PML’s Optimal Choice in Solving Helmholtz Equation

2010 ◽  
Vol 39 ◽  
pp. 312-316
Author(s):  
Bo Zhang
Keyword(s):  
Boundary Conditions ◽  
Helmholtz Equation ◽  
Numerical Experiments ◽  
Accurate Result ◽  
Perfectly Matched Layer ◽  
Optimal Choice

To solve truncation questions of calculation area(unbounded) of Helmhotlz equation, Berenger first proposed concept of Perfectly Matched Layer(PML) in 1994, the method optimizes boundary conditions and reduces computation quantities greatly. By choosing constants p,d,e of PML parameters , we obtain an optimal PML parameter in this paper . The final numerical experiments show that the result obtained by the PML parameter is almost same as accurate result of references [4].

scholarly journals Analysis of Dirichlet–Robin Iterations for Solving the Cauchy Problem for Elliptic Equations

2020 ◽  
Author(s):  
Pauline Achieng ◽  
Fredrik Berntsson ◽  
Jennifer Chepkorir ◽  
Vladimir Kozlov
Keyword(s):  
Cauchy Problem ◽  
Boundary Conditions ◽  
Helmholtz Equation ◽  
Iterative Algorithm ◽  
Elliptic Equations ◽  
Numerical Experiments ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
General Elliptic ◽  
The Cauchy Problem

Abstract The Cauchy problem for general elliptic equations of second order is considered. In a previous paper (Berntsson et al. in Inverse Probl Sci Eng 26(7):1062–1078, 2018), it was suggested that the alternating iterative algorithm suggested by Kozlov and Maz’ya can be convergent, even for large wavenumbers $$k^2$$ k 2 , in the Helmholtz equation, if the Neumann boundary conditions are replaced by Robin conditions. In this paper, we provide a proof that shows that the Dirichlet–Robin alternating algorithm is indeed convergent for general elliptic operators provided that the parameters in the Robin conditions are chosen appropriately. We also give numerical experiments intended to investigate the precise behaviour of the algorithm for different values of $$k^2$$ k 2 in the Helmholtz equation. In particular, we show how the speed of the convergence depends on the choice of Robin parameters.

scholarly journals Antireflective Boundary Conditions for Deblurring Problems

2010 ◽  
Vol 2010 ◽  
pp. 1-18 ◽  
Author(s):  
Marco Donatelli ◽  
Stefano Serra-Capizzano
Keyword(s):  
Boundary Conditions ◽  
Linear Algebra ◽  
Numerical Experiments ◽  
Computational Cost ◽  
Optimal Choice ◽  
Survey Paper ◽  
Previous Statement ◽  
Conclusion Section ◽  
The Given

This survey paper deals with the use of antireflective boundary conditions for deblurring problems where the issues that we consider are the precision of the reconstruction when the noise is not present, the linear algebra related to these boundary conditions, the iterative and noniterative regularization solvers when the noise is considered, both from the viewpoint of the computational cost and from the viewpoint of the quality of the reconstruction. In the latter case, we consider a reblurring approach that replaces the transposition operation with correlation. For many of the considered items, the anti-reflective algebra coming from the given boundary conditions is the optimal choice. Numerical experiments corroborating the previous statement and a conclusion section end the paper.

LOCAL HIGH-ORDER ABSORBING BOUNDARY CONDITIONS FOR TIME-DEPENDENT WAVES IN GUIDES

2007 ◽  
Vol 15 (01) ◽  
pp. 1-22 ◽  
Author(s):  
THOMAS HAGSTROM ◽  
MANUELA L. DE CASTRO ◽  
DAN GIVOLI ◽  
DINA TZEMACH
Keyword(s):  
Boundary Conditions ◽  
Numerical Experiments ◽  
Optimal Choice ◽  
Absorbing Boundary Conditions ◽  
High Order ◽  
Time Dependent ◽  
Time Varying ◽  
Scalar Wave ◽  
Absorbing Boundary ◽  
Free Parameters

The scalar wave equation in a two-dimensional semi-infinite wave guide is considered. The recently proposed Hagstrom–Warburton (H–W) local high-order absorbing boundary conditions (ABCs), which are based on a modification of the Higdon ABCs, are presented in this context. The P-order ABC involves the free parameters 0 < aj ≤ 1, for j = 0, 1, …, P, which have to be chosen. The choice aj = 1 for all j is shown to be satisfactory, in general, although not necessarily optimal. The optimal choice of the parameters is discussed via both theoretical analysis and numerical experiments. In addition, an adaptive scheme which controls the time-varying values of P and aj is presented and tested.

scholarly journals Atmospheric radiation boundary conditions for the Helmholtz equation

2018 ◽  
Vol 52 (3) ◽  
pp. 945-964 ◽  
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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