The Inverse Source Problem in Non-homogeneous Background Media
نویسندگان
چکیده
The scalar wave inverse source problem (ISP) is investigated for the case where the source is embedded in a non-homogeneous medium with known index of refraction proÞle n(r). It is shown that the solution to the ISP having minimum energy (so-called minimum energy source) can be obtained via a simple method of constrained optimization. This method is applied to the special case when the non-homogeneous background is spherically symmetric (n(r) = n(r)) and yields the minimum energy source in terms of a series of spherical harmonics and radial wave functions that are solutions to a Sturm-Liouville problem. The special case of a source embedded in a spherical region of constant index that differs from the background is treated in detail and results from computer simulations are presented for this case.
منابع مشابه
Saint-Venant torsion of non-homogeneous anisotropic bars
The BEM is applied to the solution of the torsion problem of non-homogeneous anisotropic non-circular prismatic bars. The problem is formulated in terms of the warping function. This formulation leads to a second order partial differential equation with variable coefficients, subjected to a generalized Neumann type boundary condition. The problem is solved using the Analog Equation Method (AEM)...
متن کاملInverse Source Problem in Nonhomogeneous Background Media
The scalar wave inverse source problem (ISP) of determining an unknown radiating source from knowledge of the field it generates outside its region of localization is investigated for the case in which the source is embedded in a non-homogeneous medium with known index of refraction profile n(r). It is shown that the solution to the ISP having minimum energy (socalled minimum energy source) can...
متن کاملInverse Source Problem in Nonhomogeneous Background Media. Part II: Vector Formulation and Antenna Substrate Performance Characterization
This paper solves analytically and illustrates numerically the full-vector, electromagnetic inverse source problem of synthesizing an unknown source embedded in a given substrate medium of volume V and radiating a prescribed exterior field. The derived formulation and results generalize previous work on the scalar version of the problem, especially the recent “Part I” paper [A.J. Devaney, E.A. ...
متن کاملNon-Fourier heat conduction equation in a sphere; comparison of variational method and inverse Laplace transformation with exact solution
Small scale thermal devices, such as micro heater, have led researchers to consider more accurate models of heat in thermal systems. Moreover, biological applications of heat transfer such as simulation of temperature field in laser surgery is another pathway which urges us to re-examine thermal systems with modern ones. Non-Fourier heat transfer overcomes some shortcomings of Fourier heat tran...
متن کاملDetermination of a Source Term in an Inverse Heat Conduction Problem by Radial Basis Functions
In this paper, we propose a technique for determining a source term in an inverse heat conduction problem (IHCP) using Radial Basis Functions (RBFs). Because of being very suitable instruments, the RBFs have been applied for solving Partial Dierential Equations (PDEs) by some researchers. In the current study, a stable meshless method will be pro- posed for solving an (I...
متن کامل