scholarly journals Generalized combined field integral equations for the iterative solution of the three-dimensional Maxwell equations

2006 ◽  
Vol 19 (8) ◽  
pp. 834-839 ◽  
Author(s):  
Marion Darbas
Keyword(s):  
Integral Equations ◽  
Maxwell Equations ◽  
Three Dimensional ◽  
Iterative Solution ◽  
Field Integral

Electromagnetic modeling of 3-D structures by the method of system iteration using integral equations

Geophysics ◽  
1992 ◽  
Vol 57 (12) ◽  
pp. 1556-1561 ◽  
Author(s):  
Zonghou Xiong
Keyword(s):  
Integral Equations ◽  
Three Dimensional ◽  
Computation Time ◽  
Iterative Solution ◽  
Matrix Inversion ◽  
Electromagnetic Modeling ◽  
Direct Inversion ◽  
Conductivity Structure ◽  
The Matrix ◽  
Earth Conductivity

A new approach for electromagnetic modeling of three‐dimensional (3-D) earth conductivity structures using integral equations is introduced. A conductivity structure is divided into many substructures and the integral equation governing the scattering currents within a substructure is solved by a direct matrix inversion. The influence of all other substructures are treated as external excitations and the solution for the whole structure is then found iteratively. This is mathematically equivalent to partitioning the scattering matrix into many block submatrices and solving the whole system by a block iterative method. This method reduces computer memory requirements since only one submatrix at a time needs to be stored. The diagonal submatrices that require direct inversion are defined by local scatterers only and thus are generally better conditioned than the matrix for the whole structure. The block iterative solution requires much less computation time than direct matrix inversion or conventional point iterative methods as the convergence depends on the number of the submatrices, not on the total number of unknowns in the solution. As the submatrices are independent of each other, this method is suitable for parallel processing.

scholarly journals A TWO-GRID TIME-DEPENDENT FORMALISM FOR THE MAXWELL EQUATION

2003 ◽  
Vol 02 (04) ◽  
pp. 537-546 ◽  
Author(s):  
DANIEL NEUHAUSER ◽  
ROI BAER
Keyword(s):  
Maxwell Equations ◽  
Three Dimensional ◽  
Reaction Dynamics ◽  
Iterative Solution ◽  
Time Dependent ◽  
Scattering Problems ◽  
One Dimensional ◽  
Initial Wave ◽  
Chemical Reaction Dynamics ◽  
Iterative Solutions

We develop a formalism for efficient iterative solutions of scattering problems involving the Maxwell equations. The methods, borrowed from recent advancements in chemical reaction dynamics, represent the scattering wavefunctions on two grids; one used for the initial wave and is one-dimensional; the other is a small three-dimensional grid padded with absorbing-potentials on which the scattered function is represented. The formalism is automatically suitable for scattering studies of transmission, reflection and scattering components of a wave. The simulations can be done with time-dependent wavepackets or direct iterative solution for the Green's function, but the results are rigorous time-independent (frequency-dependent) scattering amplitudes. Model time-dependent simulations involving up to a 100×100×100 grid for the inner wavefunction were numerically done on a simple PC.

scholarly journals Explicitly covariant form of the integral Maxwell equations

2021 ◽  
Vol 18 (1) ◽  
pp. 76
Author(s):  
J. L. Jiménez ◽  
G. Monsivais
Keyword(s):  
Integral Equations ◽  
Maxwell Equations ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Space Time ◽  
Covariant Form ◽  
Vector Form ◽  
Integral Forms ◽  
Dimensional Space Time ◽  
Three Dimensional Space

It is analyzed in detail the covariance of the integral forms of the Maxwell Equations. Different forms of writing the integral Maxwell equations in explicitly covariant form are analyzed. First we show how one of these ways can be obtained from the differential Maxwell equations, both from their usual three vector form as from their covariant four vector form. Then we discuss how this covariant integral Maxwell equations can be obtained from usual integral Maxwell equations. It is emphasized the necessity to write the usual integral equations without time derivatives. The integrations regions in the three-dimensional space and time are identified with parts of the same hyper-surface in four-dimensional space-time. This point is carefully analyzed.  Later we discuss other forms of the integral Maxwell equations. We show how these new versions can be expressed in an explicitly covariant form. 

Boundary Condition Design to Heat a Moving Object at Uniform Transient Temperature Using Inverse Formulation

2004 ◽  
Vol 126 (3) ◽  
pp. 619-626 ◽  
Author(s):  
Hakan Ertu¨rk ◽  
Ofodike A. Ezekoye ◽  
John R. Howell
Keyword(s):  
Boundary Condition ◽  
Temperature Distribution ◽  
Design Problem ◽  
Manufacturing Industry ◽  
Three Dimensional ◽  
Chemical Deposition ◽  
Iterative Solution ◽  
Conveyor Belt ◽  
Temperature History ◽  
Transient Temperature

The boundary condition design of a three-dimensional furnace that heats an object moving along a conveyor belt of an assembly line is considered. A furnace of this type can be used by the manufacturing industry for applications such as industrial baking, curing of paint, annealing or manufacturing through chemical deposition. The object that is to be heated moves along the furnace as it is heated following a specified temperature history. The spatial temperature distribution on the object is kept isothermal through the whole process. The temperature distribution of the heaters of the furnace should be changed as the object moves so that the specified temperature history can be satisfied. The design problem is transient where a series of inverse problems are solved. The process furnace considered is in the shape of a rectangular tunnel where the heaters are located on the top and the design object moves along the bottom. The inverse design approach is used for the solution, which is advantageous over a traditional trial-and-error solution where an iterative solution is required for every position as the object moves. The inverse formulation of the design problem is ill-posed and involves a set of Fredholm equations of the first kind. The use of advanced solvers that are able to regularize the resulting system is essential. These include the conjugate gradient method, the truncated singular value decomposition or Tikhonov regularization, rather than an ordinary solver, like Gauss-Seidel or Gauss elimination.

scholarly journals Imaging of bi-anisotropic periodic structures from electromagnetic near-field data

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dinh-Liem Nguyen ◽  
Trung Truong
Keyword(s):  
Inverse Scattering ◽  
Maxwell Equations ◽  
Field Data ◽  
Periodic Structures ◽  
Near Field ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Factorization Method ◽  
Unique Determination

AbstractThis paper is concerned with the inverse scattering problem for the three-dimensional Maxwell equations in bi-anisotropic periodic structures. The inverse scattering problem aims to determine the shape of bi-anisotropic periodic scatterers from electromagnetic near-field data at a fixed frequency. The factorization method is studied as an analytical and numerical tool for solving the inverse problem. We provide a rigorous justification of the factorization method which results in the unique determination and a fast imaging algorithm for the periodic scatterer. Numerical examples for imaging three-dimensional periodic structures are presented to examine the efficiency of the method.

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