Multilevel UV Method Research Articles

A Hybrid 3DMLUV-FIA Method for Scattering from a 3D Dielectric Object above a 2D Dielectric Rough Surface

The electromagnetic scattering from the composite model of a three-dimensional (3D) dielectric object located above a two-dimensional (2D) dielectric rough surface is analyzed in this work. Poggio, Miller, Chang, Harrington, Wu, and Tsai (PMCHWT) integral equations are discretized by the method of moments (MoM) into a matrix which is solved by Biconjugate Gradients Stabilized (BICGSTAB) method. Method of 3DMLUV was used for PEC object located above rough surface. Comparing to the case when object and rough surface are both PEC, the memory requirement and computational complexity for dielectric models are increased due to doubled unknown number. Moreover, compared to dielectric object in free space, the coupling between dielectric object and dielectric rough surface will result in complicated numerical simulation. To solve this problem, the updated rank based 3D Multilevel UV (3DMLUV) method is employed to reduce memory consumption and CPU time overhead. The 3DMLUV has been successfully applied in the scattering of PEC targets; however, when the object or rough surface becomes dielectric, the coupling between dielectric object and dielectric rough surface will lead to slow constriction. Therefore, the Fast Iterative Approach (FIA) is applied to further speed up the constricted speed of the matrix required in 3DMLUV. The efficiency, stability, and accuracy of the proposed method are demonstrated in a variety of scattering problems.

Roughness effects on absorption and scattering of left‐handed materials

AbstractBistatic scattering and absorptivities from both Gaussian and exponentially correlated rough surfaces of the left‐handed materials (LHMs) are studied numerically for 2‐D geometries in a numerical Maxwell model. The multilevel UV method is employed to accelerate the matrix equation solver. Accuracy is ensured by energy conservation check. Using a set of physical surface parameters of root‐mean‐square heights and correlation lengths, numerical results are illustrated for absorptivities, bistatic scattering, and bistatic transmission of the LHMs. The numerical results show that the presence of the second opposite transmission, from lower medium to upper one for exponentially correlated LHM surfaces, dramatically reduces the absorptivities and enhances the bistatic scattering remarkably. In particular, the exponentially correlated roughness has negative effect on absorption for transverse electric (TE) case. Then all absorptivities for TE case are below that of the planar interface and decrease continuously with the increasing roughness. Due to both the Brewster angle effect and the opposite transmission across exponentially correlated interface, the absorptivities for the transverse magnetic (TM) case of the LHMs increase at first and decrease subsequently down below that of the planar interface. Both polarimetric absorptive characteristics are in completely contrary to those of the right‐handed materials (RHMs), where the absorptivities for both the TE and TM cases are monotonic increasing with the increase of roughness because of its fine‐scale surface features and the increasing effective surface areas. For Gaussian correlated LHM surfaces, however, the second opposite transmission does not exist, thus does not show any evident differences from RHMs, except for the maximum transmission in different directions and beam broadening. In addition, comparisons are also made with the second‐order small perturbation method and Kirchhoff's approximation. In contrary to RHM, the second‐order small perturbation method is no longer valid for TE case for both absorptivity and scattering from exponentially correlated LHM surfaces even for very small perturbation cases. Similar to RHM surfaces, the Kirchhoff's approximation can be only valid to the LHM surfaces with Gaussian correlation function.

Monostatic scattering from two-dimensional two-layer rough surfaces using hybrid 3DMLUV-ACA method

The electromagnetic scattering from two-dimensional two-layer dielectric random rough surfaces is analyzed in this work based on Monte Carlo (MC) simulations. The random rough surface is characterized with Gaussian statistics for surface correlation length and for surface root mean square (RMS) height. The Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) surface integral equation is adopted and implemented. A rigorous three-dimensional (3-D) multilevel UV method combined with adaptive cross approximation (ACA) is proposed to solve for the unknown electric and magnetic surface currents. By calculating monostaitc statistical radar cross section (RCS) of the layered structure, the influence of the rough surface RMS height, the correlation length, the medium permittivity and the layer thickness on the scattering characteristic is investigated.

