On the hybridization of RUFD algorithm with the DM approach for solving multiscale problems

A fast non-similarity wavelet transform method, proposed earlier by the authors, is further studied. Combined with conventional techniques such as the method of moments, the boundary element method and the finite element method, the wavelet transform method can effectively handle a wide range of complicated problems which involve various complex media and conductors. The computational complexity and the CPU time for the proposed technique are presented. Studies further show that the use of non-similarity nonorthonormal cardinal spline wavelet (NS-NCSW) transform, although does not seem to reduce the computational complexity, can save a great amount of CPU time and computer memory. Numerical experiments are presented to demonstrate the merits of the proposed technique.

The Origin of Spurious Solutions in Computational Electromagnetics

This study investigates and evaluates applications of the adjoint problem and its solution in frequency-domain computational electromagnetics (CEM). The study establishes and validates adjoint-based applications including higher order parameter sampling, a posteriori error estimate evaluation, and p- and h-refinements. These applications can improve the efficiency, automation, and robustness of CEM methods. We employ a 1-D finite-element-method scattering solver, simplifying the implementation, replicability, clarity, and intuitiveness of analysis results and conclusions, which then extend naturally to higher dimensional solvers and more complicated CEM problems. While demonstrated with a higher order solver, the derived techniques apply to low-order methodology as well. This is the first demonstration of the applicability of adjoint-based a posteriori error estimation techniques to adaptive discretization refinement in frequency-domain CEM with arbitrary-order basis functions. This work introduces the application of dual-weighted residual error estimation and selective adaptivity based on error cancellation. The proposed targeted, adaptive mesh/model p- and/or h-refinement heuristics informed by adjoint element-wise error contribution estimates show near-monotonic reduction of the quantity-of-interest error with increased numbers of refined elements. In general, adjoint techniques are underutilized in CEM, and another goal of this work is to promote their future use for refinement, optimization, and uncertainty quantification.

1. The dipole moments of a number of cis- and trans-1-alkylthio-2-alkylsulfonylethenes and 1,2-bis-alkylsulfonylethenes were measured. 2. By comparing the moments found with those calculated for various rotational conformations, it was shown that for compounds with irregular groups, the method of dipole moments does not permit an unambiguous solution of the problem of geometrical isomerism around the double bond. 3. For compounds whose cis- and trans-configuration has been established by other means, the method of dipole moments yields useful information on the most profitable rotational conformers.

Recently, an integral equation discontinuous Galerkin method (IEDG) has been proposed to solve electromagnetic problems. One of the most attractive features of IEDG is the possibility to employ non-conformal mesh for the implementation of the combined field integral equation (CFIE) since the square integrable L2 basis is adopted and no continuity requirement is necessary across boundaries of adjacent elements. Moreover, IEDG provides great flexibility in terms of basis function such that different orders of basis functions with different element types can be mixed with the same discretization to best represent the currents locally. This feature also facilitates the incorporation of adaption techniques to IEDG, either through the use of higher order basis functions (p refinement) or subdivide the elements into multiple smaller pieces (h refinement). All these merits makes IEDG a very attractive candidate for the solution of multi-scale and wide-band problems such that geometry components that are smooth can be discretized using coarser elements while finer discretization can be adopted for more intricate structures. For wide-band simulations, IEDG allows one to adopt the discretization that is generated at a lower frequency for the calculation at higher frequencies through adaptively refining the elements. This helps to reduce the computational burden. However, adoption of higher frequency mesh at lower frequencies could result in the well known "sub-wavelength breakdown" problem for conventional MLFMM. The computational complexity deteriorates significantly for both multi-scale or low frequency problems. In this paper, IEDG is accelerated by hierarchical multi-level fast multipole method, especially for the problems that involve the dense mesh in a local or global scale. H-MLFMM separates the evanescent physics from radiation physics and employ different transformation of basis accordingly. For the evanescent regime, where densely discretized elements reside, it identifies a reduced set of numerically independent basis functions from the original ones via a skeletonalization algorithm, which in essence is a kernel independent algebraic data spacification algorithm. The reduced set of basis functions are named "skeletons" or "skeleton DoFs" and they are adopted to represent the interaction related with the original set of basis functions. Subsequently, significant reduction in memory consumption and CPU time per matrix-vector multiplication (MVP) are achieved through the compressed coupling matrices. With the H-MLFMM incorporated, IEDG offers a very attractive approach to solve for the wide-band EM response from a target via the mesh at midfrequency.

