Static Analysis of Numerical Algorithms

Static Analysis Numerical Algorithms

10.21236/ad1008340 ◽

2016 ◽

Author(s):

Matthew Barry ◽

Eric Bush ◽

Doug Smith ◽

Devesh Bhatt ◽

David Oglesby ◽

...

Keyword(s):

Static Analysis ◽

Numerical Algorithms

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Hypothesis on the Solvability of Parabolic Equations with nonlocal Condition

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2002.7.1.15204 ◽

2002 ◽

Vol 7 (1) ◽

pp. 93-104 ◽

Cited By ~ 10

Author(s):

Mifodijus Sapagovas

Keyword(s):

Parabolic Equation ◽

Parabolic Equations ◽

Existence And Uniqueness ◽

Nonlocal Condition ◽

Nonlocal Conditions ◽

Numerical Algorithms ◽

Uniqueness Of The Solution

Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself.

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Numerical Algorithms and Software for Spectral Factorization Problems

10.23919/acc.1988.4789735 ◽

1988 ◽

Cited By ~ 1

Author(s):

Matt Wette ◽

Alan J. Laub

Keyword(s):

Numerical Algorithms ◽

Spectral Factorization

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Preface to the special issue, CMAM 2011, no. 3.

Computational Methods in Applied Mathematics ◽

10.2478/cmam-2011-0014 ◽

2011 ◽

Vol 11 (3) ◽

pp. 272

Author(s):

Ivan Gavrilyuk ◽

Boris Khoromskij ◽

Eugene Tyrtyshnikov

Keyword(s):

Separation Of Variables ◽

Numerical Algorithms ◽

Multilevel Methods ◽

High Dimensional ◽

Special Issue ◽

High Dimensions ◽

Guiding Principle ◽

Tensor Methods ◽

Closed World ◽

The One

Abstract In the recent years, multidimensional numerical simulations with tensor-structured data formats have been recognized as the basic concept for breaking the "curse of dimensionality". Modern applications of tensor methods include the challenging high-dimensional problems of material sciences, bio-science, stochastic modeling, signal processing, machine learning, and data mining, financial mathematics, etc. The guiding principle of the tensor methods is an approximation of multivariate functions and operators with some separation of variables to keep the computational process in a low parametric tensor-structured manifold. Tensors structures had been wildly used as models of data and discussed in the contexts of differential geometry, mechanics, algebraic geometry, data analysis etc. before tensor methods recently have penetrated into numerical computations. On the one hand, the existing tensor representation formats remained to be of a limited use in many high-dimensional problems because of lack of sufficiently reliable and fast software. On the other hand, for moderate dimensional problems (e.g. in "ab-initio" quantum chemistry) as well as for selected model problems of very high dimensions, the application of traditional canonical and Tucker formats in combination with the ideas of multilevel methods has led to the new efficient algorithms. The recent progress in tensor numerical methods is achieved with new representation formats now known as "tensor-train representations" and "hierarchical Tucker representations". Note that the formats themselves could have been picked up earlier in the literature on the modeling of quantum systems. Until 2009 they lived in a closed world of those quantum theory publications and never trespassed the territory of numerical analysis. The tremendous progress during the very recent years shows the new tensor tools in various applications and in the development of these tools and study of their approximation and algebraic properties. This special issue treats tensors as a base for efficient numerical algorithms in various modern applications and with special emphases on the new representation formats.

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Static Analysis of Functionally Graded Cantilever Beam Using Finite Element Method

i-manager’s Journal on Future Engineering and Technology ◽

10.26634/jfet.4.4.174 ◽

2009 ◽

Vol 4 (4) ◽

pp. 54-56

Author(s):

N. V. Ramesh Maganti ◽

◽

Mohan Rao N. ◽

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Static Analysis ◽

Cantilever Beam ◽

Functionally Graded ◽

Element Method

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Effects of openings on the seismic behavior and performance level of concrete shear walls

10.31224/osf.io/phfyd ◽

2019 ◽

Author(s):

Hossein Alimohammadi ◽

Mostafa Dalvi Esfahani ◽

Mohammadali Lotfollahi Yaghin

Keyword(s):

Static Analysis ◽

Cross Section ◽

Seismic Behavior ◽

Shear Walls ◽

Shear Wall ◽

Constant Cross Section ◽

Added Resistance ◽

Different Shapes ◽

And Performance ◽

Abaqus Software

In this study, the seismic behavior of the concrete shear wall considering the opening with different shapes and constant cross-section has been studied, and for this purpose, several shear walls are placed under the increasingly non-linear static analysis (Pushover). These case studies modeled in 3D Abaqus Software, and the results of the ductility coefficient, hardness, energy absorption, added resistance, the final shape, and the final resistance are compared to shear walls without opening.

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