Multiresolution preconditioned multilevel UV method for analysis of planar layered finite frequency selective surface

In this article, the planar layered finite frequency selective surface (FSS) is analyzed by the mixed potential integral equation. The multiresolution (MR) preconditioned multilevel UV method is applied to accelerate the matrix-vector multiplication. The MR preconditioning technique is based on the construction of MR basis functions, which are constructed as linear combinations of Rao-Wilton-Glisson (RWG) basis functions. Therefore, the MR-preconditioner allows direct application to the multilevel UV method with RWG basis functions to speed up the convergence of the generalized minimal residual iterative solver. Numerical results demonstrate that the MR preconditioned multilevel UV method is efficient for the analysis of planar layered finite FSSs. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52: 1530–1536, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.25233

Numerical Simulation of Vector Wave Scattering From the Target and Rough Surface Composite Model With 3-D Multilevel UV Method

Numerical simulation of vector wave scattering from three-dimensional (3-D) target and rough surface composite model is investigated with a 3-D multilevel UV method. Due to the adoption of RWG basis functions for accurate modeling of vector current, the oscillation of the interaction matrix elements brings difficulty to directly apply the UV decomposition method. Based on the reordering of the interaction strength and the sampling according to the characteristics distribution of the interaction, an EM-interaction-based sampling algorithm is developed for the accurate reconstruction of the far interaction submatrix with UV decomposition method. Combined with multilevel division of the total composite model, the 3-D multilevel UV method incorporating the new sampling algorithm is developed for vector wave scattering from 3-D complex target above or on a random rough surface. The 3-D multilevel UV method yields a complexity of O(N log N) for the setup time of the impedance matrix, the solve time of the matrix iterative solution and also for the memory requirements. The accuracy and the efficiency of the 3-D multilevel UV method is compared and validated with the full MOM method and the ACA method in the tested cases. Finally, the applications of a target above or on the rough surface, for example, a ship on the sea surface, have been accomplished and analyzed.

ANALYSIS OF MICROWAVE EMISSION OF EXPONENTIALLY CORRELATED ROUGH SOIL SURFACES FROM 1.4 GHz TO 36.5 GHz

We analyzed the microwave emission from a rough soil surface with exponential correlation by characterizing its dependences of polarization, look angle, and frequency. Using the same set of physical surface parameters of rms height and correlation lengths, results are obtained for a wide range of frequencies at 1.4GHz, 5GHz, 10GHz, 18GHz, and 36.5GHz. Accurate simulations for the 2-D scattering problem are conducted by Galerkin's method with the rooftop basis function, followed by near-fleld integration, flne discretization, and cubic spline interpolation of surfaces. The multilevel UV method was employed to accelerate the solution. Accuracy is ensured by energy conservation check. Simulation results are compared with SPM, KA and AIEM. Results suggest that there exists distinct emission characteristic between the exponential and the Gaussian correlated surface. These characteristics should be very useful in developing retrieval algorithm of the soil moisture from emissivity measurements.

Full-Wave Analysis of Large-Scale Interconnects Using the Multilevel UV Method With the Sparse Matrix Iterative Approach (SMIA)

Moving towards the goal of analyzing whole printed circuit boards (PCBs) and packages using full-wave electromagnetic (EM) methods, the multilevel UV method is applied to the method-of-moments (MoM) solution of the current on large-scale interconnects. The MoM solution uses the layered media Green's functions computed using the numerical modified steepest-descent path (NMSP) method, and is applied to the exterior layers of the interconnect structure. The sparse matrix iterative approach (SMIA) is used to speed up the solution of the iterative matrix solver. The iterative solver is also accelerated by using larger blocks in the block diagonal inverse preconditioner. With the multilevel UV method, a fast solution is presented for solving the current on large-scale interconnects on thin layered structures at high frequencies. We show an example of an interconnect structure that has horizontal dimensions of 12.675 lambda t 12.876 lambda with 24\thinspace 848 current unknowns and an interconnect fractional area of approximately 31%. This problem takes a total of 21 min 20 s to solve for the current on the traces on a Pentium 3.2-GHz CPU with 4 GB of RAM.