1. The conformations of 2-benzylidenecyclohexanone, its 2-p-halo-derivatives, and pulegone were investigated by the method of dipole moments (DM). These compounds have a half-chair conformation, while the phenyl radical in the benzylidene derivatives occupies a trans-position relative to the carbonyl group. 2. For 2,6-dibenzylidenecyclohexanone and its 2,6-di-p-halo-derivatives, an envelope-type conformation was demonstrated, according to the data of DM and IR spectroscopy. 3. For benzylidenecyclohexanone oxide, a chair conformation with an axial oxygen atom of the epoxy group is preferential.

Characteristic mode (CM) analysis of multi-scale and complex targets has attracted much attention in computational electromagnetics. However, it is hard to calculate the multi-scale problems in terms of desired accuracy and stability by using conventional methods. What is more, it is a challenging work to generate a good quality mesh for the multi-scale structures including very fine features. In this paper, we present Discontinuous Galerkin (DG) surface integral equations-based theory to analyze the CMs. The multi-scale objects are firstly divided into several subdomains, and we generate the meshes of every parts independently. HRWG basis functions are adopted in our work and the characteristic currents are expanded by HRWG basis functions. In many applications, only characteristic currents with small eigenvalues are desired because they are corresponding to the modes that radiate efficiently and have large modal coefficients. Special singularity extraction schemes are chosen to treat the infinite term in the resulting integral equations since HRWG basis functions are not divergence-conforming and there is divergence operator in electric field integral equation (EFIF) and magnetic field integral equation (MFIE). In DG method, they are no requirements for normal continuity of currents across the contour of between every two subdomains, hence, the proposed method can handle both non-conformal mesh and conformal mesh. Numerical results are presented to validate the propose formulation. This work may offer great flexibility to CM analysis of multi-scale and complex structures.

In this paper, a volume scattering model for a wider variety of scatterers in vegetation remote sensing is proposed by utilizing computational electromagnetics in developing the scattering model of the scatterers. In this proposed model, both Equivalent Principle Algorithm (EPA) and Relaxed Hierarchical Equivalent Source Algorithm (RHESA) are coupled together as the computational electromagnetics method in calculating the backscattering cross section from the scatterers available in vegetation medium. This paper firstly presents the related work and its research gap, followed by the discussion on the proposed approach and the methodology in developing the model. This paper also proposes the technique to validate the developed model.

In this paper, we propose a novel loop extraction algorithm that significantly outperforms other computational electromagnetics methods. Since the algorithm does not involve loop independence tests and the rejection of candidate loops, it is also more efficient than the polynomial-time loop extraction algorithms. Further tests demonstrate that our algorithm can find a spanning tree and associated subminimal loops in linear time for a donut structure consisting of many holes

In this work, a hybrid distributed/shared memory parallelization scheme is presented for the domain green’s function method (DGFM). The DGFM is a domain decomposition based computational electromagnetics (CEM) method used for analyzing large disjoint antenna arrays. The array configurations considered consists of identical elements, with regular or irregular array layouts. The hybrid MPI/OpenMP parallelization strategy introduced in this work offers satisfactory speedup performance. This allows for the simulation of large array geometries in a distributed computing environment.

