scholarly journals Fast Computation by MLFMM-FFT with NURBS in Large Volumetric Dielectric Structures

Electronics ◽  
2021 ◽  
Vol 10 (13) ◽  
pp. 1560
Author(s):  
Alejandro Pons ◽  
Alvaro Somolinos ◽  
Ivan González ◽  
Felipe Cátedra
Keyword(s):  
Fast Multipole Method ◽  
Near Field ◽  
Three Dimensional ◽  
Solution Process ◽  
Computation Time ◽  
Iterative Solution ◽  
Hexahedral Meshes ◽  
Volumetric Objects ◽  
Computational Resources ◽  
Efficient Memory

A refinement for the computation of the rigorous part of the multi-level fast multipole method (MLFMM) of analyzing volumetric objects is presented. A scheme based on the fast Fourier technique (FFT) is proposed with the objective of reducing the computational resources required to accurately analyze large homogeneous and non-homogeneous dielectric volumes. In order to reduce the memory requirements, the storage of the near-field terms of the method of moments (MoM) matrix is performed only for the positions corresponding to a parallelepiped with the size of the level 1 block of the MLFMM, computed with the vacuum permittivity, taking advantage of the Toeplitz symmetry present in regular hexahedral meshes. The FFT avoids applying the near-field MoM matrix in the iterative solution process. The application of this approach results in huge improvements in terms of memory usage, but also a speeds up the iterative solution process because the use of three-dimensional (3D) FFTs is very efficient for computing convolutions when the number of unknowns of the problems becomes very large as happens in volumetric problems. We also propose a new approach for the numerical treatment of the transition of the dielectric permittivity between different dielectrics or between a dielectric and a free space. To validate the computation technique, the radar cross section (RCS) of several dielectric bodies is computed using the classical MLFMM approach and it is compared with the presented FFT-based-MLFMM solution. The results demonstrate that the efficient memory and computation time usage of the proposed approach.

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 Accelerated IE-GSTC Solver for Large-Scale Metasurface Field Scattering Problems using Fast Multipole Method (FMM)

2021 ◽  
Author(s):  
jordan dugan ◽  
Tom J. Smy ◽  
Shulabh Gupta
Keyword(s):  
Large Scale ◽  
Fast Multipole Method ◽  
Computation Time ◽  
Fast Multipole ◽  
Electromagnetic Propagation ◽  
Scattering Problems ◽  
Multipole Method ◽  
Scattered Fields ◽  
Computational Resources ◽  
Solution Accuracy

An accelerated Integral Equations (IE) field solver for determining scattered fields from electrically large electromagnetic metasurfaces utilizing Fast Multipole Method (FMM) is proposed and demonstrated in 2D. In the proposed method, practical general metasurfaces are expressed using an equivalent zero thickness sheet model described using surface susceptibilities, and where the total fields around it satisfy the Generalized Sheet Transition Conditions (GSTCs). While the standard IE-GSTC offers fast field computation compared to other numerical methods, it is still computationally demanding when solving electrically large problems, with a large number of unknowns. Here we accelerate the IE-GSTC method using the FMM technique by dividing the current elements on the metasurface into near- and far-groups, where either the rigorous or approximated Green’s function is used, respectively, to reduce the computation time without losing solution accuracy. Using numerical examples, the speed improvement of the FMM IE-GSTC method O(N<sup>1.5</sup>) over the standard IE-GSTC O(N<sup>3</sup>) method is confirmed. Finally, the usefulness of the FMM IE-GSTC is demonstrated by applying it to solve electromagnetic propagation inside an electrically large radio environment with strategically placed metasurfaces to improve signal coverage in blind areas, where a standard IE-GSTC solver would require prohibitively large computational resources and long simulation times.

scholarly journals Accelerated IE-GSTC Solver for Large-Scale Metasurface Field Scattering Problems using Fast Multipole Method (FMM)

2021 ◽  
Author(s):  
jordan dugan ◽  
Tom J. Smy ◽  
Shulabh Gupta
Keyword(s):  
Large Scale ◽  
Fast Multipole Method ◽  
Computation Time ◽  
Fast Multipole ◽  
Electromagnetic Propagation ◽  
Scattering Problems ◽  
Multipole Method ◽  
Scattered Fields ◽  
Computational Resources ◽  
Solution Accuracy

An accelerated Integral Equations (IE) field solver for determining scattered fields from electrically large electromagnetic metasurfaces utilizing Fast Multipole Method (FMM) is proposed and demonstrated in 2D. In the proposed method, practical general metasurfaces are expressed using an equivalent zero thickness sheet model described using surface susceptibilities, and where the total fields around it satisfy the Generalized Sheet Transition Conditions (GSTCs). While the standard IE-GSTC offers fast field computation compared to other numerical methods, it is still computationally demanding when solving electrically large problems, with a large number of unknowns. Here we accelerate the IE-GSTC method using the FMM technique by dividing the current elements on the metasurface into near- and far-groups, where either the rigorous or approximated Green’s function is used, respectively, to reduce the computation time without losing solution accuracy. Using numerical examples, the speed improvement of the FMM IE-GSTC method O(N<sup>1.5</sup>) over the standard IE-GSTC O(N<sup>3</sup>) method is confirmed. Finally, the usefulness of the FMM IE-GSTC is demonstrated by applying it to solve electromagnetic propagation inside an electrically large radio environment with strategically placed metasurfaces to improve signal coverage in blind areas, where a standard IE-GSTC solver would require prohibitively large computational resources and long simulation times.

