Large Number Of Unknowns Research Articles

An Enhanced Augmented Electric-Field Integral Equation Formulation for Dielectric Objects

A full-wave surface integral equation (SIE) method based on the augmented electric-field integral equation (A-EFIE) for dielectric objects with low-frequency stability is presented in this paper. Motivated by the A-EFIE formulation for perfect electric conductor (PEC), the internal and external problems are both augmented with the current continuity equation and renormalized to eliminate the low-frequency breakdown. Although the magnetic-field integral equation operator $\mathcal{K}$ is free of low-frequency breakdown, its matrix form is ill-conditioned and unsolvable if the traditional Rao–Wilton–Glisson (RWG) basis function is used as the testing and basis functions. As a remedy, the Buffa–Christiansen (BC) basis function is introduced to alleviate this testing issue. After this treatment, the matrix form of operator $\mathcal{K}$ is well conditioned. To solve problems with a large number of unknowns, a preconditioning scheme is introduced to accelerate the convergence and the mixed-form fast multipole algorithm (FMA) is adopted to accelerate the matrix vector product.

Complacency in the Face of Evolving Cybersecurity Norms is Hazardous

Constantly evolving legal requirements and changing technology, the business executives and board of directors members are often reluctant to adopt policies that require a high level of corporate-wide commitment. Expenditures on cybersecurity may not have concrete and identifiable benefits nor generate revenues. Corporate inertia with respect to implementing rigorous cyber-defense is understandable.There are very large number of unknowns. Corporate decision makers often receive a great amount of contradictory advice. The C-suite needs to think and act strategically. Cybersecurity challenges will not go away if ignored. The threat demands action and policies consistent with the corporation’s profile and its sector's norms.Failing to take such action means greater regulatory and litigation risk, irrespective of whether the cybersecurity posture adopted will be effective in defending against cyber-attacks. Noncompliance with cybersecurity norms are likely to damage the corporation’s reputation in the marketplace and with customers, suppliers, and other business partners. The corporation needs well thought out policies that include plans to respond to cyber-attacks and to recover from them.

A Sparsity-Constrained Preconditioned Kaczmarz Reconstruction Method for Fluorescence Molecular Tomography.

Fluorescence molecular tomography (FMT) is an imaging technique that can localize and quantify fluorescent markers to resolve biological processes at molecular and cellular levels. Owing to a limited number of measurements and a large number of unknowns as well as the diffusive transport of photons in biological tissues, the inverse problem in FMT is usually highly ill-posed. In this work, a sparsity-constrained preconditioned Kaczmarz (SCP-Kaczmarz) method is proposed to reconstruct the fluorescent target for FMT. The SCP-Kaczmarz method uses the preconditioning strategy to minimize the correlation between the rows of the forward matrix and constrains the Kaczmarz iteration results to be sparse. Numerical simulation and phantom and in vivo experiments were performed to test the efficiency of the proposed method. The results demonstrate that both the convergence and accuracy of the proposed method are improved compared with the classical memory-efficient low-cost Kaczmarz method.

Boundary Control Problems in Convective Heat Transfer with Lifting Function Approach and Multigrid Vanka-Type Solvers

AbstractThis paper deals with boundary optimal control problems for the heat and Navier-Stokes equations and addresses the issue of defining controls in function spaces which are naturally associated to the volume variables by trace restriction. For this reason we reformulate the boundary optimal control problem into a distributed problem through a lifting function approach. The stronger regularity requirements which are imposed by standard boundary control approaches can then be avoided. Furthermore, we propose a new numerical strategy that allows to solve the coupled optimality system in a robust way for a large number of unknowns. The optimality system resulting from a finite element discretization is solved by a local multigrid algorithm with domain decomposition Vanka-type smoothers. The purpose of these smoothers is to solve the optimality system implicitly over subdomains with a small number of degrees of freedom, in order to achieve robustness with respect to the regularization parameters in the cost functional. We present the results of some test cases where temperature is the observed quantity and the control quantity corresponds to the boundary values of the fluid temperature in a portion of the boundary. The control region for the observed quantity is a part of the domain where it is interesting to match a desired temperature value.

