New Approach of FEM for Eigenvalue Problems with Non-local Transition Conditions

2009 ◽  
pp. 159-167
Author(s):  
A. B. Andreev ◽  
M. R. Racheva
Keyword(s):  
Eigenvalue Problems ◽  
New Approach ◽  
Non Local ◽  
Local Transition

scholarly journals Asymptotic boundary conditions for the analysis of hydrodynamic stability of flows in regions with open boundaries

2019 ◽  
Vol 34 (1) ◽  
pp. 15-29 ◽  
Author(s):  
Andrey V. Boiko ◽  
Kirill V. Demyanko ◽  
Yuri M. Nechepurenko
Keyword(s):  
Boundary Conditions ◽  
Hydrodynamic Stability ◽  
Constant Velocity ◽  
Eigenvalue Problems ◽  
Main Flow ◽  
New Approach ◽  
Asymptotic Boundary ◽  
Open Boundaries ◽  
Temporal And Spatial ◽  
Parallel Approximation

Abstract A new approach to formulation of asymptotic boundary conditions for eigenvalue problems arising in numerical analysis of hydrodynamic stability of such shear flows as boundary layers, separations, jets, wakes, characterized by almost constant velocity of the main flow outside the shear layer or layers is proposed and justified. This approach makes it possible to formulate and solve completely the temporal and spatial stability problems in the locally-parallel approximation, reducing them to ordinary algebraic eigenvalue problems.

scholarly journals Non-local to local transition for ground states of fractional Schrödinger equations on $$\mathbb {R}^N$$

2020 ◽  
Vol 22 (3) ◽  
Author(s):  
Bartosz Bieganowski ◽  
Simone Secchi
Keyword(s):  
Ground State ◽  
Ground States ◽  
Ground State Solution ◽  
State Solution ◽  
Local Problem ◽  
Schrödinger Equations ◽  
Ground State Solutions ◽  
Fractional Schrödinger Equations ◽  
Non Local ◽  
Local Transition

Abstract We consider the nonlinear fractional problem $$\begin{aligned} (-\Delta )^{s} u + V(x) u = f(x,u)&\quad \hbox {in } \mathbb {R}^N \end{aligned}$$ ( - Δ ) s u + V ( x ) u = f ( x , u ) in R N We show that ground state solutions converge (along a subsequence) in $$L^2_{\mathrm {loc}} (\mathbb {R}^N)$$ L loc 2 ( R N ) , under suitable conditions on f and V, to a ground state solution of the local problem as $$s \rightarrow 1^-$$ s → 1 - .

A new approach to radiochromic film dosimetry based on non-local means

2020 ◽  
Vol 65 (22) ◽  
pp. 225019
Author(s):  
César Rodríguez ◽  
Alfonso López-Fernández ◽  
Diego García-Pinto
Keyword(s):  
Radiochromic Film ◽  
Film Dosimetry ◽  
New Approach ◽  
Local Means ◽  
Non Local

A new approach to capture heterogeneity in groundwater problem: An illustration with an Earth equation

2019 ◽  
Vol 14 (3) ◽  
pp. 313 ◽  
Author(s):  
Abdon Atangana ◽  
Rubayyi T. Alqahtani
Keyword(s):  
Exact Solution ◽  
Numerical Scheme ◽  
Differential Operators ◽  
New Approach ◽  
Flow Problems ◽  
The Earth ◽  
Time Differential ◽  
Geological Formation ◽  
Non Local ◽  
Real World Problems

One of the major problem faced in modeling groundwater flow problems is perhaps how to capture heterogeneity of the geological formation within which the flow takes place. In this paper, we suggested applied a newly established approach to model real world problems that combines the concept of stochastic modeling in which parameters inputs are converted into distributions and the time differential operator is replaced by non-local differential operators. We illustrated this method with the Earth equation of groundwater recharge. For each case, we provided numerical and exact solution using the newly established numerical scheme and Laplace transform. We presented some numerical simulations. The numerical graphical representations let no doubt to think that this approach is the future way of modeling complex problems.

scholarly journals A New Approach for Linear Eigenvalue Problems and Nonlinear Euler Buckling Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Meltem Evrenosoglu Adiyaman ◽  
Sennur Somali
Keyword(s):  
Eigenvalue Problems ◽  
Liouville Problem ◽  
Numerical Results ◽  
High Order Accuracy ◽  
Order Accuracy ◽  
Eigenvalues And Eigenfunctions ◽  
New Approach ◽  
Euler Buckling ◽  
Large Step ◽  
Sturm Liouville

We propose a numerical Taylor's Decomposition method to compute approximate eigenvalues and eigenfunctions for regular Sturm-Liouville eigenvalue problem and nonlinear Euler buckling problem very accurately for relatively large step sizes. For regular Sturm-Liouville problem, the technique is illustrated with three examples and the numerical results show that the approximate eigenvalues are obtained with high-order accuracy without using any correction, and they are compared with the results of other methods. The numerical results of Euler Buckling problem are compared with theoretical aspects, and it is seen that they agree with each other.

A New Approach for Simultaneous Shape and Topology Optimization Based on Implicit Topology Description Functions

2004 ◽  
Author(s):  
Xu Guo ◽  
Kang Zhao ◽  
Michael Yu Wang
Keyword(s):  
Topology Optimization ◽  
Numerical Experiments ◽  
Shape Derivative ◽  
Structural Topology ◽  
Numerical Instability ◽  
New Approach ◽  
Shape And Topology Optimization ◽  
Topology Description Function ◽  
And Topology ◽  
Non Local

In the present paper, a new approach for structural topology optimization based on implicit topology description function (TDF) is proposed. TDF is used to describe the shape/topology of a structure, which is approximated in terms of the nodal values. Then a relationship is established between the element stiffness and the values of the topology description function on its four nodes. In this way and with some non-local treatments of the design sensitivities, not only the shape derivative but also the topological derivative of the optimal design can be incorporated in the numerical algorithm in a unified way. Numerical experiments demonstrate that by employing this approach, the computational efforts associated with TDF (and level set) based algorithms can be saved. Clear optimal topologies and smooth structural boundaries free from any sign of numerical instability can be obtained simultaneously and efficiently.

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