A conformational study of 5,5′-bis-(1,3,6-trimethyluracylyl)methane (1) is carried out using molecular orbital calculations (AM1), molecular mechanics, dipole moment, and electric birefringence methods. The AM1 calculations result in good agreement with the experimental data. Populations of the helical steady states and the ways of their interconversion are determined. Dipole moments, Kerr's constants, optical anisotropies of the title compound, and some related 1,3-dimethyluracyls are measured.

In electromagnetic sounding, the detection areas of time-domain and frequency-domain electromagnetic detection methods cannot be effectively connected, and the detection processes for these two methods must be implemented separately. To combine time-domain and frequency-domain electromagnetic detection methods and simplify the detection process, a time-frequency fusion transmission method is proposed to simultaneously excite the earth to produce transient and steady-state responses. By analyzing the characteristics of the time-domain and frequency-domain excitation current waveforms, a pseudorandom transmission waveform with dead time is designed, and a transmission system for a time-frequency fusion electromagnetic detection method is developed. In this detection mode, the pseudorandom transmission waveform contains several frequencies, and the transient induction field can be received during the dead time. The time-domain and frequency-domain responses can be obtained by the same procedure. At the same time, a self-adaptive pseudoload device is designed and matched with the corresponding control sequence to reduce the influence of dead-time. The experimental results show that the self-adaptive pseudoload transmitter can effectively reduce the current fluctuation, and the time-frequency electromagnetic transmission system can effectively excite the earth to produce transient and steady-state responses. The time-frequency fusion electromagnetic transmission method proposed in this paper can be used in electromagnetic detection instruments to improve the efficiency of electromagnetic sounding.

An analytic electromagnetic calculation method for doubly fed induction generator (DFIG) in wind turbine system was presented. Based on the operation principles, steady state equivalent circuit and basic equations of DFIG, the modeling for electromagnetic calculation of DFIG was proposed. The electromagnetic calculation of DFIG was divided into three steps: the magnetic flux calculation, parameters derivation and performance checks. For each step, the detailed numeric calculation formulas were all derived. Combining the calculation formulas, the whole electromagnetic calculation procedure was established, which consisted of three iterative calculation loops, including magnetic saturation coefficient, electromotive force and total output power. All of the electromagnetic and performance data of DIFG can be calculated conveniently by the established calculation procedure, which can be used to evaluate the new designed machine. A 1.5 MW DFIG designed by the proposed procedure was built, for which the whole type tests including no-load test, load test and temperature rising test were carried out. The test results have shown that the DFIG satisfies technical requirements and the test data fit well with the calculation results which prove the correctness of the presented calculation method.

Application of the pseudospectral method in numerical calculations is well established. The method is used in several disciplines, from geology to applied mathematics. The pseudospectral method also appears in computational electromagnetism. Its implementation already has been carried out for the finite element method and finite difference time domain method. In this study, we implement the pseudospectral method for the finite difference frequency domain (FDFD) method, and hence the resulting method is called the pseudospectral frequency domain (PSFD) method. The PSFD method is compared to the FDFD method in terms of the numerical phase velocity and anisotropy. The method is extended for the nonlinear process PSFD (NL-PSFD) of second-harmonic generation. It is shown how a plane wave source at oblique incidence can be implemented, and its performance for tilted quasi-phase-matched grating is discussed. Finally, a specific method is deduced from NL-PSFD for large-volume simulation, where only second-order nonlinearity is spatially structured, and a two-dimensional nonlinear photonic crystal is simulated.

In this paper, a general comparison is presented between time-domain and frequency-domain simulation schemes of phased arrays. A series of Vivaldi arrays are simulated with finite integral time-domain (FITD) and frequency-domain finite element method (FEM) in terms of its far field characteristic like radiation pattern and gain. Three finite arrays of 10 by 10, 20 by 20, and 30 by 30 are simulated using FITD. The results are compared with that of the same arrays by linear combination of a unit Vivaldi antenna simulated with FEM. It is concluded that for small arrays time domain is more accurate while for large ones frequency domain method is more superior in terms of computer time and memory.