Engineering topics

Volakis, John L.

Publications and source records attributed to Volakis, John L..

At least 73 records · Page 4

NASA NTRS1991

A new technique for simulating composite material

This project dealt with the development on new methodologies and algorithms for the multi-spectrum electromagnetic characterization of large scale nonmetallic airborne vehicles and structures. A robust, low memory, and accurate methodology was developed which is particularly suited for modern machine architectures. This is a hybrid finite element method that combines two well known numerical solution approaches. That of the finite element method for modeling volumes and the boundary integral method which yields exact boundary conditions for terminating the finite element mesh. In addition, a variety of high frequency results were generated (such as diffraction coefficients for impedance surfaces and material layers) and a class of boundary conditions were developed which hold promise for more efficient simulations. During the course of this project, nearly 25 detailed research reports were generated along with an equal number of journal papers. The reports, papers, and journal articles are listed in the appendices along with their abstracts.

Volakis, John L.↗

NASA NTRS1991

Use of edge-based finite elements for solving three dimensional scattering problems

Edge based finite elements are free from drawbacks associated with node based vectorial finite elements and are, therefore, ideal for solving 3-D scattering problems. The finite element discretization using edge elements is checked by solving for the resonant frequencies of a closed inhomogeneously filled metallic cavity. Great improvements in accuracy are observed when compared to the classical node based approach with no penalty in terms of computational time and with the expected absence of spurious modes. A performance comparison between the edge based tetrahedra and rectangular brick elements is carried out and tetrahedral elements are found to be more accurate than rectangular bricks for a given storage intensity. A detailed formulation for the scattering problem with various approaches for terminating the finite element mesh is also presented.

Chatterjee, A.↗

NASA NTRS1991

A finite element-boundary integral method for scattering and radiation by two- and three-dimensional structures

A review of a hybrid finite element-boundary integral formulation for scattering and radiation by two- and three-composite structures is presented. In contrast to other hybrid techniques involving the finite element method, the proposed one is in principle exac, and can be implemented using a low O(N) storage. This is of particular importance for large scale applications and is a characteristic of the boundary chosen to terminate the finite-element mesh, usually as close to the structure as possible. A certain class of these boundaries lead to convolutional boundary integrals which can be evaluated via the fast Fourier transform (FFT) without a need to generate a matrix; thus, retaining the O(N) storage requirement.

Jin, Jian-Ming↗

NASA NTRS1991

Applications of the conjugate gradient FFT method in scattering and radiation including simulations with impedance boundary conditions

The theoretical and computational aspects related to the application of the Conjugate Gradient FFT (CGFFT) method in computational electromagnetics are examined. The advantages of applying the CGFFT method to a class of large scale scattering and radiation problems are outlined. The main advantages of the method stem from its iterative nature which eliminates a need to form the system matrix (thus reducing the computer memory allocation requirements) and guarantees convergence to the true solution in a finite number of steps. Results are presented for various radiators and scatterers including thin cylindrical dipole antennas, thin conductive and resistive strips and plates, as well as dielectric cylinders. Solutions of integral equations derived on the basis of generalized impedance boundary conditions (GIBC) are also examined. The boundary conditions can be used to replace the profile of a material coating by an impedance sheet or insert, thus, eliminating the need to introduce unknown polarization currents within the volume of the layer. A general full wave analysis of 2-D and 3-D rectangular grooves and cavities is presented which will also serve as a reference for future work.

Barkeshli, Kasra↗

NASA NTRS1991

A finite element-boundary integral method for scattering and radiation by two- and three-dimensional structures

A review of a hybrid finite element-boundary integral formulation for scattering and radiation by two- and three-dimensional composite structures is presented. In contrast to other hybrid techniques involving the finite element method, the proposed one is in principle exact and can be implemented using a low O(N) storage. This is of particular importance for large scale applications and is a characteristic of the boundary chosen to terminate the finite element mesh, usually as close to the structure as possible. A certain class of these boundaries lead to convolutional boundary integrals which can be evaluated via the fast Fourier transform (FFT) without a need to generate a matrix; thus, retaining the O(N) storage requirement. The paper begins with a general description of the method. A number of two- and three-dimensional applications are then given, including numerical computations which demonstrate the method's accuracy, efficiency, and capability.