Bistatic Scattering and Emissivities of Lossy Dielectric Surfaces With Exponential Correlation Functions

Bistatic scattering and emissivities of surfaces with exponential correlation functions are studied numerically for 2-D geometries in a numerical Maxwell model with 2-D simulations. Surfaces with exponential correlation functions are important for the active and passive microwave remote sensing of land surfaces. Because of the fine-scale features with large slopes of such surfaces, numerical accuracy, which is particularly important for the calculation of emissivity in passive remote sensing, is ensured by a variety of procedures in this paper. The rooftop function and Galerkin's method with numerical integration of near-field impedance matrix elements are used. Cubic spline interpolation is employed to connect knots on random rough surfaces. Numerical accuracy convergence tests are performed for numerical solutions of Maxwell equations by varying the number of points from 13 to 103 points per wavelength in the dielectric medium corresponding to 50-400 points per free wavelength. Surface lengths of up to 100 and 200 free wavelengths and root mean square heights of up to 0.4 and 0.8 free wavelengths, respectively, are used at 5 and 10 GHz to capture all the essential features. Because of the large number of surface unknowns (up to 80 000), the multilevel UV method is further used to accelerate the matrix equation solver. Numerical results are illustrated for both bistatic scattering and emissivities as functions of frequencies and incidence and scattering angles for cases of interests in microwave remote sensing. Comparisons are made with the second-order small perturbation method and Kirchhoff's approximation to reestablish the regimes of validity of these methods

Scattering by rough surface using a hybrid technique combining the multilevel UV method with the sparse matrix canonical grid method

A procedure is developed for combining efficiently the multilevel UV method with the sparse matrix canonical grid (SMCG) method in the computation of three‐dimensional (3‐D) wave scattering from random rough surface. It handles near‐ and intermediate‐field interactions by the multilevel UV method and far‐field interactions by the SMCG method. This hybrid UV/SMCG method removes the large memory requirement of both the UV method in the far field and the SMCG method in the near field. The computational complexity for the hybrid method is O(NlogN). The tradeoffs in computer memory requirement and CPU time between the UV part and the SMCG part are examined for Gaussian random rough surfaces with Gaussian correlation function and with exponential correlation function. For a surface area of 44 × 44 square wavelengths with RMS of 1 wavelength and 123,904 surface unknowns, the UV/SMCG method requires CPU of 52.2 s per iteration with total CPU of 46.6 min for 22 iterations on a single processor of CPU speed of 2.66 GHz.

Application of the Multilevel UV Method to Analyze Large Microstrip Patch Structures

The analysis of a plane wave incident on a large microstrip patch is studied using the method of moments (MoM) with the layered medium Green's functions and the rooftop basis functions. A fast numerical approach, the multilevel UV method, is employed to speed up the method of moment solution. A conjugate gradient method solver with preconditioning is applied as an iterative matrix solver to accelerate the matrix-vector multiplication. The multilevel UV method has O(N log N) complexity for CPU per iteration and memory.

Application of the multilevel UV method to calculate microwave absorption and emission of ocean foam with Kelvin's tetrakaidecahedron structure

Ocean foam is treated as densely packed air bubbles coated with thin walls of seawater. We choose a foam structure of the shapes of air bubbles based on Lord Kelvin's tetrakaidecahedron structure that has close to minimal contact surface area. We calculate the absorption coefficients from 1.5 to 36.5 GHz by using the multilevel UV method to accelerate the MoM solution. To illustrate the microwave emission, the brightness temperatures of a layer of foam above the ocean surface area calculated. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 45: 445–450, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20849

Propagation over terrain and urban environment using the multilevel UV method and a hybrid UV/SDFMM method

Propagation over terrain and urban environments are studied using 2D simulations of Maxwell equations. For the case of terrain propagation, the multilevel UV method is used to accelerate the method of moments (MoM) solution. We consider propagation over a region of 14.42 km at 1,500 MHz that has 720,896 MoM surface unknowns. For the case of the urban environment, because of the sharp rise in surface heights, we use a hybrid UV/SDFMM method. We consider a problem over 2.3 km with building heights of 18 m for 90,112 MoM surface unknowns at 900 MHz. Computations of all cases were performed with a single processor. Based on the simulations, we study fading and signal amplitude variation with distance.