pinecone/core-2020-05-10-deduplication huggingface dataset:
Nonlinear Model Reduction for Uncertainty Quantification in Large-Scale Inverse Problems

We present a model reduction approach to the solution of large-scale statistical inverse problems in a Bayesian inference setting. A key to the model reduction is an efficient representation of the non-linear terms in the reduced model. To achieve this, we present a formulation that employs masked projection of the discrete equations; that is, we compute an approximation of the non-linear term using a select subset of interpolation points. Further, through this formulation we show similarities among the existing techniques of gappy proper orthogonal decomposition, missing point estimation, and empirical interpolation via coefficient-function approximation. The resulting model reduction methodology is applied to a highly non-linear combustion problem governed by an advection–diffusion-reaction partial differential equation (PDE). Our reduced model is used as a surrogate for a finite element discretization of the non-linear PDE within the Markov chain Monte Carlo sampling employed by the Bayesian inference approach. In two spatial dimensions, we show that this approach yields accurate results while reducing the computational cost by several orders of magnitude. For the full three-dimensional problem, a forward solve using a reduced model that has high fidelity over the input parameter space is more than two million times faster than the full-order finite element model, making tractable the solution of the statistical inverse problem that would otherwise require many years of CPU time.MIT-Singapore Alliance. Computational Engineering ProgrammeUnited States. Air Force Office of Scientific Research (Contract Nos. FA9550-06-0271)National Science Foundation (U.S.) (Grant No. CNS-0540186)National Science Foundation (U.S.) (Grant No. CNS-0540372)Caja Madrid Foundation (Graduate Fellowship
An algorithm for fast optimal Latin hypercube design of experiments

CITATION: Viana, F. A. C., Venter, G. & Balabanov, V. 2010.  An algorithm for fast optimal Latin hypercube design of experiments. International Journal for Numerical Methods in Engineering, 82(2):135-156, doi:10.1002/nme.2750.The original publication is available at http://onlinelibrary.wiley.com/journal/10.1002/%28ISSN%291097-0207/This paper presents the translational propagation algorithm, a new method for obtaining optimal or near
optimal Latin hypercube designs (LHDs) without using formal optimization. The procedure requires
minimal computational effort with results virtually provided in real time. The algorithm exploits patterns
of point locations for optimal LHDs based on the ɸp criterion (a variation of the maximum distance
criterion). Small building blocks, consisting of one or more points each, are used to recreate these patterns
by simple translation in the hyperspace. Monte Carlo simulations were used to evaluate the performance of
the new algorithm for different design configurations where both the dimensionality and the point density
were studied. The proposed algorithm was also compared against three formal optimization approaches
(namely random search, genetic algorithm, and enhanced stochastic evolutionary algorithm). It was found
that (i) the distribution of the ɸp values tends to lower values as the dimensionality is increased and (ii)
the proposed translational propagation algorithm represents a computationally attractive strategy to obtain
near optimum LHDs up to medium dimensions.Post-prin
A cartesian-grid collocation technique with integrated radial basis functions for mixed boundary value problems

In this paper, high order systems are reformulated as first order systems which are then numerically solved by a collocation method. The collocation method is based on Cartesian discretisation with 1D-integrated radial basis function networks (1D-IRBFN){MaiDuy_TranCong:2007}. The present method is enhanced by a new boundary interpolation technique based on 1D-IRBFN which is introduced to obtain variable approximation at irregular points in irregular domains. The proposed method is well suited to problems with mixed boundary conditions on both regular and irregular domains. The main results obtained are (a) the boundary conditions for the reformulated problem are of Dirichlet type only; (b) the integrated RBFN approximation avoids the well known reduction of convergence rate associated with differential formulations; (c) the primary variable (e.g. displacement, temperature) and the dual variable (e.g. stress, temperature gradient) have similar convergence order; (d) the volumetric locking effects associated with incompressible materials in solid mechanics are alleviated. Numerical experiments show that the proposed method achieves very good accuracy and high convergence rates
On the formulation of closest-point projection algorithms in elastoplasticity. PartI: the variational structure

We present in this paper the characterization of the variational structure behind the discrete equations defining the closest-point projection approximation in elastoplasticity. Rate-independent and viscoplastic formulations are considered in the infinitesimal and the finite deformation range, the later in the context of isotropic finite-strain multiplicative plasticity. Primal variational principles in terms of the stresses and stress-like hardening variables are presented first, followed by the formulation of dual principles incorporating explicitly the plastic multiplier. Augmented Lagrangian extensions are also presented allowing a complete regularization of the problem in the constrained rate-independent limit. The variational structure identified in this paper leads to the proper framework for the development of new improved numerical algorithms for the integration of the local constitutive equations of plasticity as it is undertaken in Part II of this work.Peer ReviewedPostprint (author’s final draft
On the formulation of closest-point projection algorithms in elastoplasticity. Part II: globally convergent schemes

