scholarly journals Numerical tests of evolution systems, gauge conditions, and boundary conditions for 1D colliding gravitational plane waves

2002 ◽  
Vol 65 (6) ◽  
Author(s):  
J. M. Bardeen ◽  
L. T. Buchman
Keyword(s):  
Boundary Conditions ◽  
Plane Waves ◽  
Numerical Tests ◽  
Evolution Systems ◽  
Gauge Conditions

Linear Stability of a Plasma Diode

1969 ◽  
Vol 24 (8) ◽  
pp. 1235-1243 ◽  
Author(s):  
M Dobrowolny ◽  
F Engelmann ◽  
A Sestero
Keyword(s):  
Boundary Conditions ◽  
Linear Stability ◽  
Plane Waves ◽  
The Other ◽  
Other Hand ◽  
Free Particles ◽  
Plasma Diode ◽  
The Stability

AbstractThe stability of a plasma diode with respect to longitudinal oscillations is investigated. If there are free particles emitted by the electrodes, the perturbations do not have the same dynamics as they would in an infinite plasma, contrary to the case where only particles trapped in the diode are present. This can be interpreted as due to a coupling of plane waves of different wave lengths, introduced by the boundary conditions at the electrodes. The occurrence of resonant-particle effects, on the other hand, is subjected to precisely the same conditions as in an infinite plasma.

ABSORBING BOUNDARY CONDITIONS IN BLOCK GAUSS–SEIDEL METHODS FOR CONVECTION PROBLEMS

1996 ◽  
Vol 06 (04) ◽  
pp. 481-502 ◽  
Author(s):  
FREDERIC NATAF
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary ◽  
Convection Diffusion ◽  
Radiation Boundary Conditions ◽  
Convection Diffusion Equation ◽  
Numerical Tests ◽  
Radiation Boundary ◽  
Theoretical Results

In the context of convection-diffusion equation, the use of absorbing boundary conditions (also called radiation boundary conditions) is considered in block Gauss–Seidel algorithms. Theoretical results and numerical tests show that the convergence is thus accelerated.

Absorbing boundary conditions for acoustic media

Geophysics ◽  
1985 ◽  
Vol 50 (6) ◽  
pp. 892-902 ◽  
Author(s):  
R. G. Keys
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Plane Waves ◽  
Basic Element ◽  
Absorbing Boundary Conditions ◽  
Boundary Operator ◽  
Order Differential Operator ◽  
Absorbing Boundary ◽  
Boundary Operators

By decomposing the acoustic wave equation into incoming and outgoing components, an absorbing boundary condition can be derived to eliminate reflections from plane waves according to their direction of propagation. This boundary condition is characterized by a first‐order differential operator. The differential operator, or absorbing boundary operator, is the basic element from which more complicated boundary conditions can be constructed. The absorbing boundary operator can be designed to absorb perfectly plane waves traveling in any two directions. By combining two or more absorption operators, boundary conditions can be created which absorb plane waves propagating in any number of directions. Absorbing boundary operators simplify the task of designing boundary conditions to reduce the detrimental effects of outgoing waves in many wave propagation problems.

FACTORIZATION OF THE CONVECTION-DIFFUSION OPERATOR AND THE SCHWARZ ALGORITHM

1995 ◽  
Vol 05 (01) ◽  
pp. 67-93 ◽  
Author(s):  
F. NATAF ◽  
F. ROGIER
Keyword(s):  
Boundary Conditions ◽  
Rate Of Convergence ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Interface Conditions ◽  
Diffusion Operator ◽  
Convection Diffusion ◽  
Numerical Tests ◽  
Schwarz Algorithm ◽  
Theoretical Results

In the original Schwarz algorithm, Dirichlet boundary conditions are used as interface conditions. We consider the use of the operators arising from the factorization of the convection-diffusion operator as transmission conditions. The rate of convergence is then significantly higher. Theoretical results are proven and numerical tests are shown.

scholarly journals One- and Multi-dimensional CWENOZ Reconstructions for Implementing Boundary Conditions Without Ghost Cells