Flow rate and total discharge estimations in gas-well blowouts

Despite multitier safeguards in any drilling operation, blowouts do occur. When such accidents take place, the total discharge of hydrocarbons becomes the focal point for all concerned, including the operator, the service provider, and the regulatory body. Rate estimation becomes a daunting task with scant information about the formation and fluids at the time of the accident. Given that new regulatory guidelines require such estimates for any offshore drilling, systematic investigation is imperative.This study presents an analytical model coupling the flow in a reservoir/wellbore system of a gas well. The model considers flow in the tubing, annulus and riser, and the attendant heat transfer in this formulation/wellbore system. To gauge safety concerns, a commercially available plume dispersion model is used to examine consequences of a blowout under various wind speed scenarios in the absence of any ignition source. In the event of gas ignition, the energy of the explosion of the flammable gas is estimated with an empirical method in terms of trinitrotoluene (TNT) equivalency. The energy released by the jet fire associated with flammable gas is also evaluated.Two published field cases provided insight into the model's applicability in actual situations and some perspective on solution quality. However, given the large number of unknowns in any setting, we adopted the statistical design of experiments to understand the impact of independent variables. These variables include formation permeability, connected reservoir pore-volume, and restrictions in flow path, among others. Overall, the model results are in agreement with the previous findings. Specifically, we observed that reservoir permeability controls the flow rate; hence, the cumulative production for a given flow cross-sectional area in the well. In addition, the reservoir pore-volume connected to the well has a large impact on the rate of production decline; therefore, the total discharge volume.

A Study of Sparse Matrix Methods on New Hardware

Modeling of numerous scientific and engineering problems, such as multi-physic problems and analysis of electrical power systems, amounts to the solution of large scale linear systems. The main characteristics of such systems are the large sparsity ratio and the large number of unknowns that can reach thousands or even millions of equations. As a result, efficient solution of sparse large-scale linear systems is of great importance in order to enable analysis of such problems. Direct and iterative algorithms are the prevalent methods for solution of linear systems. Advances in computer hardware provide new challenges and capabilities for sparse solvers. The authors present a comprehensive evaluation of some, state of the art, sparse methods (direct and iterative) using modern computing platforms, aiming to determine the performance boundaries of each solver on different hardware infrastructures. By identifying the potential performance bottlenecks of out-of-core direct methods, the authors present a series of optimizations that increase their efficiency on flash-based systems.

Substructure isolation and damage identification using free responses

Structural health monitoring (SHM) has become a hot and intensively researched field in civil engineering. Thereinto, damage identification play an important role in maintaining structural integrity and safety. Many effective methods have been proposed for damage identification. However, accurate global identification of large real-world structures is not easy due to their complex and often unknown boundary conditions, nonlinear components, insensitivity of global response to localized damages, etc. Furthermore, global identification often requires lots of sensors and involves large number of unknowns. This is costly, rarely feasible in practice, and usually yields severely ill-conditioned identification problems. Substructuring approach is a possible solution: substructuring methods can focus on local small substructures; they need only a few sensors placed on the substructure and yield smaller and numerically much more feasible identification problems. This paper proposed an improved substructure method using local free response for substructure damage identification. The virtual supports are constructed by Substructure Isolation Method (SIM) using the linear combination of the substructural responses. The influence of the global errors is isolated by adding the virtual supports on the main degree of freedoms (DOFs) of the substructure. Through the correlation analysis, the substructural modes are selected and used for damage identification of the substructure. A plain model of cable stayed bridge is used for the verification of the proposed method.

