Multiscale Orthogonal Finite-Element Reduction-Recovery method for transient analysis of integrated circuits and package problems

A theoretical investigation into the cooperativity effect involving anionic hydrogen bond, thermodynamic property and aromaticity in Cl−⋯benzonitrile⋯H2O ternary complex

A direct domain-decomposition-based time-domain finite-element method of linear complexity is developed to overcome the challenge of simulating a wide range of geometrical scales present in an integrated circuit (IC) system. Via a set of orthogonal prism vector basis functions, we decompose the entire 3-D system of an IC problem into 2-D subsystems and then into 1-D subsystems with negligible computational cost. We then further decompose each 1-D subsystem into two domains, one with conductors and the other one with dielectrics. A direct solution without any iteration is proposed to solve the resulting system in linear complexity. Furthermore, the method allows for the use of different meshes in different domains. Numerical simulations of ICs and package problems have demonstrated the accuracy, linear complexity, and meshing flexibility of the proposed method.

In this paper, the semi-orthogonal compactly supported spline wavelets are used as basis functions for the efficient solution of the thin-wire electric field integral equation (EFIE) in frequency domain. The method of moments (MoM) is used via the Galerkin procedure. Conventional MoM directly applied to the EFIE, leads to dense matrix which often becomes computationally intractable when large-scale problems are approached. To overcome these difficulties, wavelets can be used as a basis set so obtaining the generation of a sparse matrix; this is due to the local supports and the vanishing moments properties of the wavelets. In the paper, this technique is applied to analyze electromagnetic transients in a lightning protection systems schematized as a thin-wire structure. The study is carried out in frequency domain; a discrete fast Fourier transform algorithm can be used to compute time profiles of the electromagnetic interesting quantities. The unknown longitudinal currents are expressed by using multiscale wavelet expansions. Thus, the thin-wire EFIE is converted into a matrix equation by the Galerkin method. Results for linear spline wavelets along with their comparison with conventional MoM that uses triangular basis functions and the point matching procedure are presented, for two case studies. Good agreement has been reached with a strong reduction of the computational complexity.

We present a formulation of the explicitly correlated second-order Møller-Plesset (MP2-F12) energy in which all nontrivial post-mean-field steps are formulated with linear computational complexity in system size. The two key ideas are the use of pair-natural orbitals for compact representation of wave function amplitudes and the use of domain approximation to impose the block sparsity. This development utilizes the concepts for sparse representation of tensors described in the context of the domain based local pair-natural orbital-MP2 (DLPNO-MP2) method by us recently [Pinski et al., J. Chem. Phys. 143, 034108 (2015)]. Novel developments reported here include the use of domains not only for the projected atomic orbitals, but also for the complementary auxiliary basis set (CABS) used to approximate the three- and four-electron integrals of the F12 theory, and a simplification of the standard B intermediate of the F12 theory that avoids computation of four-index two-electron integrals that involve two CABS indices. For quasi-1-dimensional systems (n-alkanes), the ON DLPNO-MP2-F12 method becomes less expensive than the conventional ON(5) MP2-F12 for n between 10 and 15, for double- and triple-zeta basis sets; for the largest alkane, C200H402, in def2-TZVP basis, the observed computational complexity is N(∼1.6), largely due to the cubic cost of computing the mean-field operators. The method reproduces the canonical MP2-F12 energy with high precision: 99.9% of the canonical correlation energy is recovered with the default truncation parameters. Although its cost is significantly higher than that of DLPNO-MP2 method, the cost increase is compensated by the great reduction of the basis set error due to explicit correlation.

