Sharif Digital Repository

Evaluating the statistical dimension is a common tool to determine the asymptotic phase transition in compressed sensing problems with Gaussian ensemble. Unfortunately, the exact evaluation of the statistical dimension is very difficult and it has become standard to replace it with an upper-bound. To ensure that this technique is suitable, [1] has introduced an upper-bound on the gap between the statistical dimension and its approximation. In this work, we first show that the error bound in [1] in some low-dimensional models such as total variation and ell _{1} analysis minimization becomes poorly large. Next, we develop a new error bound which significantly improves the estimation gap... 

In this paper, an adaptive FE analysis is presented based on error estimation, adaptive mesh refinement and data transfer for enriched plasticity continua in the modelling of strain localization. As the classical continuum models suffer from pathological mesh-dependence in the strain softening models, the governing equations are regularized by adding rotational degrees-of-freedom to the conventional degrees-of-freedom. Adaptive strategy using element elongation is applied to compute the distribution of required element size using the estimated error distribution. Once a new mesh is generated, state variables and history-dependent variables are mapped from the old finite element mesh to the... 

It is well-known that the conventional reproducing kernel particle method (RKPM) is unfavorable when dealing with the derivative type essential boundary conditions [1-3]. To remedy this issue a group of meshless methods in which the derivatives of a function can be incorporated in the formulation of the corresponding interpolation operator will be discussed. Formulation of generalized moving least squares (GMLS) on a domain and GMLS on a finite set of points will be presented. The generalized RKPM will be introduced as the discretized form of GMLS on a domain. Another method that helps to deal with derivative type essential boundary conditions is the gradient RKPM which incorporates the... 

A decade has passed since the first appearance of the superconvergent patch recovery (SPR) method introduced by Zienkiewicz and Zhu [The superconvergence patch recovery and a posteriori error estimates, part I: the recovery techniques, Int. J. Numer. Methods Eng. 33 (1992) 1331-1364; The superconvergence patch recovery and a posteriori error estimates, part II: error estimates and adaptivity, Int. J. Numer. Methods Eng. 33 (1992) 1365-1380; Superconvergence and the superconvergent patch recovery, Finite Elem. Anal. Des. 19 (1995) 11-23]. The method is now widely used in engineering practices for its robustness and efficiency in computer implementation. This paper presents an extension of the... 

In this paper, an adaptive finite element procedure is presented in modeling of mixed-mode cohesive crack propagation via the modified superconvergent path recovery technique. The adaptive mesh refinement is performed based on the Zienkiewicz-Zhu error estimator. The weighted-SPR recovery technique is employed to improve the accuracy of error estimation. The Espinosa-Zavattieri bilinear cohesive zone model is applied to implement the traction-separation law. It is worth mentioning that no previous information is necessary for the path of crack growth and no region of the domain is necessary to be filled by the cohesive elements. The maximum principal stress criterion is employed for... 

In this paper, two adaptive refinement techniques are presented for enhancing the capability of the new kind of finite volume method called meshless finite volume (MFV) method in which the moving least squares (MLS) approximation technique is employed. The proposed algorithms perform by inserting new nodes in large error regions identified using the Zienkiewicz-Zhu (Z-Z) error estimator and the T-Belytschko (TB) stress recovery scheme. In the first method referred as CV-based adaptive refinement, the new nodes are inserted at the vertices of control volumes with higher errors. The second method, referred as GA-based adaptive refinement, contains two schemes where an adaptive refinement... 

Advanced reservoir characterization methods can yield geological models at a very fine resolution, containing 1011–1018 cells, while the common reservoir simulators can only handle much lower numbers of cells due to computer hardware limitations. The process of coarsening a fine-scale model to a simulation model is known as upscaling. Predicting the accuracy of simulation results over an upscaled grid with respect to the fine grid is highly important, as it can yield the optimum upscaling process. In this paper, permeability-based and velocity-based a priori error estimation techniques are proposed by introducing image processing-based comparison methods in the context of upscaling. The... 

In this letter, we address the theoretical limitations in estimating the mixing matrix in noisy sparse component analysis (SCA) for the two-sensor case. We obtain the Cramer-Rao lower bound (CRLB) error estimation of the mixing matrix. Using the Bernouli-Gaussian (BG) sparse distribution, and some simple assumptions, an approximation of the Fisher information matrix (FIM) is calculated. Moreover, this CRLB is compared to some of the main methods of mixing matrix estimation in the literature. © 2008 IEEE  

Flow velocity is an important characteristic of the fluidic mediums. In this article, we introduce a molecular based flow velocity meter consisting of a molecule releasing node and a receiver that counts these molecules. We consider both flow velocity detection and estimation problems, which are employed in different applications. For the flow velocity detection, we obtain the maximum a posteriori (MAP) decision rule. To analyze the performance of the proposed flow velocity detector, we obtain the error probability, its Gaussian approximation and Chernoff information (CI) upper bound, and investigate the optimum and sub-optimum sampling times accordingly. We show that, for binary hypothesis,... 