Three-Dimensional Conjugate Heat Transfer Simulation of an Internally-Cooled Gas Turbine Vane

2003 ◽  
Author(s):  
William D. York ◽  
James H. Leylek
Keyword(s):  
Heat Transfer ◽  
Gas Turbine ◽  
Conjugate Heat Transfer ◽  
Three Dimensional ◽  
Solution Process ◽  
Iterative Solution ◽  
Operating Conditions ◽  
Turbine Vane ◽  
Internally Cooled ◽  
Heat Transfer Simulation

A conjugate numerical methodology was employed to predict the metal temperature of a three-dimensional gas turbine vane at two different engine-realistic operating conditions. The vane was cooled internally by air flowing through ten round, radially-oriented channels. The conjugate heat transfer approach allows the simultaneous solution of the external flow, internal convection, and conduction within the metal vane, eliminating the need for multiple, decoupled solutions, which are time-consuming and inherently less accurate when combined. Boundary conditions were specified only for the inlet and exit of the vane passage and the coolant channels, while the solid and fluid zones were coupled by energy conservation at the interfaces, a condition that was maintained throughout the iterative solution process. Validation of the methodology was accomplished through the comparison of the predicted aerodynamic loading curves and the midspan temperature distribution on the vane external surface with data from a linear cascade experiment in the literature. The superblock, unstructured numerical grid consisted of nearly seven million finite-volumes to allow accurate resolution of flowfield features and temperature gradients within the metal. Two models for turbulence closure were used for comparison: the standard k-ε model and a realizable version of the k-ε model. The predictions with the realizable k-ε model exhibited the best agreement with the experimental data, with maximum differences in normalized temperature of less than ten percent in each case. The present study shows that the conjugate heat transfer simulation is a viable tool in gas turbine design, and it serves as a platform on which to base future work with more complex geometries and cooling schemes.

Practical electron tomography

1995 ◽  
Vol 53 ◽  
pp. 742-743
Author(s):  
C.L. Woodcock
Keyword(s):  
Electron Tomography ◽  
Tomographic Reconstruction ◽  
Three Dimensional ◽  
3D Shape ◽  
Computational Resources ◽  
Shape Of Particles

Despite the potential of the technique, electron tomography has yet to be widely used by biologists. This is in part related to the rather daunting list of equipment and expertise that are required. Thanks to continuing advances in theory and instrumentation, tomography is now more feasible for the non-specialist. One barrier that has essentially disappeared is the expense of computational resources. In view of this progress, it is time to give more attention to practical issues that need to be considered when embarking on a tomographic project. The following recommendations and comments are derived from experience gained during two long-term collaborative projects.Tomographic reconstruction results in a three dimensional description of an individual EM specimen, most commonly a section, and is therefore applicable to problems in which ultrastructural details within the thickness of the specimen are obscured in single micrographs. Information that can be recovered using tomography includes the 3D shape of particles, and the arrangement and dispostion of overlapping fibrous and membranous structures.

scholarly journals Rapid Growth of TiO2 Nanoflowers via Low-Temperature Solution Process: Photovoltaic and Sensing Applications

Materials ◽  
2019 ◽  
Vol 12 (4) ◽  
pp. 566 ◽  
Author(s):  
M. Akhtar ◽  
Ahmad Umar ◽  
Swati Sood ◽  
InSung Jung ◽  
H. Hegazy ◽  
...  
Keyword(s):  
Low Temperature ◽  
Anatase Phase ◽  
Three Dimensional ◽  
Solution Process ◽  
Dye Sensitized Solar Cell ◽  
Sensor Applications ◽  
Dye Sensitized ◽  
Sensing Applications ◽  
Density Growth ◽  
Temperature Solution

This paper reports the rapid synthesis, characterization, and photovoltaic and sensing applications of TiO2 nanoflowers prepared by a facile low-temperature solution process. The morphological characterizations clearly reveal the high-density growth of a three-dimensional flower-shaped structure composed of small petal-like rods. The detailed properties confirmed that the synthesized nanoflowers exhibited high crystallinity with anatase phase and possessed an energy bandgap of 3.2 eV. The synthesized TiO2 nanoflowers were utilized as photo-anode and electron-mediating materials to fabricate dye-sensitized solar cell (DSSC) and liquid nitroaniline sensor applications. The fabricated DSSC demonstrated a moderate conversion efficiency of ~3.64% with a maximum incident photon to current efficiency (IPCE) of ~41% at 540 nm. The fabricated liquid nitroaniline sensor demonstrated a good sensitivity of ~268.9 μA mM−1 cm−2 with a low detection limit of 1.05 mM in a short response time of 10 s.

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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