A hierarchical construction of LR meshes in 2D

Bressan, Andrea; Jüttler, Bert

doi:10.1016/j.cagd.2015.06.002

Cited by 27 publications

(52 citation statements)

References 16 publications

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“…In result, the CBCT approach was compared with 2D mesh topology and CBCT to provide better results in terms of end-to-end latency, network latency, packet latency, sink bandwidth, loss probability, link utilization and energy consumption of a topology. Similarly, the role of LR meshes in 2D was discussed in (Bressan et al, 2015). It shows a construction of LR-spaces whose bases are composed of locally linearly independent B-splines which also form a partition of unity.…”

Section: Two Dimensional (2d) Meshmentioning

confidence: 99%

State-of-art review of information diffusion models and their impact on social network vulnerabilities

Razaque

Rizvi

Khan

et al. 2022

Journal of King Saud University - Computer and Information Scie

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a b s t r a c tWith the development of information society and network technology, people increasingly depend on information found on the Internet. At the same time, the models of information diffusion on the Internet are changing as well. However, these models experience the problem due to the fast development of network technologies. There is no thorough research in regards to the latest models and their applications and advantages. As a result, it is essential to have a comprehensive study of information diffusion models.The primary goal of this research is to provide a comparative study on the existing models such as the Ising model, Sznajd model, SIR model, SICR model, Game theory and social networking services models. We discuss several of their applications with the existing limitations and further categorizations. Vulnerabilities and privacy challenges of information diffusion models are extensively explored. Furthermore, categorization including strengths and weaknesses are discussed. Finally, limitations and recommendations are suggested with diverse solutions for the improvement of the information diffusion models and envisioned future research directions.

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Section: Two Dimensional (2d) Meshmentioning

confidence: 99%

State-of-art review of information diffusion models and their impact on social network vulnerabilities

Razaque

Rizvi

Khan

et al. 2022

Journal of King Saud University - Computer and Information Scie

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“…In this section we show that hierarchical B-splines and multipatch domains fit into the localized sum factorization framework presented in this paper. Other generating systems without global tensor-product structure (like hierarchical LR splines [6]) could be analyzed in similar ways. The same holds if adaptivity and multipatch discretizations are combined.…”

Section: Localized Sum Factorization For Some Non-tensor-product Basesmentioning

confidence: 99%

Sum factorization techniques in Isogeometric Analysis

Bressan

Takacs

2019

Computer Methods in Applied Mechanics and Engineering

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The fast assembling of stiffness and mass matrices is a key issue in isogeometric analysis, particularly if the spline degree is increased. We present two algorithms based on the idea of sum factorization, one for matrix assembling and one for matrix-free methods, and study the behavior of their computational complexity in terms of the spline order p. Opposed to the standard approach, these algorithms do not apply the idea element-wise, but globally or on macro-elements. If this approach is applied to Gauss quadrature, the computational complexity grows as p d+2 instead of p 2d+1 as previously achieved.

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“…To derive the upper bound, we need to transform (7) by subtracting a(v, η) from left-(LHS) and right-hand side (RHS) and by setting η = e. Thus, one obtains the error identity…”

Section: Functional Approach To the Error Controlmentioning

confidence: 99%

Functional approach to the error control in adaptive IgA schemes for elliptic boundary value problems

Matculevich

2018

Journal of Computational and Applied Mathematics

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This work presents a numerical study of functional type a posteriori error estimates for IgA approximation schemes in the context of elliptic boundary-value problems. Along with the detailed discussion of the most crucial properties of such estimates, we present the algorithm of a reliable solution approximation together with the scheme of an efficient a posteriori error bound generation. In this approach, we take advantage of B-(THB-) spline's high smoothness for the auxiliary vector function reconstruction, which, at the same time, allows to use much coarser meshes and decrease the number of unknowns substantially. The most representative numerical results, obtained during a systematic testing of error estimates, are presented in the second part of the paper. The efficiency of the obtained error bounds is analysed from both the error estimation (indication) and the computational expenses points of view. Several examples illustrate that functional error estimates (alternatively referred to as the majorants and minorants of deviation from an exact solution) perform a much sharper error control than, for instance, residual-based error estimates. Simultaneously, assembling and solving routines for an auxiliary variables reconstruction, which generate the majorant (or minorant) of an error, can be executed several times faster than the routines for a primal unknown.

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A hierarchical construction of LR meshes in 2D

Cited by 27 publications

References 16 publications

State-of-art review of information diffusion models and their impact on social network vulnerabilities

State-of-art review of information diffusion models and their impact on social network vulnerabilities

Sum factorization techniques in Isogeometric Analysis

Functional approach to the error control in adaptive IgA schemes for elliptic boundary value problems

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