Numerical Methods for the Helmholtz Equation with Non-Reflecting Boundary Conditions in Exterior Domains

The paper presents some theoretical and practical issues, particularly useful to users of numerical methods, especially finite element method for the behaviour modelling of the foam materials. Given the characteristics of specific behaviour of the foam materials, the requirement which has to be taken into consideration is the compression, inclusive impact with bodies more rigid then a foam material, when this is used alone or in combination with other materials in the form of composite laminated with various boundary conditions. The results and conclusions presented in this paper are the results of our investigations in the field and relates to the use of LS-Dyna program, but many observations, findings and conclusions, have a general character, valid for use of any numerical analysis by FEM programs.

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Non-Deteriorating Numerical Methods and Artificial Boundary Conditions for the Long-Term Integration of Maxwell's Equations

10.21236/ada427296 ◽

2004 ◽

Author(s):

Semyon T. Tsynkov

Keyword(s):

Numerical Methods ◽

Boundary Conditions ◽

Maxwell’S Equations ◽

Maxwell's Equations ◽

Artificial Boundary ◽

Artificial Boundary Conditions

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L p ‐estimates of the Stokes resolvent with nonhomogeneous Dirichlet boundary conditions in 3D exterior domains

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.7624 ◽

2021 ◽

Author(s):

Paul Deuring

Keyword(s):

Boundary Conditions ◽

Dirichlet Boundary ◽

Dirichlet Boundary Conditions ◽

Exterior Domains

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Atmospheric radiation boundary conditions for the Helmholtz equation

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2017059 ◽

2018 ◽

Vol 52 (3) ◽

pp. 945-964 ◽

Cited By ~ 4

Author(s):

Hélène Barucq ◽

Juliette Chabassier ◽

Marc Duruflé ◽

Laurent Gizon ◽

Michael Leguèbe

Keyword(s):

Boundary Conditions ◽

Helmholtz Equation ◽

Acoustic Waves ◽

Numerical Study ◽

Outgoing Wave ◽

Atmospheric Radiation ◽

Angle Of Incidence ◽

Radiation Boundary Conditions ◽

Radiation Boundary ◽

Dirichlet To Neumann Map

This work offers some contributions to the numerical study of acoustic waves propagating in the Sun and its atmosphere. The main goal is to provide boundary conditions for outgoing waves in the solar atmosphere where it is assumed that the sound speed is constant and the density decays exponentially with radius. Outgoing waves are governed by a Dirichlet-to-Neumann map which is obtained from the factorization of the Helmholtz equation expressed in spherical coordinates. For the purpose of extending the outgoing wave equation to axisymmetric or 3D cases, different approximations are implemented by using the frequency and/or the angle of incidence as parameters of interest. This results in boundary conditions called atmospheric radiation boundary conditions (ARBC) which are tested in ideal and realistic configurations. These ARBCs deliver accurate results and reduce the computational burden by a factor of two in helioseismology applications.

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