This paper presents the formulation of numerical algorithms for the solution of the closest-point projection equations that appear in typical implementations of return mapping algorithms in elastoplasticity. The main motivation behind this work is to avoid the poor global convergence properties of a straight application of a Newton scheme in the solution of these equations, the so-called Newton-CPPM. The mathematical structure behind the closest-point projection equations identified in Part I of this work delineates clearly different strategies for the successful solution of these equations. In particular, primal and dual closest-point projection algorithms are proposed, in non-augmented and augmented Lagrangian versions for the imposition of the consistency condition. The primal algorithms involve a direct solution of the original closest-point projection equations, whereas the dual schemes involve a two-level structure by which the original system of equations is staggered, with the imposition of the consistency condition driving alone the iterative process. Newton schemes in combination with appropriate line search strategies are considered, resulting in the desired asymptotically quadratic local rate of convergence and the sought global convergence character of the iterative schemes. These properties, together with the computational performance of the different schemes, are evaluated through representative numerical examples involving different models of finite-strain plasticity. In particular, the avoidance of the large regions of no convergence in the trial state observed in the standard Newton-CPPM is clearly illustrated.Peer ReviewedPostprint (author’s final draft
On the optimum support size in meshfree methods: a variational adaptivity approach with maximum-entropy approximants

We present a method for the automatic adaption of the support size of meshfree basis functions in the context of the numerical approximation of boundary value problems stemming from a minimum principle.\ud
The method is based on a variational approach, and the central idea is that the variational principle selects both the discretized physical fields and the discretization parameters, here those defining the support size of each basis function. We consider local maximum-entropy approximation schemes, which exhibit smooth basis functions with respect to both space and the discretization parameters (the node location and the locality parameters). We illustrate by the Poisson, linear and non-linear elasticity problems the effectivity of the method, which produces very accurate solutions with very coarse discretizations and finds unexpected patterns of the support size of the shape functions. Copyright 2009 John Wiley & Sons, Ltd.Postprint (published version
Numerical aspects associated with the implementation of a finite strain, elasto-viscoelastic–viscoplastic constitutive theory in principal stretches

This paper treats the numerical implementation of a finite strain, elasto-viscoelastic-viscoplastic constitutive model for semi-crystalline polymers, written in principal stretches. A parallel configuration of the three model elements is used that enables the decoupled algorithmic treatment of each response within a stress update numerical scheme. The numerical aspects associated with the use of principal stretch constitutive expressions in a tensor space numerical environment are initially developed for the general cases of any elastic or inelastic constitutive element. Included is the formulation of the closed-form, consistent tangential modulus tensor. The principal space algorithmic treatments of the elastic, viscoelastic and viscoplastic elements are then used as specific examples. Of particular importance is the development of a principal space, closest point projection return mapping algorithm for viscoplasticity including isotropic strain hardening. Preliminary numerical examples are presented to illustrate the versatility of the model
A generalized finite element formulation for arbitrary basis functions : from isogeometric analysis to XFEM

Many of the formulations of cm-rent research interest, including iosogeometric methods and the extended finite element method, use nontraditional basis functions. Some, such as subdivision surfaces, may not have convenient analytical representations. The concept of an element, if appropriate at all, no longer coincides with the traditional definition. Developing a new software for each new class of basis functions is a large research burden, especially, if the problems involve large deformations, non-linear materials, and contact. The objective of this paper is to present a method that separates as much as possible the generation and evaluation of the basis functions from the analysis, resulting in a formulation that can be implemented within the traditional structure of a finite clement program but that permits the use of arbitrary sets of basis functions that are defined only through the input file. Elements ranging from a traditional linear four-node tetrahedron through a higher-order element combining XFEM and isogeometric analysis may be specified entirely through an input file without any additional programming. Examples of this framework to applications with Lagrange elements, isogeometric elements, and XFEM basis functions for fracture are presented
eXtended Stochastic Finite Element Method for the numerical simulation of heterogenous materials with random material interfaces