A Statistical-Measure-Based Adaptive Land Cover Classification Algorithm by Efficient Utilization of Polarimetric SAR Observables

The polarimetric information contained in polarimetric synthetic aperture radar (SAR) images represents great potential for characterization of natural and urban surfaces. However, it is still challenging to identify different land cover classes with polarimetric data. Most of the classification algorithms presented earlier have used a fixed value of polarimetric indexes for segregation of a particular land cover type from other classes. However, the value of these polarimetric indexes may change accordingly with change in observation site, temporal acquisition, environmental conditions, and calibration differences among various systems. Thus, the value of polarimetric indexes for segregation of each land cover type has to be tuned in order to cope with these changes. Therefore, in this paper, a decision-tree-based adaptive land cover classification technique has been proposed for labeling of different clusters to their own classes. The proposed method uses spatial-statistics-based expressions (i.e., median “ M” and standard deviation “ S”) of best-selected polarimetric indexes on the basis of a separability index criterion for creating the decision boundary among various classes. In order to make the system adaptive in nature, unknown terms have been included in the expressions. Due to the dependence of a developed nonlinear relationship of overall classification accuracy (OA) on large number of unknowns, a genetic algorithm (GA) approach has been used, which provides optimum values of considered polarimetric indexes for automatic segregation of different classes. The proposed algorithm is successfully tested and validated on ALOS PALSAR quad-pol data.

An Iterative Domain Decomposition Method for Solving Wave Propagation Problems

Solving electromagnetic wave propagation problems with the finite-element method results in a large number of unknowns due to the necessity of modeling an extensive portion of the surroundings of the conducting structures. These equation systems are often ill-conditioned because of the great material differences as well as changes in size between neighboring elements. In addition, the resulting matrices are indefinite. Common iterative methods exhibit poor convergence due to these conditions. Direct solution techniques result in high memory requirements. The aim of this article is to present an approach with smaller memory demand than the direct methods and better convergence properties than common iterative techniques. An iterative method based on domain decomposition is presented and compared to various conventional iterative and direct solution techniques.

A second order PVM flux limiter method. Application to magnetohydrodynamics and shallow stratified flows

In this work we propose a second order flux limiter finite volume method, named PVM-2U-FL, that only uses information of the two external waves of the hyperbolic system. This method could be seen as a natural extension of the well known WAF method introduced by E.F. Toro in [23]. We prove that independently of the number of unknowns of the 1D system, it recovers the second order accuracy at regular zones, while in presence of discontinuities, the scheme degenerates to PVM-2U method, which can be seen as an improvement of the HLL method (see [6,10]). Another interesting property of the method is that it does not need any spectral decomposition of the Jacobian or Roe matrix associated to the flux function. Therefore, it can be easily applied to systems with a large number of unknowns or in situations where no analytical expression of the eigenvalues or eigenvectors are known. In this work, we apply the proposed method to magnetohydrodynamics and to stratified multilayer flows. Comparison with the two-waves WAF and HLL-MUSCL methods are also presented. The numerical results show that PVM-2U-FL is the most efficient and accurate among them.

System-Level Thermal Modeling Using Nonconformal Domain Decomposition and Model-Order Reduction

To keep up with increasing modeling complexity arising from 3-D integration, novel thermal modeling methods are required to tackle large-scale 3-D systems. In this paper, we propose a system-level thermal modeling method using nonconformal domain decomposition and Krylov space-based model-order reduction (MOR) for both steady-state and transient analysis. To efficiently model a 3-D system, the system is divided into separate domains with independent meshing grids using nonconformal domain decomposition. As a result, reduced-order models can be created for individual domains with MOR ports, which can reduce the computational challenge of performing MOR for the entire system with a large number of unknowns and ports. The connectivity between domains is captured using coupling matrices via Lagrange multipliers and Schur complements. In addition, the proposed method can efficiently handle varying design parameters, such as air convection coefficient and thermal conductivity without performing parameterized MOR. The modeling results show that the proposed method can efficiently simulate 3-D systems with hundreds of ports with a speed-up of 20×, compared with just thermal modeling using domain decomposition.