Jin, Jian-Ming↗

NASA NTRS1991

Task reports on developing techniques for scattering by 3D composite structures and to generate new solutions in diffraction theory using higher order boundary conditions

There are two tasks described in this report. First, an extension of a two dimensional formulation is presented for a three dimensional body of revolution. A Fourier series expansion of the vector electric and magnetic fields is employed to reduce the dimensionality of the system, and an exact boundary condition is employed to terminate the mesh. The mesh termination boundary is chosen such that it leads to convolutional boundary operators for low O(n) memory demand. Second, rigorous uniform geometrical theory of diffraction (UTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. Ray solutions are obtained which remain valid in the transition region and reduce uniformly those in the deep lit and shadow regions. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder.

Volakis, John L.↗

NASA NTRS1991

A finite element conjugate gradient FFT method for scattering

Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.

Collins, Jeffery D.↗

NASA NTRS1991

Analytical solutions with Generalized Impedance Boundary Conditions (GIBC)

Rigorous uniform geometrical theory of diffraction (UTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. In particular, ray solutions are obtained which remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. These involve new transition functions in place of the usual Fock-type integrals, characteristics to the impedance cylinder. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. The diffraction coefficients for the convex cylinder are obtained via a generalization of the corresponding ones for the circular cylinder.

Syed, H. H.↗

NASA NTRS1991

High frequency scattering by a smooth coated cylinder simulated with generalized impedance boundary conditions

Rigorous uniform geometrical theory of diffraction (UGTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. In particular, ray solutions are obtained which remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. These involve new transition functions in place of the usual Fock-type integrals, characteristic to the impedance cylinder. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. As usual, the diffraction coefficients for the convex cylinder are obtained via a generalization of the corresponding ones for the circular cylinder.

Syed, Hasnain H.↗

NASA NTRS1991

A combined finite element-boundary element formulation for solution of axially symmetric bodies

A new method is presented for the computation of electromagnetic scattering from axially symmetric bodies. To allow the simulation of inhomogeneous cross sections, the method combines the finite element and boundary element techniques. Interior to a fictitious surface enclosing the scattering body, the finite element method is used which results in a sparce submatrix, whereas along the enclosure the Stratton-Chu integral equation is enforced. By choosing the fictitious enclosure to be a right circular cylinder, most of the resulting boundary integrals are convolutional and may therefore be evaluated via the FFT with which the system is iteratively solved. In view of the sparce matrix associated with the interior fields, this reduces the storage requirement of the entire system to O(N) making the method attractive for large scale computations. The details of the corresponding formulation and its numerical implementation are described.

Collins, Jeffrey D.↗

NASA NTRS1991

A finite-element-boundary integral formulation for scattering by three-dimensional cavity-backed apertures

A numerical technique is proposed for the electromagnetic characterization of the scattering by a three-dimensional cavity-backed aperture in an infinite ground plane. The technique combines the finite element and boundary integral methods to formulate a system of equations for the solution of the aperture fields and those inside the cavity. Specifically, the finite element method is used to formulate the fields in the cavity region and the boundary integral approach is used in conjunction with the equivalence principle to represent the fields above the ground plane. Unlike traditional approaches, the proposed technique does not require a knowledge of the cavity's Green's function and is, therefore, applicable to arbitrary shape depressions and material fillings. Furthermore, the proposed formulation leads to a system having a partly full and partly sparse as well as symmetric and banded matrix which can be solved efficiently using special algorithms.

Jin, Jian-Ming↗

NASA NTRS1990

A combined finite element-boundary integral formulation for solution of two-dimensional scattering problems via CGFFT

A new technique is presented for computing the scattering by 2-D structures of arbitrary composition. The proposed solution approach combines the usual finite element method with the boundary-integral equation to formulate a discrete system. This is subsequently solved via the conjugate gradient (CG) algorithm. A particular characteristic of the method is the use of rectangular boundaries to enclose the scatterer. Several of the resulting boundary integrals are therefore convolutions and may be evaluated via the fast Fourier transform (FFT) in the implementation of the CG algorithm. The solution approach offers the principal advantage of having O(N) memory demand and employs a 1-D FFT versus a 2-D FFT as required with a traditional implementation of the CGFFT algorithm. The speed of the proposed solution method is compared with that of the traditional CGFFT algorithm, and results for rectangular bodies are given and shown to be in excellent agreement with the moment method.

