Exact Controllability to Solve the Helmholtz Equation with Absorbing Boundary Conditions

2016 ◽  
pp. 107-122
Keyword(s):  
Boundary Conditions ◽  
Helmholtz Equation ◽  
Exact Controllability ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary

OPTIMAL CONVERGENCE OF NON-OVERLAPPING SCHWARZ METHODS FOR THE HELMHOLTZ EQUATION

2005 ◽  
Vol 13 (03) ◽  
pp. 525-545 ◽  
Author(s):  
FRÉDÉRIC MAGOULÈS ◽  
ROMAN PUTANOWICZ
Keyword(s):  
Boundary Conditions ◽  
Helmholtz Equation ◽  
Absorbing Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Absorbing Boundary ◽  
Comparative Performance ◽  
Schwarz Method ◽  
Wide Range ◽  
Schwarz Algorithm ◽  
Overlapping Schwarz

The non-overlapping Schwarz method with absorbing boundary conditions instead of the Dirichlet boundary conditions is an efficient variant of the overlapping Schwarz method for the Helmholtz equation. These absorbing boundary conditions defined on the interface between the subdomains are the key ingredients to obtain a fast convergence of the iterative Schwarz algorithm. In a one-way subdomains splitting, non-local optimal absorbing boundary conditions can be obtained and leads to the convergence of the Schwarz algorithm in a number of iterations equal to the number of subdomains minus one. This paper investigates different local approximations of these optimal absorbing boundary conditions for finite element computations in acoustics. Different approaches are presented both in the continuous and in the discrete analysis, including high-order optimized continuous absorbing boundary conditions, and discrete absorbing boundary conditions based on algebraic approximation. A wide range of new numerical experiments performed on unbounded acoustics problems demonstrate the comparative performance and the robustness of the proposed methods on general unstructured mesh partitioning.

Toward perfectly absorbing boundary conditions for Euler equations

AIAA Journal ◽  
1999 ◽  
Vol 37 ◽  
pp. 912-918
Author(s):  
M. E. Hayder ◽  
Fang Q. Hu ◽  
M. Y. Hussaini
Keyword(s):  
Boundary Conditions ◽  
Euler Equations ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary

scholarly journals Dirichlet absorbing boundary conditions for classical and peridynamic diffusion-type models

2020 ◽  
Vol 66 (4) ◽  
pp. 773-793 ◽  
Author(s):  
Arman Shojaei ◽  
Alexander Hermann ◽  
Pablo Seleson ◽  
Christian J. Cyron
Keyword(s):  
Boundary Conditions ◽  
Materials Science ◽  
Unbounded Domains ◽  
Diffusion Models ◽  
Absorbing Boundary Conditions ◽  
The Finite Element Method ◽  
Absorbing Boundary ◽  
Diffusion Type ◽  
2D And 3D ◽  
Accuracy And Stability

Abstract Diffusion-type problems in (nearly) unbounded domains play important roles in various fields of fluid dynamics, biology, and materials science. The aim of this paper is to construct accurate absorbing boundary conditions (ABCs) suitable for classical (local) as well as nonlocal peridynamic (PD) diffusion models. The main focus of the present study is on the PD diffusion formulation. The majority of the PD diffusion models proposed so far are applied to bounded domains only. In this study, we propose an effective way to handle unbounded domains both with PD and classical diffusion models. For the former, we employ a meshfree discretization, whereas for the latter the finite element method (FEM) is employed. The proposed ABCs are time-dependent and Dirichlet-type, making the approach easy to implement in the available models. The performance of the approach, in terms of accuracy and stability, is illustrated by numerical examples in 1D, 2D, and 3D.

Absorbing boundary conditions for the TLM method

1992 ◽  
Vol 40 (11) ◽  
pp. 2095-2099 ◽  
Author(s):  
J.A. Morente ◽  
J.A. Porti ◽  
M. Khalladi
Keyword(s):  
Boundary Conditions ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary ◽  
Tlm Method
Sign in / Sign up

Export Citation Format

Share Document