Whittle-Matérn priors for Bayesian statistical inversion with applications in electrical impedance tomography

We study flexible and proper smoothness priors for Bayesian statistical inverse problems by using Whittle-Matern Gaussian random fields. We review earlier results on finite-difference approximations of certain Whittle-Matern random field in $\mathbb{R}^2$. Then we derive finite-element method approximations and show that the discrete approximations can be expressed as solutions of sparse stochastic matrix equations. Such equations are known to be computationally efficient and useful in inverse problems with a large number of unknowns. &nbsp The presented construction of Whittle-Matern correlation functions allows both isotropic or anisotropic priors with adjustable parameters in correlation length and variance. These parameters can be used, for example, to model spatially varying structural information of unknowns. &nbsp As numerical examples, we apply the developed priors to two-dimensional electrical impedance tomography problems.

Modeling tools for dengue risk mapping - a systematic review.

IntroductionThe global spread and the increased frequency and magnitude of epidemic dengue in the last 50 years underscore the urgent need for effective tools for surveillance, prevention, and control. This review aims at providing a systematic overview of what predictors are critical and which spatial and spatio-temporal modeling approaches are useful in generating risk maps for dengue.MethodsA systematic search was undertaken, using the PubMed, Web of Science, WHOLIS, Centers for Disease Control and Prevention (CDC) and OvidSP databases for published citations, without language or time restrictions. A manual search of the titles and abstracts was carried out using predefined criteria, notably the inclusion of dengue cases. Data were extracted for pre-identified variables, including the type of predictors and the type of modeling approach used for risk mapping.ResultsA wide variety of both predictors and modeling approaches was used to create dengue risk maps. No specific patterns could be identified in the combination of predictors or models across studies. The most important and commonly used predictors for the category of demographic and socio-economic variables were age, gender, education, housing conditions and level of income. Among environmental variables, precipitation and air temperature were often significant predictors. Remote sensing provided a source of varied land cover data that could act as a proxy for other predictor categories. Descriptive maps showing dengue case hotspots were useful for identifying high-risk areas. Predictive maps based on more complex methodology facilitated advanced data analysis and visualization, but their applicability in public health contexts remains to be established.ConclusionsThe majority of available dengue risk maps was descriptive and based on retrospective data. Availability of resources, feasibility of acquisition, quality of data, alongside available technical expertise, determines the accuracy of dengue risk maps and their applicability to the field of public health. A large number of unknowns, including effective entomological predictors, genetic diversity of circulating viruses, population serological profile, and human mobility, continue to pose challenges and to limit the ability to produce accurate and effective risk maps, and fail to support the development of early warning systems.Electronic supplementary materialThe online version of this article (doi:10.1186/1476-072X-13-50) contains supplementary material, which is available to authorized users.

Reservoir management using streamline-based flood efficiency maps and application to rate optimization

Abstract 3-D streamlines provide an effective tool for reservoir management because of their ability to display reservoir flow and well connections in a physically intuitive manner. Streamlines have been extensively used to investigate the interaction between heterogeneity and well patterns and also for rate allocation and pattern balancing. More recently, streamlines have been used in conjunction with constrained optimization techniques for improving waterflood performance via rate control. Field scale rate optimization problems, however, involve highly complex reservoir models, production and facilities constraints and a large number of unknowns, making them inaccessible for routine waterflood management. In this paper we provide a simple and easy to use workflow for waterflood rate optimization using streamline-based flood efficiency maps that display the flux and time of flight distribution amongst producing wells. We demonstrate the use of flood efficiency map to optimize the injection/production rates to maximize waterflood sweep efficiency by equalizing the average time of flight (TOF) amongst the producing wells in regional basis. Our optimization approach is extremely efficient because it relies on simple analytic calculations to compute weighting factors for injection and production rates to minimize the TOF variance amongst producing wells. Because the approach does not rely on formal and complex optimization tools, it is particularly well-suited for large-scale field application. Also, the approach can be used with both streamline and finite difference simulators. For finite-difference simulations, the streamlines and time of flight are derived from the flux field generated by the simulator. Multiple examples are presented to support the robustness and efficiency of the proposed waterflood management scheme. These include 2D synthetic examples for validation and a 3D field application.

