20:I[654155,["/_next/static/chunks/bb923814e1f4d2e9.js","/_next/static/chunks/dd3ee9f5b7716ca6.js","/_next/static/chunks/4204a0ae82542ca8.js","/_next/static/chunks/1270dead247da766.js","/_next/static/chunks/6e1aa89a642f40be.js","/_next/static/chunks/2d7aa753e81324a8.js","/_next/static/chunks/8ffd0b71567920d8.js","/_next/static/chunks/67ea6dfd21f16c5f.js","/_next/static/chunks/24eb4379f68013fd.js","/_next/static/chunks/b8cd775ffdf935bd.js","/_next/static/chunks/983103cd9eb7b428.js","/_next/static/chunks/263f2cdcb9aa2341.js","/_next/static/chunks/294b9525248c8e5f.js"],"default"] 21:T4e0,An overview of computational methods to model fracture in brittle and quasi-brittle materials is given. The overview focuses on continuum models for fracture. First, numerical difficulties related to modelling fracture for quasi-brittle materials will be discussed. Different techniques to eliminate or circumvent those difficulties will be described subsequently. In that context, regularization techniques such as nonlocal models, gradient enhanced models, viscous models, cohesive zone models, and smeared crack models will be discussed. The main focus of this paper will be on computational methods for discrete fracture (discrete cracks). Element erosion technques, inter-element separation methods, the embedded finite element method (EFEM), the extended finite element method (XFEM), meshfree methods (MMs), boundary elements (BEMs), isogeometric analysis, and the variational approach to fracture will be reviewed elucidating advantages and drawbacks of each approach. As tracking the crack path is of major concern in computational methods that preserve crack path continuity, one section will discuss different crack tracking techniques. Finally, cracking criteria will be reviewed before the paper ends with future research perspectives.22:T483,Iterative methods are currently the solvers of choice for large sparse linear systems of equations. However, it is well known that the key factor for accelerating, or even allowing for, convergence is the preconditioner. The research on preconditioning techniques has characterized the last two decades. Nowadays, there are a number of different options to be considered when choosing the most appropriate preconditioner for the specific problem at hand. The present work provides an overview of the most popular algorithms available today, emphasizing the respective merits and limitations. The overview is restricted to algebraic preconditioners, that is, general-purpose algorithms requiring the knowledge of the system matrix only, independently of the specific problem it arises from. Along with the traditional distinction between incomplete factorizations and approximate inverses, the most recent developments are considered, including the scalable multigrid and parallel approaches which represent the current frontier of research. A separate section devoted to saddle-point problems, which arise in many different applications, closes the paper.23:T49b,A simple recursive method is presented for performing the inverse dispersion modeling of an unknown number of (localized) sources, given a finite number of noisy concentration data acquired by an array of detectors. Bayesian probability theory is used to address the problem of selecting the source model which is most plausible in view of the given concentration dataset and all the available prior information. The recursive algorithm involves subtracting a predicted concentration signal arising from a source model consisting of N localized sources from the measured concentration data for increasing values of N and examining the resulting residual data to determine if the residuals are consistent with the estimated noise level in the concentration data. The method is illustrated by application to a real concentration dataset obtained from an atmos

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