each time step, parameters in simple static models of the fracture (e.g. a single displacement discontinuity) are identified. The approach adopted in this paper is not to regard the sequence of sampled elastostatic data as independent, but rather to treat the data as linked by the coupled elastic-lubrication equations that govern the propagation of the evolving hydraulic fracture. We combine the Extended Kalman Filter (EKF) with features of a recently developed implicit numerical scheme to solve the coupled free boundary problem in order to form a novel algorithm to identify the evolving fracture geometry. Numerical experiments demonstrate that, despite excluding significant physical processes in the forward numerical model, the EKF-numerical algorithm is able to compensate for the un-modeled dynamics by using the information fed back from tiltmeter data. Indeed the proposed algorithm is able to provide reasonably faithful estimates of the fracture geometry, which are shown to converge to the actual hydraulic fracture geometry as the number of tiltmeters is increased. Since the location of tiltmeters can affect the resolution of the method, the algorithm can also be used to design the deployment of tiltmeters to optimize the resolution in regions of particular interest.

Uncertainty quantification in numerical simulation of particle-laden flows

Numerical models can help to push forward the knowledge about complex dynamic physical systems. Modern approaches employ detailed mathematical models, taking into consideration inherent uncertainties on input parameters (phenomenological parameters or boundary and initial conditions, among others). Particle-laden flows are complex physical systems found in nature, generated due to the (possible small) spatial variation on the fluid density promoted by the carried particles. They are one of the main mechanisms responsible for the deposition of sediments on the seabed. A detailed understanding of particle-laden flows, often referred to as turbidity currents, helps geologists to understand the mechanisms that give rise to reservoirs, strategic in oil exploration. Uncertainty quantification (UQ) provides a rational framework to assist in this task, by combining sophisticated computational models with a probabilistic perspective in order to deepen the knowledge about the physics of the problem and to access the reliability of the results obtained with numerical simulations. This work presents a stochastic analysis of sediment deposition resulting from a turbidity current considering uncertainties on the initial sediment concentrations and particles settling velocities. The statistical moments of the deposition mapping, like other important features of the currents, are approximated by a Sparse Grid Stochastic Collocation method that employ a parallel flow solver for the solution of the deterministic problems associated to the grid points. The whole procedure is supported and steered by a scientific workflow management engine designed for high performance computer applications.

Identification of non-newtonian rheological parameter through an inverse formulation

In this work, we introduce an inverse formulation to be applied in the identification of a rheological parameter associated to non-Newtonian fluids. It is built upon a creeping flow through a 4 to 1 axisymmetric abrupt contraction. The fluid is modeled by the Generalized Newtonian Fluid constitutive equation. The viscosity function is based on the one proposed by Souza Mendes et al. (1995). It predicts an extensional elastic behavior, controlled by a rheological parameter q , which is the parameter determined via the proposed identification procedure. The numerical solution of the forward problem, needed in the iterative procedure introduced by the inverse formulation, is obtained through the finite volume method. A sensitivity analysis is also performed to evaluate the effect of the parameter q on the dimensionless pressure drop through the contraction. The optimization algorithm is based on an iterative method to find the minimum of the cost function, which is given by the least square difference between numerical and experimental values of the dimensionless pressure drop. The gradient method was used to update the parameter q , starting from the cost function gradient. The results obtained with the sensitivity analysis validated the adequacy of the proposed cost function, which is a key aspect on the identification formulation. Moreover, it shows that the method provides an attractive alternative for estimation of rheological properties.