A starting-point strategy for interior-point algorithms for shakedown analysis of engineering structures

Lower-bound shakedown analysis leads to nonlinear convex optimization problems with large numbers of unknowns and constraints, the solution of which can be obtained efficiently by interior-point algorithms. The performance of these algorithms strongly depends on the choice of the starting point. In general, starting points should be located inside the feasible region. In addition, they should also be well centred. Although there exist several heuristics for the construction of suitable starting points, these are restricted, as long as only the mathematical procedure is considered without taking into account the nature of the underlying mechanical problem. Thus, in this article, a strategy is proposed for choosing appropriate starting points for interior-point algorithms applied to shakedown analysis. This strategy is based on both the mathematical characteristics and the physical meaning of the variables involved. The efficiency of the new method is illustrated by numerical examples from the field of power plant engineering.

Multilevel fast multipole method based on a potential formulation for 3D electromagnetic scattering problems

A combination of the multilevel fast multipole method (MLFMM) and boundary element method (BEM) can solve large scale photonics problems of arbitrary geometry. Here, MLFMM-BEM algorithm based on a scalar and vector potential formulation, instead of the more conventional electric and magnetic field formulations, is described. The method can deal with multiple lossy or lossless dielectric objects of arbitrary geometry, be they nested, in contact, or dispersed. Several examples are used to demonstrate that this method is able to efficiently handle 3D photonic scatterers involving large numbers of unknowns. Absorption, scattering, and extinction efficiencies of gold nanoparticle spheres, calculated by the MLFMM, are compared with Mie's theory. MLFMM calculations of the bistatic radar cross section (RCS) of a gold sphere near the plasmon resonance and of a silica coated gold sphere are also compared with Mie theory predictions. Finally, the bistatic RCS of a nanoparticle gold-silver heterodimer calculated with MLFMM is compared with unmodified BEM calculations.

Direct Matrix Solution of Linear Complexity for Surface Integral-Equation-Based Impedance Extraction of Complicated 3-D Structures

We develop a linear-complexity direct matrix solution for the surface integral equation (IE)-based impedance extraction of arbitrarily shaped 3-D nonideal conductors embedded in a dielectric material. A direct inverse of a highly irregular system matrix composed of both dense and sparse matrix blocks is obtained in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> ) complexity with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> being the matrix size. It outperforms state-of-the-art impedance solvers, be they direct solvers or iterative solvers, with fast central processing unit (CPU) time, modest memory consumption, and without sacrificing accuracy, for both small and large number of unknowns. The inverse of a 2.68-million-unknown matrix arising from the extraction of a large-scale 3-D interconnect having 128 buses, which is a matrix solution for 2.68 million right-hand sides, was obtained in less than 1.5 GB memory and 1.3 h on a single CPU running at 3 GHz.

A new min-max methodology for computing optimised obstacle avoidance steering manoeuvres of ground vehicles

In this paper, a new methodology for computing optimised obstacle avoidance steering manoeuvres for ground vehicles is presented and discussed. Most of the existing methods formulate the obstacle avoidance problem as an optimal control problem which is hard to solve or as a numerical optimisation problem with a large number of unknowns. This method is based on a reformulation of Pontryagin's Maximum Principle and leads to the solution of an adjustable time optimal controller. The control input is significantly simplified and permits its application in a sample and hold sense. Furthermore, with the proposed approach the maximum tyre forces exerted during the manoeuvre are minimised. In this study, it is shown how to ‘warm start’ the proposed algorithm and which constraints to ‘relax’. Numerical examples and benchmark tests illustrate the performance of the proposed controller and compare it with other standard controllers. A sensitivity analysis for different vehicle parameters is performed and finally conclusions are drawn. A significant advantage of the method is the small computational complexity. The overall simplicity of the controller makes it attractive for application on autonomous vehicles.

