Lattice Function for the Iterated Helmholtz Operator

2011 ◽  
pp. 270-291
Keyword(s):  
Helmholtz Operator ◽  
Lattice Function

scholarly journals Cramér-Rao Bound Study of Multiple Scattering Effects in Target Separation Estimation

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Edwin A. Marengo ◽  
Paul Berestesky
Keyword(s):  
Multiple Scattering ◽  
Born Approximation ◽  
Single Scattering ◽  
Scattering Data ◽  
Approximation Model ◽  
Scattering Parameters ◽  
Helmholtz Operator ◽  
Scattering Effects ◽  
Cramer Rao Bound ◽  
Multiple Scattering Effects

The information about the distance of separation between two-point targets that is contained in scattering data is explored in the context of the scalar Helmholtz operator via the Fisher information and associated Cramér-Rao bound (CRB) relevant to unbiased target separation estimation. The CRB results are obtained for the exact multiple scattering model and, for reference, also for the single scattering or Born approximation model applicable to weak scatterers. The effects of the sensing configuration and the scattering parameters in target separation estimation are analyzed. Conditions under which the targets' separation cannot be estimated are discussed for both models. Conditions for multiple scattering to be useful or detrimental to target separation estimation are discussed and illustrated.

scholarly journals A Numerical Method for SolvingTwo-Dimensional Nonlinear Parabolic ProblemsBased on a Preconditioning Operator

2020 ◽  
Vol 25 (4) ◽  
pp. 531-545
Author(s):  
Amir Hossein Salehi Shayegan ◽  
Ali Zakeri ◽  
Seyed Mohammad Hosseini
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Parabolic Problem ◽  
Time Variable ◽  
Two Dimensional ◽  
Helmholtz Operator ◽  
Mesh Free ◽  
Nonlinear Parabolic ◽  
Spline Finite Element ◽  
Mesh Free Method

This article considers a nonlinear system of elliptic problems, which is obtained by discretizing the time variable of a two-dimensional nonlinear parabolic problem. Since the system consists of ill-conditioned problems, therefore a stabilized, mesh-free method is proposed. The method is based on coupling the preconditioned Sobolev space gradient method and WEB-spline finite element method with Helmholtz operator as a preconditioner. The convergence and error analysis of the method are given. Finally, a numerical example is solved by this preconditioner to show the efficiency and accuracy of the proposed methods.

Automatic differentiation and lattice function matching

1997 ◽  
Author(s):  
Jean-François Ostiguy ◽  
Leo Michelotti ◽  
James A. Holt
Keyword(s):  
Automatic Differentiation ◽  
Lattice Function

scholarly journals A computing method for bending problem of thin plate on Pasternak foundation

2020 ◽  
Vol 12 (7) ◽  
pp. 168781402093933
Author(s):  
Jiarong Gan ◽  
Hong Yuan ◽  
Shanqing Li ◽  
Qifeng Peng ◽  
Huanliang Zhang
Keyword(s):  
Boundary Conditions ◽  
Helmholtz Equation ◽  
Integral Equations ◽  
Thin Plate ◽  
Laplace Equation ◽  
Two Dimensional ◽  
Pasternak Foundation ◽  
Helmholtz Operator ◽  
Numerical Computing ◽  
Matlab Programming

The governing equation of the bending problem of simply supported thin plate on Pasternak foundation is degraded into two coupled lower order differential equations using the intermediate variable, which are a Helmholtz equation and a Laplace equation. A new solution of two-dimensional Helmholtz operator is proposed as shown in Appendix 1. The R-function and basic solutions of two-dimensional Helmholtz operator and Laplace operator are used to construct the corresponding quasi-Green function. The quasi-Green’s functions satisfy the homogeneous boundary conditions of the problem. The Helmholtz equation and Laplace equation are transformed into integral equations applying corresponding Green’s formula, the fundamental solution of the operator, and the boundary condition. A new boundary normalization equation is constructed to ensure the continuity of the integral kernels. The integral equations are discretized into the nonhomogeneous linear algebraic equations to proceed with numerical computing. Some numerical examples are given to verify the validity of the proposed method in calculating the problem with simple boundary conditions and polygonal boundary conditions. The required results are obtained through MATLAB programming. The convergence of the method is discussed. The comparison with the analytic solution shows a good agreement, and it demonstrates the feasibility and efficiency of the method in this article.

Dirichlet-Type Problems for the Two-Dimensional Helmholtz Operator in Complex Quaternionic Analysis

2016 ◽  
Vol 13 (6) ◽  
pp. 4901-4916 ◽  
Author(s):  
Juan Bory-Reyes ◽  
Ricardo Abreu-Blaya ◽  
Luis M. Hernández-Simon ◽  
Baruch Schneider
Keyword(s):  
Quaternionic Analysis ◽  
Two Dimensional ◽  
Helmholtz Operator ◽  
Dirichlet Type
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