Collins, Jeffery D.↗

NASA NTRS1990

Electromagnetic scattering from two-dimensional thick material junctions

The problem of the plane wave diffraction is examined by an arbitrary symmetric two dimensional junction, where Generalized Impedance Boundary Conditions (GIBCs) and Generalized Sheet Transition Conditions (GSTCs) are employed to simulate the slabs. GIBCs and GSTCs are constructed for multilayer planar slabs of arbitrary thickness and the resulting GIBC/GSTC reflection coefficients are compared with exact counterparts to evaluate the GIBCs/GSTCs. The plane wave diffraction by a multilayer material slab recessed in a perfectly conducting ground plane is formulated and solved via the Generalized Scattering Matrix Formulation (GDMF) in conjunction with the dual integral equation approach. Various scattering patterns are computed and validated with exact results where possible. The diffraction by a material discontinuity in a thick dielectric/ferrite slab is considered by modelling the constituent slabs with GSTCs. A non-unique solution in terms of unknown constants is obtained, and these constants are evaluated for the recessed slab geometry by comparison with the solution obtained therein. Several other simplified cases are also presented and discussed. An eigenfunction expansion method is introduced to determine the unknown solution constants in the general case. This procedure is applied to the non-unique solution in terms of unknown constants; and scattering patterns are presented for various slab junctions and compared with alternative results where possible.

Ricoy, M. A.↗

NASA NTRS1990

TE scattering by a two-dimensional groove in a ground plane using higher order boundary conditions

Higher order boundary conditions involve derivatives of the fields beyond the first and were recently shown to be more effective than traditional first order conditions in modeling dielectric coatings and layers. In this report an application of a third order generalized boundary condition to scattering by a filled rectangular groove is presented. Deficiencies of such higher-order boundary conditions are addressed and a correction is proposed for the present case. As part of the process of examining and correcting the accuracy of the proposed generalized boundary conditions, an exact solution is developed and a comparison is provided with a solution based on the standard impedance boundary condition.

Barkeshli, Kasra↗

NASA NTRS1990

Task reports on developing techniques for scattering by 3D composite structures and to generate new solutions in diffraction theory using higher order boundary conditions

There are two tasks described in this report. First, an extension of a two dimensional formulation is presented for a three dimensional body of revolution. With the introduction of a Fourier expansion of the vector electric and magnetic fields, a coupled two dimensional system is generated and solved via the finite element method. An exact boundary condition is employed to terminate the mesh and the fast fourier transformation is used to evaluate the boundary integrals for low O(n) memory demand when an iterative solution algorithm is used. Second, the diffraction by a material discontinuity in a thick dielectric/ferrite layer is considered by modeling the layer as a distributed current sheet obeying generalized sheet transition conditions (GSTC's).

Volakis, John L.↗

NASA NTRS1990

A finite element conjugate gradient FFT method for scattering

An extension of a two dimensional formulation is presented for a three dimensional body of revolution. With the introduction of a Fourier expansion of the vector electric and magnetic fields, a coupled two dimensional system is generated and solved via the finite element method. An exact boundary condition is employed to terminate the mesh and the fast fourier transformation (FFT) is used to evaluate the boundary integrals for low O(n) memory demand when an iterative solution algorithm is used. By virtue of the finite element method, the algorithm is applicable to structures of arbitrary material composition. Several improvements to the two dimensional algorithm are also described. These include: (1) modifications for terminating the mesh at circular boundaries without distorting the convolutionality of the boundary integrals; (2) the development of nonproprietary mesh generation routines for two dimensional applications; (3) the development of preprocessors for interfacing SDRC IDEAS with the main algorithm; and (4) the development of post-processing algorithms based on the public domain package GRAFIC to generate two and three dimensional gray level and color field maps.

Collins, Jeffery D.↗

NASA NTRS1990

Analytical solutions with Generalized Impedance Boundary Conditions (GIBC)

The diffraction by a material discontinuity in a thick dielectric/ferrite layer is considered by modeling the layer as a distributed current sheet obeying generalized sheet transition conditions (GSTC's). The sheet currents are then formulated and solved via the standard dual integral equation approach. This yields the diffracted field in terms of unknown constants which underscore the non-uniqueness of the GSTC current sheet representation. The constants are dependent on the geometry and properties of the discontinuity and are determined by enforcing field continuity across the material junction. This requires the field internal to the slab which are determined from the external ones via analytic continuity. Results are given which validate the solution and demonstrate the importance of the constants.

Ricoy, Mark A.↗

NASA NTRS1990

Users manual for AUTOMESH-2D: A program of automatic mesh generation for two-dimensional scattering analysis by the finite element method

AUTOMESH-2D is a computer program specifically designed as a preprocessor for the scattering analysis of two dimensional bodies by the finite element method. This program was developed due to a need for reproducing the effort required to define and check the geometry data, element topology, and material properties. There are six modules in the program: (1) Parameter Specification; (2) Data Input; (3) Node Generation; (4) Element Generation; (5) Mesh Smoothing; and (5) Data File Generation.

Hua, Chongyu↗