The research of thermoelastic deformation models with thin elliptic boundary contours plates and accounting uncertainty factors

2020 ◽  
Vol 1679 ◽  
pp. 052023
Author(s):  
V E Bolnokin ◽  
V I Storozhev ◽  
Duong Minh Hai ◽  
D I Mutin
Keyword(s):  
Elliptic Boundary ◽  
Thermoelastic Deformation ◽  
Uncertainty Factors ◽  
Deformation Models

On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value

2006 ◽  
Vol 11 (4) ◽  
pp. 323-329 ◽  
Author(s):  
G. A. Afrouzi ◽  
S. H. Rasouli
Keyword(s):  
Boundary Value Problems ◽  
Positive Solution ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Smooth Bounded Domain ◽  
Elliptic Boundary Value ◽  
Existence Of Positive Solutions

This study concerns the existence of positive solutions to classes of boundary value problems of the form−∆u = g(x,u), x ∈ Ω,u(x) = 0, x ∈ ∂Ω,where ∆ denote the Laplacian operator, Ω is a smooth bounded domain in RN (N ≥ 2) with ∂Ω of class C2, and connected, and g(x, 0) < 0 for some x ∈ Ω (semipositone problems). By using the method of sub-super solutions we prove the existence of positive solution to special types of g(x,u).

Exponentially Convergent Approximation to the Elliptic Solution Operator

2006 ◽  
Vol 6 (4) ◽  
pp. 386-404 ◽  
Author(s):  
Ivan. P. Gavrilyuk ◽  
V.L. Makarov ◽  
V.B. Vasylyk
Keyword(s):  
Green Function ◽  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Solution Operator ◽  
Hyperbolic Operator ◽  
Elliptic Solution ◽  
Elliptic Boundary Value ◽  
Sine Family ◽  
The Green Function

AbstractWe develop an accurate approximation of the normalized hyperbolic operator sine family generated by a strongly positive operator A in a Banach space X which represents the solution operator for the elliptic boundary value problem. The solution of the corresponding inhomogeneous boundary value problem is found through the solution operator and the Green function. Starting with the Dunford — Cauchy representation for the normalized hyperbolic operator sine family and for the Green function, we then discretize the integrals involved by the exponentially convergent Sinc quadratures involving a short sum of resolvents of A. Our algorithm inherits a two-level parallelism with respect to both the computation of resolvents and the treatment of different values of the spatial variable x ∈ [0, 1].

Perancangan Strategi Penjualan Menggunakan Dinamika Sistem Pada CV. Gajah Mungkur

2020 ◽  
Vol 5 (4) ◽  
pp. 215
Author(s):  
Maulana Hassan Syafrudin ◽  
Nunung Nurhasanah
Keyword(s):  
Swot Analysis ◽  
Online Marketing ◽  
Dynamics Simulation ◽  
Scenario Simulation ◽  
Dynamic Approach ◽  
Product Price ◽  
Output Analysis ◽  
Uncertainty Factors ◽  
The Right ◽  
A Company

<p><em>Abstrak</em> – <strong>CV. Gajah Mungkur adalah salah satu perusahaan yang bergerak di bidang bordir kain. Perusahaan ini mengalami pasang surut penjualan produknya selama dua tahun terakhir. Untuk itu dalam penelitian ini menggunakan strategi seperti analisis SWOT sebagai pendekatan perusahaan menghadapi persaingan bisnis penjualan serta pendekatan dinamika sistem dalam memberikan rekomendasi terhadap keputusan atau kebijakan perusahaan terkait nilai omset penjualan dan nilai profit perusahan yang dipengaruhi oleh faktor ketidakpastian (uncertainty). Berdasarkan hasil pengolahan ANP dengan software Super Decisions, didapatkan bahwa alternatif strategi yang tepat bagi perusahaan CV. Gajah Mungkur untuk melanjutkan proses bisnisnya yang lebih baik adalah dengan cara memberikan promo diskon dan melakukan pemasaran secara online. Berdasarkan analisis output hasil simulasi skenario, bahwa bila perusahaan menerapkan skenario diskon harga produk sebesar 5% perusahaan akan mendapatkan penambahan jumlah penjualan sebanyak 139.258 unit. Kemudian bila perusahaan menerapkan skenario diskon produk sebesar 10% perusahaan akan mendapatkan penambahan jumlah penjualan sebanyak 151.918 unit. Selanjutnya adalah bila perusahaan menerapkan skenario diskon produk sebesar 15% perusahaan akan mendapatkan penambahan jumlah penjualan sebanyak 164.577 unit. Selain itu bila perusahaan menerapkan pemasaran secara online, bila perusahaan menerapkan promosi online salah satunya di online shop shopee maka perusahaan akan mendapatkan penambahan jumlah penjualan sebanyak 174.533 unit.</strong></p><p><em>Abstract</em> - <strong>CV. Gajah Mungkur is one of the companies engaged in fabric embroidery. This company has experienced ups and downs in the sales of its products as per the data for the last two years. For this reason, this study uses strategies such as SWOT analysis as a company approach to dealing with sales business competition as well as a system dynamic approach in providing recommendations on company decisions or policies related to the value of sales turnover and the value of company profits which are influenced by uncertainty factors. The results of this study are based on the results of ANP processing with Super Decisions, it was found that the right alternative strategy for CV. Gajah Mungkur, to continue its better business process, is by providing discount promos and marketing online. Based on the output analysis scenario simulation results, that if the company applies a 5% discount on product price scenarios, the company will get an additional sales volume of 139,258 units. Then if the company applies a product discount scenario of 10%, the company will get an additional sales number of 151,918 units. Furthermore, if the company applies a product discount scenario of 15%, the company will get an additional sales number of 164,577 units. Besides, if the company implements online marketing, if the company implements online promotions, one of which is the online shopee, the company will get an additional sales number of 174,533 unit.</strong></p><p><strong><em>Keywords - </em></strong><em>SWOT, ANP, System Dynamics Simulation</em><em>.</em></p>

scholarly journals Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver

2021 ◽  
Author(s):  
Alexander Haberl ◽  
Dirk Praetorius ◽  
Stefan Schimanko ◽  
Martin Vohralík
Keyword(s):  
Adaptive Algorithm ◽  
Adaptive Mesh Refinement ◽  
Elliptic Boundary ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Picard Iteration ◽  
Optimal Rate ◽  
Stopping Criteria ◽  
Element Discretization ◽  
Fully Adaptive

