Multilevel Green's Function Interpolation Method Research Articles

An OpenMP Parallelized Multilevel Green's Function Interpolation Method Accelerated by Fast Fourier Transform Technique

A parallelized multilevel Green's function interpolation method (MLGFIM) accelerated by fast Fourier transform (FFT) technique is proposed. The difficulties in applying various improved interpolation schemes to effectively reduce the number of interpolation points are overcome by using the FFT technique. In order to accelerate the convergence property of the iterative solution using the proposed algorithm, a recently proposed preconditioning scheme, i.e., multiplicative Calderon preconditioner is adopted to transform the first kind integral operator to the second kind, albeit an increase of computer memory storage requirement. An OpenMP parallel implementation of the MLGFIM-FFT algorithm on a share-memory computer system is developed to analyze various electrically large electromagnetic scattering problems including a NASA almond, a 20-wavelength cylinder capped with two half spheres, and a 37-wavelength cylinder array. Numerical results illustrate good computational performance of the proposed algorithm.

Comparison of Interpolating Functions and Interpolating Points in Full-Wave Multilevel Green's Function Interpolation Method

The difficulty for the solution of full-wave electromagnetic problems using multilevel Green's function interpolation method (MLGFIM) lies in applying interpolating approaches to efficiently and accurately approximate Green's function with rapidly changing phase term. We compare various interpolating schemes when radial basis function (RBF) is employed for the interpolation of scattered data of Green's function. We show that the infinitely smooth Gaussian (GA) RBF has the best interpolation accuracy. In order to improve the interpolation efficiency, a new kind of staggered Tartan grid is proposed. A good calculation method for the shape parameter in GA RBF is given to solve its sensitivity to the group size and the number of interpolation points. Based on the analysis of variation of the number of interpolation points with electric length of the group, adaptive choice of the types of interpolation functions and interpolation points are employed. Numerical examples show that the computational efficiency of this new interpolation scheme is much improved over the previously reported ones.

Multilevel Green's function interpolation method for analysis of 3-D frequency selective structures using volume/surface integral equation

In this paper, we present the multilevel Green's function interpolation method (MLGFIM) for analyses of three-dimensional doubly periodic structures consisting of dielectric media and conducting objects. The volume integral equation (VIE) and surface integral equation (SIE) are adopted, respectively, for the inhomogeneous dielectric and conducting objects in a unit cell. Conformal basis functions defined on curvilinear hexahedron and quadrilateral elements are used to solve the volume/surface integral equation (VSIE). Periodic boundary conditions are introduced at the boundaries of the unit cell. Computation of the space-domain Green's function is accelerated by means of Ewald's transformation. A periodic octary-cube-tree scheme is developed to allow adaptation of the MLGFIM for analyses of doubly periodic structures. The proposed algorithm is first validated by comparison with published data in the open literature. More complex periodic structures, such as dielectric coated conducting shells, folded dielectric structures, photonic bandgap structures, and split ring resonators (SRRs), are then simulated to illustrate that the MLGFIM has a computational complexity of O(N) when applied to periodic structures.

MULTILEVEL GREEN'S FUNCTION INTERPOLATION METHOD SOLUTION OF VOLUME/SURFACE INTEGRAL EQUATION FOR MIXED CONDUCTING/BI-ISOTROPIC OBJECTS

This paper proposes a multilevel Green's function interpolation method (MLGFIM) to solve electromagnetic scattering from objects comprising both conductor and bi-isotropic objects using volume/surface integral equation (VSIE). Based on equivalence principle, the volume integral equation (VIE) in terms of volume electric and magnetic ∞ux densities and surface integral equation (SIE) in terms of surface electric current density are flrst formulated for inhomogeneous bi-isotropic and conducting objects, respectively, and then are discretized using the method of moments (MoM). The MLGFIM is adopted to speed up the iterative solution of the resultant equation and reduces the memory requirement. Numerical examples are presented to show good accuracy and versatility of the proposed algorithm in dealing with a wide array of scattering problems.

