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AuthorAmato, Nancy M. (45)Liang, Faming (22)Genton, Marc G. (20)Guermond, Jean-Luc (18)Efendiev, Yalchin R. (17)View MoreJournalComputer Graphics Forum (9)IEEE Transactions on Visualization and Computer Graphics (9)SIAM Journal on Numerical Analysis (9)Inverse Problems (7)Journal of Computational Physics (7)View MoreKAUST Grant Number

KUS-C1-016-04 (319)

PublisherElsevier BV (50)Institute of Electrical and Electronics Engineers (IEEE) (46)Springer Science + Business Media (34)Wiley-Blackwell (34)Society for Industrial & Applied Mathematics (SIAM) (26)View MoreSubjectFinite elements (11)Finite element method (7)Adaptive mesh refinement (5)Stochastic approximation Monte Carlo (5)Atherosclerosis (4)View MoreTypeArticle (236)Conference Paper (51)Book Chapter (32)Year (Issue Date)2016 (3)2015 (16)2014 (33)2013 (65)2012 (78)View MoreItem AvailabilityMetadata Only (310)Open Access (9)

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A maximum-principle preserving finite element method for scalar conservation equations

Guermond, Jean-Luc; Nazarov, Murtazo (Computer Methods in Applied Mechanics and Engineering, Elsevier BV, 2014-04) [Article]

This paper introduces a first-order viscosity method for the explicit approximation of scalar conservation equations with Lipschitz fluxes using continuous finite elements on arbitrary grids in any space dimension. Provided the lumped mass matrix is positive definite, the method is shown to satisfy the local maximum principle under a usual CFL condition. The method is independent of the cell type; for instance, the mesh can be a combination of tetrahedra, hexahedra, and prisms in three space dimensions. © 2014 Elsevier B.V.

A new class of massively parallel direction splitting for the incompressible Navier–Stokes equations

Guermond, J.L.; Minev, P.D. (Computer Methods in Applied Mechanics and Engineering, Elsevier BV, 2011-06) [Article]

We introduce in this paper a new direction splitting algorithm for solving the incompressible Navier-Stokes equations. The main originality of the method consists of using the operator (I-∂xx)(I-∂yy)(I-∂zz) for approximating the pressure correction instead of the Poisson operator as done in all the contemporary projection methods. The complexity of the proposed algorithm is significantly lower than that of projection methods, and it is shown the have the same stability properties as the Poisson-based pressure-correction techniques, either in standard or rotational form. The first-order (in time) version of the method is proved to have the same convergence properties as the classical first-order projection techniques. Numerical tests reveal that the second-order version of the method has the same convergence rate as its second-order projection counterpart as well. The method is suitable for parallel implementation and preliminary tests show excellent parallel performance on a distributed memory cluster of up to 1024 processors. The method has been validated on the three-dimensional lid-driven cavity flow using grids composed of up to 2×109 points. © 2011 Elsevier B.V.

A New Approach to the Modeling and Analysis of Fracture through Extension of Continuum Mechanics to the Nanoscale

Sendova, T.; Walton, J. R. (Mathematics and Mechanics of Solids, SAGE Publications, 2010-02-15) [Article]

In this paper we focus on the analysis of the partial differential equations arising from a new approach to modeling brittle fracture based on an extension of continuum mechanics to the nanoscale. It is shown that ascribing constant surface tension to the fracture surfaces and using the appropriate crack surface boundary condition given by the jump momentum balance leads to a sharp crack opening profile at the crack tip but predicts logarithmically singular crack tip stress. However, a modified model, where the surface excess property is responsive to the curvature of the fracture surfaces, yields bounded stresses and a cusp-like opening profile at the crack tip. Further, two possible fracture criteria in the context of the new theory are discussed. The first is an energy-based crack growth condition, while the second employs the finite crack tip stress the model predicts. The classical notion of energy release rate is based upon the singular solution, whereas for the modeling approach adopted here, a notion analogous to the energy release rate arises through a different mechanism associated with the rate of working of the surface excess properties at the crack tip. © The Author(s), 2010.

A new approach to nonlinear constrained Tikhonov regularization

Ito, Kazufumi; Jin, Bangti (Inverse Problems, IOP Publishing, 2011-09-16) [Article]

We present a novel approach to nonlinear constrained Tikhonov regularization from the viewpoint of optimization theory. A second-order sufficient optimality condition is suggested as a nonlinearity condition to handle the nonlinearity of the forward operator. The approach is exploited to derive convergence rate results for a priori as well as a posteriori choice rules, e.g., discrepancy principle and balancing principle, for selecting the regularization parameter. The idea is further illustrated on a general class of parameter identification problems, for which (new) source and nonlinearity conditions are derived and the structural property of the nonlinearity term is revealed. A number of examples including identifying distributed parameters in elliptic differential equations are presented. © 2011 IOP Publishing Ltd.

A new class of fractional step techniques for the incompressible Navier–Stokes equations using direction splitting

Guermond, Jean-Luc; Minev, Peter D. (Comptes Rendus Mathematique, Elsevier BV, 2010-05) [Article]

A new direction-splitting-based fractional time stepping is introduced for solving the incompressible Navier-Stokes equations. The main originality of the method is that the pressure correction is computed by solving a sequence of one-dimensional elliptic problems in each spatial direction. The method is very simple to program in parallel, very fast, and has exactly the same stability and convergence properties as the Poisson-based pressure-correction technique, either in standard or rotational form. © 2010 Académie des sciences.