2021 ◽  
Author(s):  
M. Semplice ◽  
E. Travaglia ◽  
G. Puppo
Keyword(s):  
Boundary Conditions ◽  
The Novel ◽  
Two Dimensional ◽  
Finite Volume Schemes ◽  
Third Order ◽  
One Dimensional ◽  
Numerical Tests ◽  
Ghost Cells ◽  
The One ◽  
Appl Math

AbstractWe address the issue of point value reconstructions from cell averages in the context of third-order finite volume schemes, focusing in particular on the cells close to the boundaries of the domain. In fact, most techniques in the literature rely on the creation of ghost cells outside the boundary and on some form of extrapolation from the inside that, taking into account the boundary conditions, fills the ghost cells with appropriate values, so that a standard reconstruction can be applied also in the boundary cells. In Naumann et al. (Appl. Math. Comput. 325: 252–270. 10.1016/j.amc.2017.12.041, 2018), motivated by the difficulty of choosing appropriate boundary conditions at the internal nodes of a network, a different technique was explored that avoids the use of ghost cells, but instead employs for the boundary cells a different stencil, biased towards the interior of the domain. In this paper, extending that approach, which does not make use of ghost cells, we propose a more accurate reconstruction for the one-dimensional case and a two-dimensional one for Cartesian grids. In several numerical tests, we compare the novel reconstruction with the standard approach using ghost cells.

scholarly journals PARTIAL WAVE BASIS ADAPTED TO EXTERIOR BOUNDARY CONDITIONS OF AN ELASTIC PLATE

2021 ◽  
Vol 20 (1) ◽  
pp. 35-43
Author(s):  
Sergiu Cojocaru ◽  
Keyword(s):  
Boundary Conditions ◽  
Elastic Plate ◽  
Functional Form ◽  
Standard Treatment ◽  
Plane Waves ◽  
Equation Of Motion ◽  
Elastic Vibration ◽  
Vibration Modes ◽  
Elastic Plates ◽  
Partial Waves

An approach to describing normal elastic vibration modes in confined systems is presented. In a standard treatment of the problem, the displacement field is represented by a superposition of partial waves of a general form, e.g., plane waves. The unknown coefficients of superposition are then obtained from the equation of motion and the full set of boundary conditions. In the proposed approach, the functional form of partial waves is chosen in such a way as to satisfy the boundary conditions on exterior surfaces identically, i.e., even if the unknown quantities determined by the remaining constraints are found in an approximation, numerically or analytically. Some examples of solutions for composite elastic plates are discussed to illustrate the efficiency of the approach and its relevance for applications.

scholarly journals Sweeping preconditioners for stratified media in the presence of reflections

2020 ◽  
Vol 1 (4) ◽  
Author(s):  
Janosch Preuß ◽  
Thorsten Hohage ◽  
Christoph Lehrenfeld
Keyword(s):  
Boundary Conditions ◽  
Harmonic Wave ◽  
Absorbing Boundary Conditions ◽  
Stratified Medium ◽  
Stratified Media ◽  
Absorbing Boundary ◽  
Small Perturbations ◽  
Numerical Tests ◽  
Time Harmonic ◽  
Dirichlet To Neumann Operator

Abstract In this paper we consider sweeping preconditioners for time harmonic wave propagation in stratified media, especially in the presence of reflections. In the most famous class of sweeping preconditioners Dirichlet-to-Neumann operators for half-space problems are approximated through absorbing boundary conditions. In the presence of reflections absorbing boundary conditions are not accurate resulting in an unsatisfactory performance of these sweeping preconditioners. We explore the potential of using more accurate Dirichlet-to-Neumann operators within the sweep. To this end, we make use of the separability of the equation for the background model. While this improves the accuracy of the Dirichlet-to-Neumann operator, we find both from numerical tests and analytical arguments that it is very sensitive to perturbations in the presence of reflections. This implies that even if accurate approximations to Dirichlet-to-Neumann operators can be devised for a stratified medium, sweeping preconditioners are limited to very small perturbations.

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