AbstractWe consider a second-order elliptic boundary value problem with strongly monotone and Lipschitz-continuous nonlinearity. We design and study its adaptive numerical approximation interconnecting a finite element discretization, the Banach–Picard linearization, and a contractive linear algebraic solver. In particular, we identify stopping criteria for the algebraic solver that on the one hand do not request an overly tight tolerance but on the other hand are sufficient for the inexact (perturbed) Banach–Picard linearization to remain contractive. Similarly, we identify suitable stopping criteria for the Banach–Picard iteration that leave an amount of linearization error that is not harmful for the residual a posteriori error estimate to steer reliably the adaptive mesh-refinement. For the resulting algorithm, we prove a contraction of the (doubly) inexact iterates after some amount of steps of mesh-refinement/linearization/algebraic solver, leading to its linear convergence. Moreover, for usual mesh-refinement rules, we also prove that the overall error decays at the optimal rate with respect to the number of elements (degrees of freedom) added with respect to the initial mesh. Finally, we prove that our fully adaptive algorithm drives the overall error down with the same optimal rate also with respect to the overall algorithmic cost expressed as the cumulated sum of the number of mesh elements over all mesh-refinement, linearization, and algebraic solver steps. Numerical experiments support these theoretical findings and illustrate the optimal overall algorithmic cost of the fully adaptive algorithm on several test cases.

scholarly journals Constructing Adaptive Deformation Models for Estimating DEM Error in SBAS-InSAR Based on Hypothesis Testing

2021 ◽  
Vol 13 (10) ◽  
pp. 2006
Author(s):  
Jun Hu ◽  
Qiaoqiao Ge ◽  
Jihong Liu ◽  
Wenyan Yang ◽  
Zhigui Du ◽  
...  
Keyword(s):  
Time Series ◽  
Hypothesis Testing ◽  
Surface Deformation ◽  
A Priori ◽  
Least Square ◽  
Deformation Model ◽  
Phase Time ◽  
Testing Theory ◽  
Sbas Insar ◽  
Deformation Models

The Interferometric Synthetic Aperture Radar (InSAR) technique has been widely used to obtain the ground surface deformation of geohazards (e.g., mining subsidence and landslides). As one of the inherent errors in the interferometric phase, the digital elevation model (DEM) error is usually estimated with the help of an a priori deformation model. However, it is difficult to determine an a priori deformation model that can fit the deformation time series well, leading to possible bias in the estimation of DEM error and the deformation time series. In this paper, we propose a method that can construct an adaptive deformation model, based on a set of predefined functions and the hypothesis testing theory in the framework of the small baseline subset InSAR (SBAS-InSAR) method. Since it is difficult to fit the deformation time series over a long time span by using only one function, the phase time series is first divided into several groups with overlapping regions. In each group, the hypothesis testing theory is employed to adaptively select the optimal deformation model from the predefined functions. The parameters of adaptive deformation models and the DEM error can be modeled with the phase time series and solved by a least square method. Simulations and real data experiments in the Pingchuan mining area, Gaunsu Province, China, demonstrate that, compared to the state-of-the-art deformation modeling strategy (e.g., the linear deformation model and the function group deformation model), the proposed method can significantly improve the accuracy of DEM error estimation and can benefit the estimation of deformation time series.

Extending the unified transform: curvilinear polygons and variable coefficient PDEs

2018 ◽  
Vol 40 (2) ◽  
pp. 976-1004 ◽  
Author(s):  
Matthew J Colbrook
Keyword(s):  
Fourier Transforms ◽  
Elliptic Boundary ◽  
Neumann Boundary ◽  
Integral Transforms ◽  
Variable Coefficients ◽  
Central Component ◽  
Unknown Boundary ◽  
Boundary Values ◽  
Global Relation ◽  
Chebyshev Interpolation

Abstract We provide the first significant extension of the unified transform (also known as the Fokas method) applied to elliptic boundary value problems, namely, we extend the method to curvilinear polygons and partial differential equations (PDEs) with variable coefficients. This is used to solve the generalized Dirichlet-to-Neumann map. The central component of the unified transform is the coupling of certain integral transforms of the given boundary data and of the unknown boundary values. This has become known as the global relation and, in the case of constant coefficient PDEs, simply links the Fourier transforms of the Dirichlet and Neumann boundary values. We extend the global relation to PDEs with variable coefficients and to domains with curved boundaries. Furthermore, we provide a natural choice of global relations for separable PDEs. These generalizations are numerically implemented using a method based on Chebyshev interpolation for efficient and accurate computation of the integral transforms that appear in the global relation. Extensive numerical examples are provided, demonstrating that the method presented in this paper is both accurate and fast, yielding exponential convergence for sufficiently smooth solutions. Furthermore, the method is straightforward to use, involving just the construction of a simple linear system from the integral transforms, and does not require knowledge of Green’s functions of the PDE. Details on the implementation are discussed at length.

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