In this paper, the continuum damage mechanics model originally proposed by Lemaitre (Journal of Engineering Materials and Technology. 1985; 107: 83-89) is presented through an adaptive finite element method for three-dimensional ductile materials. The macro-crack initiation-propagation criterion is used based on the distribution of damage variable in the continuum damage model. The microcrack closure effect is incorporated to simulate the damage evolution more realistic. The Zienkiewicz-Zhu posteriori error estimator is employed in conjunction with a weighted Superconvergence Patch Recovery (SPR) technique at each patch to improve the accuracy of error estimation and data transfer process.... 

In this paper, an adaptive finite element analysis is presented for 3D modeling of non-planar curved crack growth. The fracture mechanical evaluation is performed based on a general technique for non-planar curved cracks. The Schollmann's crack kinking criterion is used for the process of crack propagation in 3D problems. The Zienkiewicz-Zhu error estimator is employed in conjunction with a weighted SPR technique at each patch to improve the accuracy of error estimation. Applying the proposed technique to 3D non-planar curved crack growth problems shows significant improvements particularly at the boundaries and near crack tip regions. Several numerical examples are presented to illustrate... 

In this paper, the three-dimensional automatic adaptive mesh refinement is presented in modeling the crack propagation based on the modified superconvergent patch recovery technique. The technique is developed for the mixed mode fracture analysis of different fracture specimens. The stress intensity factors are calculated at the crack tip region and the crack propagation is determined by applying a proper crack growth criterion. An automatic adaptive mesh refinement is employed on the basis of modified superconvergent patch recovery (MSPR) technique to simulate the crack growth by applying the asymptotic crack tip solution and using the collapsed quarter-point singular tetrahedral elements... 

In this paper, the three-dimensional adaptive finite element modeling is presented for cohesive fracture analysis of non-planer crack growth. The technique is performed based on the Zienkiewicz-Zhu error estimator by employing the modified superconvergent patch recovery procedure for the stress recovery. The Espinosa-Zavattieri bilinear constitutive equation is used to describe the cohesive tractions and displacement jumps. The 3D cohesive fracture element is employed to simulate the crack growth in a non-planar curved pattern. The crack growth criterion is proposed in terms of the principal stress and its direction. Finally, several numerical examples are analyzed to demonstrate the... 

In this paper, the continuum damage mechanics model originally proposed by Lemaitre [1] is presented through an adaptive finite element method for three-dimensional ductile materials. The macro-crack initiation-propagation criterion is used based on the distribution of damage variable in the continuum damage model. The micro-crack closure effect is incorporated to simulate the damage evolution more realistic. The Zienkiewicz-Zhu posteriori error estimator is employed in conjunction with a weighted superconvergence patch recovery (SPR) technique at each patch to improve the accuracy of error estimation and data transfer process. Finally, the robustness and accuracy of proposed computational... 

Over the past few years, radiation-induced transient errors, also referred to as soft errors, have been a severe threat to the data integrity of high-end and mainstream processors. Recent studies show that cache memories are among the most vulnerable components to soft errors within high-performance processors. Accurate modeling of the Vulnerability Factor (VF) is an essential step towards developing cost-effective protection techniques for cache memory. Although Fault Injection (FI) techniques can provide relatively accurate VF estimations they are often very time consuming. To overcome the limitation, recent analytical models were proposed to compute the cache VF in a timely fashion. In... 

In this letter, we propose a sparsity promoting feedback acquisition and reconstruction scheme for sensing, encoding and subsequent reconstruction of spectrally sparse signals. In the proposed scheme, the spectral components are estimated utilizing a sparsity-promoting, sliding-window algorithm in a feedback loop. Utilizing the estimated spectral components, a level signal is predicted and sign measurements of the prediction error are acquired. The sparsity promoting algorithm can then estimate the spectral components iteratively from the sign measurements. Unlike many batch-based compressive sensing algorithms, our proposed algorithm gradually estimates and follows slow changes in the... 

In this paper, the data transfer operators are developed in 3D large plasticity deformations using superconvergent patch recovery (SPR) method. The history-dependent nature of plasticity problems necessitates the transfer of all relevant variables from the old mesh to new one, which is performed in three main stages. In the first step, the history-dependent internal variables are transferred from the Gauss points of old mesh to nodal points. The variables are then transferred from nodal points of old mesh to nodal points of new mesh. Finally, the values are computed at the Gauss points of new mesh using their values at nodal points. As the solution procedure, in general, cannot be...