Density functional B3LYP calculations of the electric field gradient at the metal site in small linear cadmium model complexes and two larger structures are presented. The results are compared to those by Hartree−Fock, second-order Møller−Plesset, and experiment. The quality of the cadmium basis set is tested by augmenting the uncontracted basis set of Kellö and Sadlej with additional basis functions. B3LYP generally gives an electric field gradient which is smaller in magnitude than Hartree−Fock with a reduction of the electric field gradient in the range 0.1−1.4 atomic units (au) or 15−30% for the examined complexes. This reduction of the electric field gradient seems to be caused by a larger cancellation of p- and d-contributions from the Cd atomic orbitals than for the other methods. The second-order Møller−Plesset result for the electric field gradient lies between B3LYP and Hartree−Fock, except for the complex chloroglycylglycinato(imidazole)cadmium. The changes of the electric field gradient between tested basis sets are up to 0.2 au or 6% and smaller than the variations between different methods. The addition of tight functions to the cadmium basis set has a smaller effect than extra basis functions in the range already spanned. Comparing to experiment, B3LYP gives the best result for dimethylcadmium. For the two larger cadmium complexes Hartree−Fock and second-order Møller−Plesset are closer to the measured values, but crystal effects are neglected making the comparison with experiment more uncertain than for dimethylcadmium.

We present a model order reduction algorithm for linear time-invariant descriptor systems of arbitrary derivative order that incorporates sensitivity analysis for network parameters in respect to design parameters. It is based on implicit moment matching via rational Krylov subspace methods with adaptive choice of expansion points and number of moments based on an error indicator. Additionally, we demonstrate how parametric reduced order models can be obtained at nearly no extra costs, such that parameter studies are extremely accelerated. The finite element model of a yaw rate sensor MEMS device has been chosen as a numerical example, but our method is also applicable to systems arising in modeling and simulation of electromagnetics, electrical circuits, machine tools, heat conduction and other phenomena.

Summary Density functional theory (DFT) trends in Gibbs free energies and enthalpies were thoroughly studied in calcite. Different coordination was applied for ionic species that exist in seawater and smartwater as well as for carboxylic acids presented in crude oil at distinct two primary hydration sites: >CO3H, >CaOH. The studied hydration sites were proposed based on electro-kinetics besides surface titration experimental studies.17, 18 Interfacial energy runs using the Gaussian 09 suits of program21, with Becke’s three parameter exchange and Lee Yang Parr corrected correlation functional (B3LYP) and 3-21G basis set, based on previous surface sites were performed to account for stability, reactivity and wettability alteration. The calculations predict the most stable complexes for calcite are, CO3H, CaO-, CO3Ca, CO3Mg , CaCO3-, CaHCO , CaH2O+ and CaSO4-. We also demonstrate that free ion species are having a higher free energy in seawater than in case of a complex and thus indicates a more reactivity of complex species to interact with rock sites. Furthermore, corresponding values of free energy and enthalpy change of ions association with calcite surface provided insights about complexes that are most favorable at the surface. This study proposes a mathematical correlation between thermochemistry profiles and wettability alteration, which expresses to us how the surface affinity for a certain organic compound compares with its affinity for water. The calculations agrees with previous experiment findings especially in case of Ca+2, Mg+2, SO4-2,MgOH+1 ,OH-1, and NaCl. Some reversed trend can be explained by the smaller size of the basis set used in the calculations. The results of this insights help in understating the interaction mechanism of this unique systems in order to modify reactivity for enhancing oil recovery (EOR) purposes, and to use the outcomes of this study to pose questions and directions for continuing theoretical efforts destined at linking macroscopic reactivity in case of altering wettability with molecular-level understanding.

This paper presents a game theoretic model and an iterative bidding framework for the service request prioritizing and scheduling problem in Software as a Service (SaaS) environments. We focus on a type of settings in which the service provider's existing capacity is over demanded and customers' service requests are constrained with completion times. To gain more profit, the provider needs to prioritize customers' requests based on their profitability and schedule as many profitable requests as possible. The prioritizing and scheduling problem is considered in a strategic setting in which customers' values on the service requests are their private information that is not known to the provider, which calls for economic based models. The key issue here is how to maximize economic social welfare across all customers given the presence of customers' self-interests. We propose an iterative bidding framework as a multilateral negotiation platform for the service provider and its customers to allocate compute capacity among service requests. The proposed bidding framework is evaluated by a computational study. The data from the experiments show that the proposed approach produces near optimal solutions with moderate information revelation. It also scales well to large size problem instances.