International audienceAn eXtended Stochastic Finite Element Method has been recently proposed for the numerical solution of partial differential equations defined on random domains. This method is based on a mariage between the eXtended Finite Element Method and spectral stochastic methods. In this paper, we propose an extension of this method for the numerical simulation of random multi-phased materials. The random geometry of material interfaces is described implicitly by using random level-set functions. A fixed deterministic finite element mesh, which is not conforming the random interfaces, is then introduced in order to approximate the geometry and the solution. Classical spectral stochastic finite element approximation spaces are not able to capture the irregularities of the solution field with respect to spatial and stochastic variables, which leads to a deterioration of the accuracy and convergence properties of the approximate solution. In order to recover optimal convergence properties of the approximation, we propose an extension of the partition of unity method to the spectral stochastic framework. This technique allows the enrichment of approximation spaces with suitable functions based on an a priori knowledge of the irregularities in the solution. Numerical examples illustrate the efficiency of the proposed method and demonstrate the relevance of the enrichment procedure
Limit analysis of plates and slabs using a meshless equilibrium formulation

A meshless Element-Free Galerkin (EFG) equilibrium formulation is proposed to compute the limit loads which can be sustained by plates and slabs. In the formulation pure moment fields are approximated using a moving least-squares technique, which means that the resulting fields are smooth over the entire problem domain. There is therefore no need to enforce continuity conditions at interfaces within the problem domain, which would be a key part of a comparable finite element formulation. The collocation method is used to enforce the strong form of the equilibrium equations and a stabilized conforming nodal integration scheme is introduced to eliminate numerical instability problems. The combination of the collocation method and the smoothing technique means that equilibrium only needs to be enforced at the nodes, and stable and accurate solutions can be obtained with minimal computational effort. The von Mises and Nielsen yield criteria which are used in the analysis of plates and slabs, respectively, are enforced by introducing second-order cone constraints, ensuring that the resulting optimization problem can be solved using efficient interior-point solvers. Finally, the efficacy of the procedure is demonstrated by applying it to various benchmark plate and slab problems
eXtended ﬁnite element methods for thin cracked plates with Kirchhoff–Love theory\ud

A modelization of cracked plates under bending loads in the XFEM framework is addressed. The Kirchhoff–Love model is considered. It is well suited for very thin plates commonly used for instance in aircraft structures. Reduced HCT and FVS elements are used for the numerical discretization.\ud
Two kinds of strategies are proposed for the enrichment around the crack tip with, for both of them, an enrichment area of ﬁxed size (i.e. independant of the mesh size parameter). In the ﬁrst one, each degree of freedom inside this area is enriched with the nonsmooth functions that describe the asymptotic displacement near the crack tip. The second strategy consists in introducing these functions in the ﬁnite element basis with a single degree of freedom for each one. An integral matching is then used in order to ensure the C1 continuity of the solution at the interface between the enriched and the non-enriched areas. Finally, numerical convergence results for these strategies are presented and discussed
Micromechanics of High Temperature Hydrogen Attack

Hydrogen attack is a material degradation process that occurs at elevated temperatures in hydrogen-rich environments, such as found in petro-chemical installations. Weldments in components such as reactor vessels are particularly susceptible to hydrogen attack. This paper discusses a multi-scale micromechanics modeling approach in which the chemico-mechanical damage processes at sub-micron scale are coupled to the macroscopic behavior through a series of size-scale transitions. A simulation of hydrogen attack in a welded reactor serves as an illustration of the approach.
Thin shell analysis from scattered points with maximum-entropy approximants

This is the accepted version of the following article: [Millán, D., Rosolen, A. and Arroyo, M. (2011), Thin shell analysis from scattered points with maximum-entropy approximants. Int. J. Numer. Meth. Engng., 85: 723–751. doi:10.1002/nme.2992], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.2992/abstractWe present a method to process embedded smooth manifolds using sets of points alone. This method avoids any global parameterization and hence is applicable to surfaces of any genus. It combines three ingredients: (1) the automatic detection of the local geometric structure of the manifold by statistical learning methods; (2) the local parameterization of the surface using smooth meshfree (here maximum-entropy) approximants; and (3) patching together the local representations by means of a partition of unity. Mesh-based methods\ud
can deal with surfaces of complex topology, since they rely on the element-level parameterizations, but cannot handle high-dimensional manifolds, whereas previous meshfree methods for thin shells consider a global parametric domain, which seriously limits the kinds of surfaces that can be treated. We present the implementation of the method in the context of Kirchhoff–Love shells, but it is applicable to other calculations on manifolds in any dimension. With the smooth approximants, this fourth-order partial differential equation is treated directly. We show the good performance of the method on the basis of the classical obstacle course. Additional calculations exemplify the flexibility of the proposed approach in treating surfaces of complex topology and geometry.Peer ReviewedPostprint (author's final draft
Highly efficient optimization mesh movement method based on proper orthogonal decomposition