A negative-norm least-squares method for time-harmonic Maxwell equations

Copeland, Dylan M. (Journal of Mathematical Analysis and Applications, Elsevier BV, 2012-04) [Article]

This paper presents and analyzes a negative-norm least-squares finite element discretization method for the dimension-reduced time-harmonic Maxwell equations in the case of axial symmetry. The reduced equations are expressed in cylindrical coordinates, and the analysis consequently involves weighted Sobolev spaces based on the degenerate radial weighting. The main theoretical results established in this work include existence and uniqueness of the continuous and discrete formulations and error estimates for simple finite element functions. Numerical experiments confirm the error estimates and efficiency of the method for piecewise constant coefficients. © 2011 Elsevier Inc.

A physics informed emulator for laser-driven radiating shock simulations

McClarren, Ryan G.; Ryu, D.; Paul Drake, R.; Grosskopf, Michael; Bingham, Derek; Chou, Chuan-Chih; Fryxell, Bruce; van der Holst, Bart; Paul Holloway, James; Kuranz, Carolyn C.; Mallick, Bani; Rutter, Erica; Torralva, Ben R. (Reliability Engineering & System Safety, Elsevier BV, 2011-09) [Article]

This work discusses the uncertainty quantification aspect of quantification of margin and uncertainty (QMU) in the context of two linked computer codes. Specifically, we present a physics based reduction technique to deal with functional data from the first code and then develop an emulator for this reduced data. Our particular application deals with conditions created by laser deposition in a radiating shock experiment modeled using the Lagrangian, radiation-hydrodynamics code Hyades. Our goal is to construct an emulator and perform a sensitivity analysis of the functional output from Hyades to be used as an initial condition for a three-dimensional code that will compute the evolution of the radiating shock at later times. Initial attempts at purely statistical data reduction techniques, were not successful at reducing the number of parameters required to describe the Hyades output. We decided on an alternate approach using physical arguments to decide what features/locations of the output were relevant (e.g., the location of the shock front or the location of the maximum pressure) and then used a piecewise linear fit between these locations. This reduced the number of outputs needed from the emulator to 40, down from the O(1000) points in the Hyades output. Then, using Bayesian MARS and Gaussian process regression, we were able to build emulators for Hyades and study sensitivities to input parameters. © 2011 Elsevier Ltd. All rights reserved.

A Computational Agent-Based Modeling Approach for Competitive Wireless Service Market

Douglas, C C; Hyoseop Lee,; Wonsuck Lee, (2011 International Conference on Information Science and Applications, Institute of Electrical and Electronics Engineers (IEEE), 2011-04) [Conference Paper]

Using an agent-based modeling method, we study market dynamism with regard to wireless cellular services that are in competition for a greater market share and profit. In the proposed model, service providers and consumers are described as agents who interact with each other and actively participate in an economically well-defined marketplace. Parameters of the model are optimized using the Levenberg-Marquardt method. The quantitative prediction capabilities of the proposed model are examined through data reproducibility using past data from the U.S. and Korean wireless service markets. Finally, we investigate a disruptive market event, namely the introduction of the iPhone into the U.S. in 2007 and the resulting changes in the modeling parameters. We predict and analyze the impacts of the introduction of the iPhone into the Korean wireless service market assuming a release date of 2Q09 based on earlier data. © 2011 IEEE.

A correction technique for the dispersive effects of mass lumping for transport problems

Guermond, Jean-Luc; Pasquetti, Richard (Computer Methods in Applied Mechanics and Engineering, Elsevier BV, 2013-01) [Article]

This paper addresses the well-known dispersion effect that mass lumping induces when solving transport-like equations. A simple anti-dispersion technique based on the lumped mass matrix is proposed. The method does not require any non-trivial matrix inversion and has the same anti-dispersive effects as the consistent mass matrix. A novel quasi-lumping technique for P2 finite elements is introduced. Higher-order extensions of the method are also discussed. © 2012 Elsevier B.V.

A Heckman Selection- t Model

Marchenko, Yulia V.; Genton, Marc G. (Journal of the American Statistical Association, Informa UK Limited, 2012-03) [Article]

Sample selection arises often in practice as a result of the partial observability of the outcome of interest in a study. In the presence of sample selection, the observed data do not represent a random sample from the population, even after controlling for explanatory variables. That is, data are missing not at random. Thus, standard analysis using only complete cases will lead to biased results. Heckman introduced a sample selection model to analyze such data and proposed a full maximum likelihood estimation method under the assumption of normality. The method was criticized in the literature because of its sensitivity to the normality assumption. In practice, data, such as income or expenditure data, often violate the normality assumption because of heavier tails. We first establish a new link between sample selection models and recently studied families of extended skew-elliptical distributions. Then, this allows us to introduce a selection-t (SLt) model, which models the error distribution using a Student's t distribution. We study its properties and investigate the finite-sample performance of the maximum likelihood estimators for this model. We compare the performance of the SLt model to the conventional Heckman selection-normal (SLN) model and apply it to analyze ambulatory expenditures. Unlike the SLNmodel, our analysis using the SLt model provides statistical evidence for the existence of sample selection bias in these data. We also investigate the performance of the test for sample selection bias based on the SLt model and compare it with the performances of several tests used with the SLN model. Our findings indicate that the latter tests can be misleading in the presence of heavy-tailed data. © 2012 American Statistical Association.

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