1,721,001 research outputs found
Anisotropic and Optimized FFT-Based Iterative Electromagnetic Solver for the PEEC Method
Full text linkFast Fourier transform (FFT)-accelerated integral-equation-based electromagnetic (EM) simulators have gained attraction for their capability to compute parasitics of arbitrarily shaped and large-scale voxelized structures on a desktop computer. Yet, FFT-based solvers have limitations due to the necessity of using voxels of the same size in all three Cartesian dimensions and suffer in the case of geometries with far-apart objects that require meshing also the air between them, resulting in a huge number of voxels and, thus, of unknowns. This work aims to overcome both these limitations by developing a systematic anisotropic strategy to compute matrix–vector products using the FFT-based approach and to remove the air existing between objects without sacrificing the desirable features of the FFT-based approach. The proposed approach is presented in the framework of the partial element equivalent circuit (PEEC) method, but it is well suited to be used also with other integral equation-based methods. The accuracy, efficiency, and applicability of the proposed anisotropic and optimized FFT (aoFFT)-based PEEC solver are demonstrated in the example of two structures requiring to use voxels of different sizes along the three Cartesian dimensions and with a large portion of air between the objects
Ab initio calculation of the reflectance anisotropy of surfaces: The triangle method
No full textWe modify the analytic linear tetrahedron method to calculate the optical properties of surfaces. As st test case, the reflectance anisotropy of InP(110) is calculated within the density-functional theory in the local-density approximation. The convergence with respect to the number of k points and the choice of the triangles is extensively discussed. The resulting spectra are interpreted and compared with experimental results
Theoretical study of As overlayers on InP(110) surface: optical properties
No full textThe reflectance anisotropy of the As/InP(110) surface is calculated by using an ab initio plane-wave pseudopotential method. We analyze different models of As coverage, ranging from non-reacted epitaxial layers to exchange-reacted geometries. Comparison with experimental data confirms that the annealed, highly ordered surface phase can be described by an InAs monolayer on the InP substrate (exchange reacted model), whereas the reflectance anisotropy of the as-grown, poorly ordered As/InP surface probably is dominated by disorder effects. (C) 1998 Elsevier Science B.V. All rights reserved
Rigorous dc Solution of Partial Element Equivalent Circuit Models including Conductive, Dielectric, and Magnetic Materials
No full textThis paper presents a rigorous derivation of the dc solution of three-dimensional partial element equivalent circuit (PEEC) formulation extended to include simultaneously conductive, dielectric, and magnetic materials. The circuit interpretation of Maxwell's equations provided by the PEEC method allows to reformulate the dc modeling task in such a way that physical phenomena are fully exploited. Indeed, since the displacements currents are identically zero in dielectrics, Kirchhoff's current law is enforced in terms of charge conservation internally to dielectrics or at the interface between dielectrics and other materials. A well-posed problem is achieved by adding the charges as new unknowns and identifying the disconnected objects. Two numerical examples are presented demonstrating the accuracy of the proposed method when compared to the dc solution as extracted by the fast Fourier transform of the impulse response and a finite element method simulation
Accelerated Partial Inductance Evaluation via Cubic Spline Interpolation for the PEEC Method
No full textEfficient partial elements computation for the non-orthogonal PEEC method including conductive, dielectrics and magnetic materials
No full textThe partial-element equivalent circuit method is a well-known numerical technique that is used to solve Maxwell's equations in their integral equation form. The application of the partial-element equivalent circuit (PEEC) method to modeling domains with non-orthogonal three-dimensional geometries requires the computation of the interaction integrals to be performed numerically, thus slowing down the overall computation. This work presents a new technique that allows improving the computation of the interaction integrals of the PEEC method for non-orthogonal geometries under the quasi-static hypothesis. To this purpose, a voxelization approach that automatically decomposes non-orthogonal volumes in elementary parallelepipeds is used, allowing the implementation of closed-form formulas for the interaction integrals and completely avoiding numerical integration. The proposed approach is applied to three example problems exhibiting very good accuracy and excellent speed-up compared with the standard one using the numerical integration.The partial element equivalent circuit method is a well-known numerical technique that is used to solve Maxwell’s equations in their integral equation form. The application of the PEEC method to modeling domains with non-orthogonal three-dimensional geometries requires the computation of the interaction integrals to be performed numerically, thus slowing down the overall computation. This work presents a new technique that allows improving the computation of the interaction integrals of the PEEC method for non-orthogonal geometries under the quasi-static hypothesis. To this purpose, a voxelization approach that automatically decomposes non-orthogonal volumes in elementary parallelepipeds is used, allowing the implementation of closed-form formulas for the interaction integrals and completely avoiding numerical integration. The proposed approach is applied to three example problems exhibiting very good accuracy and excellent speed-up compared to the standard one using the numerical integration
Full-wave computation of the electric field in the partial element equivalent circuit method using taylor series expansion of the retarded green's function
No full textThis article presents new analytical formulas for the efficient computation of the full-wave electric field generated by conductive, dielectric, and magnetic media in the framework of the partial element equivalent circuit (PEEC) method. To this aim, the full-wave Green's function is handled by the Taylor series expansion leading to three types of integrals for which new analytical formulas are provided in order to avoid slower numerical integration. An orthogonal (Manhattan type) tessellation of the geometries is assumed, and the electrical quantities, i.e., currents, charges, and magnetization, are expanded in space through rectangular basis functions. The full-wave electric field radiated by charges, currents, and magnetization is computed analytically in the postprocessing step. The proposed closed-form computation of the electric field is tested using two examples, comparing the results obtained by the derived analytical formulas with the results from a finite element method solver
Efficient computation of partial elements for non-orthogonal PEEC meshes
No full textThe partial element equivalent circuit (PEEC) method has proven to be able to provide a valid solution method of the Maxwell's equations in the time as well as the frequency domain. The extension of the basic PEEC approach to non-orthogonal geometries has significantly expanded the applicability of the method. The computation of interaction integrals is typically performed numerically and it results to be time-consuming. This work presents a new flexible and accurate computational method for determining the partial inductances in the quasi-static limit. More specifically, an automatic decomposition of the non-orthogonal geometries into parallelepipeds is proposed so that analytical formulas which are available in this case can be used. The accuracy, and speed of the proposed method is compared with standard integration routines exhibiting a satisfactory accuracy and reduced computation time
On the Decoupling of Integrals in the Surface PEEC Method
No full textElectromagnetic problems can be solved by using the integral form of Maxwell equations. The Surface Partial Element Equivalent Circuit (S-PEEC) method is an integral equation-based method that is suitable when high-frequency effects, such as skin and proximity effect, are dominant. However, the computation of interaction quadruple integrals is computationally expensive and numerically unstable due to singularities. In previous work, we proved how to decouple one of the quadruple integrals, and showed the gaining in stability and computational time. In this work, we extend the result to the second integral with the curl of the Green's function. Numerical examples prove the acceleration in terms of computational time achieved with the proposed approach. Future work will focus on integration strategy and further optimization of the proposed algorithm
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