Multi-objective design of antenna structures using variable-fidelity EM simulations and co-kriging

A methodology for low-cost multi-objective design of antenna structures is proposed. To reduce the computational effort of the design process the initial Pareto front is obtained by optimizing the response surface approximation (RSA) model obtained from low-fidelity EM simulations of the antenna structure of interest. The front is further refined by iterative incorporation of a limited number of high-fidelity training points into the RSA surrogate using co-kriging. Our considerations are illustrated using two examples of antenna structure

Ab initio calculation of the shift photocurrent by Wannier interpolation

We describe and implement a first-principles algorithm based on maximally-localized Wannier functions for calculating the shift-current response of piezoelectric crystals in the independent-particle approximation. The proposed algorithm presents several advantages over existing ones, including full gauge invariance, low computational cost, and a correct treatment of the optical matrix elements with nonlocal pseudopotentials. Band-truncation errors are avoided by a careful formulation of $k\cdot p$ perturbation theory within the subspace of wannierized bands. The needed ingredients are the matrix elements of the Hamiltonian and of the position operator in the Wannier basis, which are readily available at the end of the wannierization step. If the off-diagonal matrix elements of the position operator are discarded, our expressions reduce to the ones that have been used in recent tight-binding calculations of the shift current. We find that this `diagonal' approximation can introduce sizeable errors, highlighting the importance of carefully embedding the tight-binding model in real space for an accurate description of the charge transfer that gives rise to the shift current.Comment: 13 pages, 7 figure

Robust variable-fidelity optimization of microwave filters using co-Kriging and trust regions

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Formation of Black Holes in Topologically Massive Gravity

We present an exact solution in 3-dimensional topologically massive gravity with negative cosmological constant which dynamically interpolates between a past horizon and a chiral AdS pp-wave. Similarly, upon time reversal, one obtains an AdS pp-wave with a future event horizonComment: Improved presentation. Extended discussion of linear stability and regularity of the metric. Added reference

Variable-fidelity electromagnetic simulations and co-kriging for accurate modeling of antennas

Accurate and fast models are indispensable in contemporary antenna design. In this paper, we describe the low-cost antenna modeling methodology involving variable-fidelity electromagnetic (EM) simulations and co-Kriging. Our approach exploits sparsely sampled accurate (high-fidelity) EM data as well as densely sampled coarse-discretization (low-fidelity) EM simulations that are accommodated into one model using the co-Kriging technique. By using coarse-discretization simulations, the computational cost of creating the antenna model is greatly reduced compared to conventional approaches, where high-fidelity simulations are directly used to set up the model. At the same time, the modeling accuracy is not compromised. The proposed technique is demonstrated using three examples of antenna structures. Comparisons with conventional modeling based on high-fidelity data approximation, as well as applications for antenna design, are also discussed

Cost-efficient modeling of antenna structures using Gradient Enhanced Kriging

Reliable yet fast surrogate models are indispensable in the design of contemporary antenna structures. Data-driven models, e.g., based on Gaussian Processes or support-vector regression, offer sufficient flexibility and speed, however, their setup cost is large and grows very quickly with the dimensionality of the design space. In this paper, we propose cost-efficient modeling of antenna structures using Gradient-Enhanced Kriging. In our approach, the training data set contains, apart from the EM-simulation responses of the structure at hand, also derivative data at the respective training locations obtained at little extra cost using adjoint sensitivity techniques. We demonstrate that introduction of the derivative information into the model allows for considerable reduction of the model setup cost (in terms of the number of training points required) without compromising its predictive power. The Gradient-Enhanced Kriging technique is illustrated using a dielectric resonator antenna structure. Comparison with conventional Kriging interpolation is also provided

Trench width dependant deeply etched surface-defined InP gratings for low-cost high speed DFB/DBR

In this paper we are reporting a fabrication process for multi-section telecom lasers based on surface defined lateral gratings, which is compatible with low-cost high-throughput nano-imprint lithography. A new grating definition process is developed, which allow a better control of the cross section geometry to obtain higher coupling strength

Symmetric polynomials and lpl^p inequalities for certain intervals of pp

We prove some sufficient conditions implying $l^p$ inequalities of the form $||x||_p \leq ||y||_p$ for vectors $x, y \in [0,\infty)^n$ and for $p$ in certain positive real intervals. Our sufficient conditions are strictly weaker than the usual majorization relation. The conditions are expressed in terms of certain homogeneous symmetric polynomials in the entries of the vectors. These polynomials include the elementary symmetric polynomials as a special case. We also give a characterization of the majorization relation by means of symmetric polynomials.Comment: 21 pages - Revised version of 18 April, 2010: Added example of Theorem 1, pages 11-13. To appear in Houston J. of Mat