In this paper, we implement the method of proper orthogonal decomposition (POD) to generate a reduced order model (ROM) of an optimization-based mesh movement scheme. In this study it is shown that POD can be used effectively to generate an ROM, that accurately reproduces the full order mesh movement algorithm, with a decrease in computational time of over 99%. We further introduce a novel training procedure whereby the POD models are generated in a fully automated fashion. The technology is applicable to any mesh movement method and enables potential reductions of up to four orders of magnitude in mesh movement related costs. The proposed model can be implemented without having to pre-train the POD model, to any fluid-structure interaction code with an existing mesh movement scheme.http://www3.interscience.wiley.com/journal/1430/homeai201
The finite element method for the mechanically-based model of non-local continuum

In this paper the finite element method (FEM) for the mechanically based non-local elastic continuum model is proposed. In such a model each volume element of the domain is considered mutually interacting with the others, beside classical interactions involved by the Cauchy stress field, by means of central body forces that are monotonically decreasing with their inter-distance and proportional to the product of the interacting volume elements. The constitutive relations of the long-range interactions involve the product of the relative displacement of the centroids of volume elements by a proper, distance-decaying function, which accounts for the decrement of the long-range interactions as long as distance increases. In this study, the elastic problem involving long-range central interactions for isotropic elastic continuum will be solved with the aid of the FEM. The accuracy of the solution obtained with the proposed FEM code is compared with other solutions obtained with Galerkins' approximation as well as with finite difference method. Moreover, a parametric study regarding the effect of the material length scale in the mechanically based model and in the Kr"oner-Eringen non-local elasticity has been investigated for a plane elasticity proble
X-FEM in isogeometric analysis for linear fracture mechanics

The extended finite element method (X-FEM) has proven to be an accurate, robust method for solving problems in fracture mechanics. X-FEM has typically been used with elements using linear basis functions, although some work has been performed using quadratics. In the current work, the X-FEM formulation is incorporated into isogeometric analysis to obtain solutions with higher order convergence rates for problems in linear fracture mechanics. In comparison with X-FEM with conventional finite elements of equal degree, the NURBS-based isogeometric analysis gives equal asymptotic convergence rates and equal accuracy with fewer degrees of freedom (DOF). Results for linear through quartic NURBS basis functions are presented for a multiplicity of one or a multiplicity equal the degree
A large deformation frictional contract formulation using NURBS-based isogeometric analysis

Cataloged from PDF version of article.This paper focuses on the application of NURBS-based isogeometric analysis to Coulomb frictional contact problems between deformable bodies, in the context of large deformations. A mortar-based approach is presented to treat the contact constraints, whereby the discretization of the continuum is performed with arbitrary order NURBS, as well as C0-continuous Lagrange polynomial elements for comparison purposes. The numerical examples show that the proposed contact formulation in conjunction with the NURBS discretization delivers accurate and robust predictions. Results of lower quality are obtained from the Lagrange discretization, as well as from a different contact formulation based on the enforcement of the contact constraints at every integration point on the contact surface. Copyright © 2011 John Wiley & Sons, Ltd
On the techniques for constructing admissible stress fields in model
  verification: Performances on engineering examples

Robust global/goal-oriented error estimation is used nowadays to control the
approximate finite element solutions obtained from simulation. In the context
of Computational Mechanics, the construction of admissible stress fields (\ie
stress tensors which verify the equilibrium equations) is required to set up
strict and guaranteed error bounds (using residual based error estimators) and
plays an important role in the quality of the error estimates. This work
focuses on the different procedures used in the calculation of admissible
stress fields, which is a crucial and technically complicated point. The three
main techniques that currently exist, called the element equilibration
technique (EET), the star-patch equilibration technique (SPET), and the element
equilibration + star-patch technique (EESPT), are investigated and compared
with respect to three different criteria, namely the quality of associated
error estimators, computational cost and easiness of practical implementation
into commercial finite element codes. The numerical results which are presented
focus on industrial problems; they highlight the main advantages and drawbacks
of the different methods and show that the behavior of the three estimators,
which have the same convergence rate as the exact global error, is consistent.
Two- and three-dimensional experiments have been carried out in order to
compare the performance and the computational cost of the three different
approaches. The analysis of the results reveals that the SPET is more accurate
than EET and EESPT methods, but the corresponding computational cost is higher.
Overall, the numerical tests prove the interest of the hybrid method EESPT and
show that it is a correct compromise between quality of the error estimate,
practical implementation and computational cost.Comment: 39 page