Parallel simulation of patient‐specific atherosclerotic arteries for the enhancement of intravascular ultrasound diagnostics

PurposeThe purpose of this paper is to present a computational framework for the simulation of patient‐specific atherosclerotic arterial walls. Such simulations provide information regarding the mechanical stress distribution inside the arterial wall and may therefore enable improved medical indications for or against medical treatment. In detail, the paper aims to provide a framework which takes into account patient‐specific geometric models obtained by in vivo measurements, as well as a fast solution strategy, giving realistic numerical results obtained in reasonable time.Design/methodology/approachA method is proposed for the construction of three‐dimensional geometrical models of atherosclerotic arteries based on intravascular ultrasound virtual histology data combined with angiographic X‐ray images, which are obtained on a routine basis in the diagnostics and medical treatment of cardiovascular diseases. These models serve as a basis for finite element simulations where a large number of unknowns need to be calculated in reasonable time. Therefore, the finite element tearing and interconnecting‐dual primal (FETI‐DP) domain decomposition method is applied, to achieve an efficient parallel solution strategy.FindingsIt is shown that three‐dimensional models of patient‐specific atherosclerotic arteries can be constructed from intravascular ultrasound virtual histology data. Furthermore, the application of the FETI‐DP domain decomposition method leads to a fast numerical framework. In a numerical example, the importance of three‐dimensional models and thereby fast solution algorithms is illustrated by showing that two‐dimensional approximations differ significantly from the 3D solution.Originality/valueThe decision for or against intravascular medical treatment of atherosclerotic arteries strongly depends on the mechanical situation of the arterial wall. The framework presented in this paper provides computer simulations of stress distributions, which therefore enable improved indications for medical methods of treatment.

Continuous modeling of metabolic networks with gene regulation in yeast and in vivo determination of rate parameters

A continuous model of a metabolic network including gene regulation to simulate metabolic fluxes during batch cultivation of yeast Saccharomyces cerevisiae was developed. The metabolic network includes reactions of glycolysis, gluconeogenesis, glycerol and ethanol synthesis and consumption, the tricarboxylic acid cycle, and protein synthesis. Carbon sources considered were glucose and then ethanol synthesized during growth on glucose. The metabolic network has 39 fluxes, which represent the action of 50 enzymes and 64 genes and it is coupled with a gene regulation network which defines enzyme synthesis (activities) and incorporates regulation by glucose (enzyme induction and repression), modeled using ordinary differential equations. The model includes enzyme kinetics, equations that follow both mass-action law and transport as well as inducible, repressible, and constitutive enzymes of metabolism. The model was able to simulate a fermentation of S. cerevisiae during the exponential growth phase on glucose and the exponential growth phase on ethanol using only one set of kinetic parameters. All fluxes in the continuous model followed the behavior shown by the metabolic flux analysis (MFA) obtained from experimental results. The differences obtained between the fluxes given by the model and the fluxes determined by the MFA do not exceed 25% in 75% of the cases during exponential growth on glucose, and 20% in 90% of the cases during exponential growth on ethanol. Furthermore, the adjustment of the fermentation profiles of biomass, glucose, and ethanol were 95%, 95%, and 79%, respectively. With these results the simulation was considered successful. A comparison between the simulation of the continuous model and the experimental data of the diauxic yeast fermentation for glucose, biomass, and ethanol, shows an extremely good match using the parameters found. The small discrepancies between the fluxes obtained through MFA and those predicted by the differential equations, as well as the good match between the profiles of glucose, biomass, and ethanol, and our simulation, show that this simple model, that does not rely on complex kinetic expressions, is able to capture the global behavior of the experimental data. Also, the determination of parameters using a straightforward minimization technique using data at only two points in time was sufficient to produce a relatively accurate model. Thus, even with a small amount of experimental data (rates and not concentrations) it was possible to estimate the parameters minimizing a simple objective function. The method proposed allows the obtention of reasonable parameters and concentrations in a system with a much larger number of unknowns than equations. Hence a contribution of this study is to present a convenient way to find in vivo rate parameters to model metabolic and genetic networks under different conditions.