Conditionally stable linear problems and the Carleman formula

1991 ◽  
Vol 31 (6) ◽  
pp. 875-880
Author(s):  
L. A. Aizenberg ◽  
N. N. Tarkhanov
Keyword(s):  
Carleman Formula ◽  
Linear Problems ◽  
Stable Linear

Coprime Factorizations in Stable Linear Systems

1988 ◽  
Author(s):  
Charles A. Desoer ◽  
A. Nazli Gundes ◽  
M. Guntekin Kabuli
Keyword(s):  
Linear Systems ◽  
Coprime Factorizations ◽  
Stable Linear

scholarly journals Collocation Methods for High-Order Well-Balanced Methods for Systems of Balance Laws

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1799
Author(s):  
Irene Gómez-Bueno ◽  
Manuel Jesús Castro Díaz ◽  
Carlos Parés ◽  
Giovanni Russo
Keyword(s):  
High Order ◽  
Collocation Methods ◽  
Quadrature Formulas ◽  
Balance Laws ◽  
Source Terms ◽  
Time Step ◽  
Systems Of Balance Laws ◽  
Reconstruction Operator ◽  
Non Linear ◽  
Linear Problems

In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced reconstruction operator. Moreover, they introduced a procedure to modify any standard reconstruction operator, like MUSCL, ENO, CWENO, etc., in order to be well-balanced. This strategy involves a non-linear problem at every cell at every time step that consists in finding the stationary solution whose average is the given cell value. In a recent paper, a fully well-balanced method is presented where the non-linear problems to be solved in the reconstruction procedure are interpreted as control problems. The goal of this paper is to introduce a new technique to solve these local non-linear problems based on the application of the collocation RK methods. Special care is put to analyze the effects of computing the averages and the source terms using quadrature formulas. A general technique which allows us to deal with resonant problems is also introduced. To check the efficiency of the methods and their well-balance property, they have been applied to a number of tests, ranging from easy academic systems of balance laws consisting of Burgers equation with some non-linear source terms to the shallow water equations—without and with Manning friction—or Euler equations of gas dynamics with gravity effects.

scholarly journals Impact of Geometrical Imperfections on Estimation of Buckling and Limit Loads in a Silo Segment Using the Vibration Correlation Technique

Materials ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 567
Author(s):  
Łukasz Żmuda-Trzebiatowski ◽  
Piotr Iwicki
Keyword(s):  
Natural Frequencies ◽  
Vibration Mode ◽  
Mode Shapes ◽  
Correlation Technique ◽  
Limit Loads ◽  
Linear Buckling ◽  
Geometrical Imperfections ◽  
Linear Problems ◽  
Formed Channel ◽  
Corrugated Wall

The paper examines effectiveness of the vibration correlation technique which allows determining the buckling or limit loads by means of measured natural frequencies of structures. A steel silo segment with a corrugated wall, stiffened with cold-formed channel section columns was analysed. The investigations included numerical analyses of: linear buckling, dynamic eigenvalue and geometrically static non-linear problems. Both perfect and imperfect geometries were considered. Initial geometrical imperfections included first and second buckling and vibration mode shapes with three amplitudes. The vibration correlation technique proved to be useful in estimating limit or buckling loads. It was very efficient in the case of small and medium imperfection magnitudes. The significant deviations between the predicted and calculated buckling and limit loads occurred when large imperfections were considered.

Angularly Stable Linear-to-Circular Polarizing Reflectors for Multiple Beam Antennas

2021 ◽  
pp. 1-1
Author(s):  
Salvador Mercader-Pellicer ◽  
Wenxing Tang ◽  
Daniele Bresciani ◽  
Herve Legay ◽  
Nelson J. G. Fonseca ◽  
...  
Keyword(s):  
Multiple Beam ◽  
Stable Linear

Schur complement spectral bounds for large hybrid FETI-DP clusters and huge three-dimensional scalar problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Zdeněk Dostál ◽  
Tomáš Brzobohatý ◽  
Oldřich Vlach
Keyword(s):  
Condition Number ◽  
Three Dimensional ◽  
Schur Complement ◽  
Decomposition Methods ◽  
Stiffness Matrices ◽  
Spectral Bounds ◽  
Schur Complements ◽  
Linear Problems ◽  
Primal Method ◽  
Large Clusters

Abstract Bounds on the spectrum of Schur complements of subdomain stiffness matrices with respect to the interior variables are key ingredients of the convergence analysis of FETI (finite element tearing and interconnecting) based domain decomposition methods. Here we give bounds on the regular condition number of Schur complements of “floating” clusters arising from the discretization of 3D Laplacian on a cube decomposed into cube subdomains. The results show that the condition number of the cluster defined on a fixed domain decomposed into m × m × m cube subdomains connected by face and optionally edge averages increases proportionally to m. The estimates support scalability of unpreconditioned H-FETI-DP (hybrid FETI dual-primal) method. Though the research is most important for the solution of variational inequalities, the results of numerical experiments indicate that unpreconditioned H-FETI-DP with large clusters can be useful also for the solution of huge linear problems.

Submilliamp long-wavelength InP-based vertical-cavity surface-emitting laser with stable linear polarisation

2000 ◽  
Vol 36 (13) ◽  
pp. 1124 ◽  
Author(s):  
M. Ortsiefer ◽  
R. Shau ◽  
M. Zigldrum ◽  
G. Böhm ◽  
F. Köhler ◽  
...  
Keyword(s):  
Cavity Surface ◽  
Long Wavelength ◽  
Vertical Cavity Surface ◽  
Surface Emitting Laser ◽  
Vertical Cavity ◽  
Linear Polarisation ◽  
Stable Linear
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