We present a fast adaptive PARAFAC decomposition algorithm with low computational complexity. The proposed algorithm generalizes the Orthonormal Projection Approximation Subspace Tracking (OPAST) approach for tracking a class of third-order tensors which have one dimension growing with time. It has linear complexity, good convergence rate and good estimation accuracy. To deal with large-scale problems, a parallel implementation can be applied to reduce both computational complexity and storage. We illustrate the effectiveness of our algorithm in comparison with the state-of-the-art algorithms through simulation experiments.

BatTri: A two-dimensional bathymetry-based unstructured triangular grid generator for finite element circulation modeling

A generic numerical tool has been developed to compute/optimize the sensitivity of array antenna receiver systems. This antenna system simulator is comprised of an ElectroMagnetic (EM) simulator and a MicroWave simulator (MW) for modeling the signal and noise characteristics of each receiver component. This analysis includes accurate modeling of the background noise (sky+ground), which is essential in radio astronomical applications, as well as the losses, reflections and noise contributions that occur in the microwave beamforming network. Validation has been carried out for a 4x1 monopole array receiver system. The modeled absolute power levels for a noisy 'hot' and 'cold' environment are in very good agreement with the measured noise power levels.

We present an adaptive refinement algorithm for T-splines on unstructured 2D meshes. While for structured 2D meshes, one can refine elements alternatingly in horizontal and vertical direction, such an approach cannot be generalized directly to unstructured meshes, where no two unique global mesh directions can be assigned. To resolve this issue, we introduce the concept of direction indices, i.e., integers associated to each edge, which are inspired by theory on higher-dimensional structured T-splines. Together with refinement levels of edges, these indices essentially drive the refinement scheme. We combine these ideas with an edge subdivision routine that allows for I-nodes, yielding a very flexible refinement scheme that nicely distributes the T-nodes, preserving global linear independence, analysis-suitability (local linear independence) except in the vicinity of extraordinary nodes, sparsity of the system matrix, and shape regularity of the mesh elements. Further, we show that the refinement procedure has linear complexity in the sense of guaranteed upper bounds on a) the distance between marked and additionally refined elements, and on b) the ratio of the numbers of generated and marked mesh elements.

The convergence rate of iterative methods can vary in an unpredictable way. It is related to the matrix condition number, which is notoriously bad for the electric field integral equation in the large-scale electromagnetic problems. Therefore, an efficient direct solution—a multilevel compressed block decomposition (MLCBD) algorithm based on the adaptive cross-approximation algorithm—is applied to overcome this problem; it is very efficient for the monostatic problems. Simulation results of the objects up and below ground in half space demonstrate that the proposed MLCBD method is efficient for analyzing electromagnetic problems. Copyright © 2013 John Wiley & Sons, Ltd.

Exploring mathematical approximation for the time spans of transfer operations in parcel transshipment terminals

Behavior of impact and explosion is complicated and usually involves large deformation and multi- material interaction of different phases. Failure and fragmentation of structure caused by impact or explosion also need to be considered. Simulation of impact and explosion problem requires a powerful numerical tool. The material point method, MPM, combines the advantages of Eulerian and Lagrangian description of motion. It eliminates the drawbacks of numerical difficulties associated with mesh distortion and element entanglement in Lagrangian and with the advected quantities in Eulerian description. Therefore the MPM is well suitable to the impact and explosive problems, which involves large deformation and interaction of different materials. A three dimensional material point method code, MPM3D, is developed. The linear hardening plasticity, Johnson-Cook plasticity and high explosive material model are implemented. Three kinds of equation of state (EOS) are implemented to calculate the pressure of different materials under extreme load. They are Gruneisen EOS for solid material, JWL EOS for explosive products, linear polynomial EOS for air. Numerical examples including Taylor bar impact, debris cloud and cylinder test are given to investigate the performance of MPM3D, which show that MPM is much more efficient than FEM and SPH in simulating hypervelocity impact and explosion problems, especially in large scale problems.