SOLUTION TO ELECTROMAGNETIC SCATTERING BY BI-ISOTROPIC MEDIA USING MULTILEVEL GREEN'S FUNCTION INTERPOLATION METHOD

In this paper, a multilevel Green's function interpolation method (MLGFIM) is developed to analyze electromagnetic scattering from an arbitrarily shaped three-dimensional objects comprised of both conductor and bi-isotropic media. The fleld decomposition method is adopted to split the homogeneous bi-isotropic media into two uncoupled isotropic media instead of direct calculation of complicated Green's function in bi-isotropic material. The problem is formulated using the Paggio-Miller-Chang-Harrington-Wu- Tsai (PMCHWT) approach for multiple homogeneous isotropic media and electric fleld approach for conducting bodies. The resultant integral equations are discretized by the method of moment (MoM) and iteratively solved by MLGFIM. Numerical examples illustrate accuracy of this algorithm and CPU time of O(N logN) and memory requirement of O(N).

An Improved Multilevel Green's Function Interpolation Method With Adaptive Phase Compensation

An improved multilevel Green's function interpolation method (MLGFIM) with adaptive phase compensation (APC) is proposed. The difficulty in applying interpolation approaches to the fast varying phase term in the integral equation kernel for full-wave electromagnetic (EM) simulations is eradicated by using the phase compensation and adaptive direction separation (ADS). The multilevel tree structure in MLGFIM keeps the number of direction separation invariant at all levels, attributing to the recursive interpolation with multilevel phase compensation. The proposed MLGFIM-APC in conjunction with the Lagrange-Chebyshev interpolation yield an O(N log N) CPU time and O(N) computer memory requirement for surface scattering problems. By introducing a transition level, the MLGFIM-APC can adaptively incorporate interpolation techniques of conventional interpolation (CI), transition interpolation (TI) and phase-compensation interpolation (PI), corresponding to electromagnetic simulation of problems of small, moderate, and large electrical sizes, respectively. Large-scale microstrip antenna arrays are simulated to illustrate the accuracy and efficiency of the proposed method. It is found that the CPU time scales better than O(N log N) for these co-planar problems.

COMBING MULTILEVEL GREEN'S FUNCTION INTERPOLATION METHOD WITH VOLUME LOOP BASES FOR INDUCTANCE EXTRACTION PROBLEMS

In this paper,a fast integral equation method is developed for extracting the inductances in RF ICs,RF MEMs,IC packages,and deep submicron ICs etc. This method combines a recently developed Multilevel Green's Function Interpolation Method (MLGFIM) (1,2) with the volume integral equation discretized using Volume Loop (VL) basis functions. In it,instead of using the filaments model to simulate the currents flowing in the inductors,we use the conventional SWG basis functions for this kind of basis functions is flexible for problems with complex geometries. The shortest path finding algorithm is also used to find the source loop basis functions. The inductance extractions from the straight line,the spiral inductors,the bump,and the parallel buses in this paper demonstrate the validity and efficiency of this hybrid method.

The Implementation of Multilevel Green's Function Interpolation Method for Full-Wave Electromagnetic Problems

We extend the multilevel Green's function interpolation method (MLGFIM) developed for quasi-electrostatic problems to full-wave simulations. The difficulty in applying the interpolation approach lies in the additional rapidly changing phase term associated with the full-wave Green's functions. To enhance the efficiency and accuracy of the full-wave Green's function interpolation, a scattered point set consisting of two staggered Tartan grids in conjunction with radial basis function interpolation is employed. To further reduce the computational complexity, the QR factorization technique is applied to compress the low rank Green's function matrices. For electromagnetic scattering from PEC spheres up to a diameter of eight wavelengths, the proposed method compares well with Mie's scattering in accuracy and shows the O(NlogN) efficiency. As the method is "kernel independent", its extension to structures in layered medium is straightforward. In the numerical simulations of finite microstrip patch arrays up to 11 by 11 elements, the proposed method demonstrates very favorable dependencies of CPU time and memory storage requirement versus the number of unknowns

A new multilevel Green's function interpolation method for large-scale low-frequency EM simulations

In this paper, a new multilevel Green's function interpolation method (MLGFIM) is presented to solve integral equations for large-scale electrostatic problems. In MLGFIM, the problem domain is first divided into multilevel cubes. Next, the peer-level Green's function interpolation technique is employed, and then, a new lower-to-upper-level Green's function interpolation technique is devised. They are used with the multilevel discretization to speed up the matrix-vector multiplications in the iterative solution in which a computational complexity of O(N) is achieved. The MLGFIM is used to extract the capacitances encountered in radio frequency integrated circuits (RFICs) and microelectromechanical systems. Moreover, to demonstrate its efficiency both in simulation speed and memory storage requirement, MLGFIM is compared with FastCap for free space problems and applied to extract capacitances from multilayered structures. For problems with 375,000 unknowns, the proposed method only requires 343 MB of computer memory.