High precision swept volume approximation with conservative error bounds

In technical design processes in the automotive industry, digital prototypes rapidly gain importance, because they allow for a detection of design errors in early development stages. The technical design process includes the computation of swept volumes for maintainability analysis and clearance checks. The swept volume is very useful, for example, to identify problem areas where a safety distance might not be kept. With the explicit construction of the swept volume an engineer gets evidence on how the shape of components that come too close have to be modified.rnIn this thesis a concept for the approximation of the outer boundary of a swept volume is developed. For safety reasons, it is essential that the approximation is conservative, i.e., that the swept volume is completely enclosed by the approximation. On the other hand, one wishes to approximate the swept volume as precisely as possible. In this work, we will show, that the one-sided Hausdorff distance is the adequate measure for the error of the approximation, when the intended usage is clearance checks, continuous collision detection and maintainability analysis in CAD. We present two implementations that apply the concept and generate a manifold triangle mesh that approximates the outer boundary of a swept volume. Both algorithms are two-phased: a sweeping phase which generates a conservative voxelization of the swept volume, and the actual mesh generation which is based on restricted Delaunay refinement. This approach ensures a high precision of the approximation while respecting conservativeness.rnThe benchmarks for our test are amongst others real world scenarios that come from the automotive industry.rnFurther, we introduce a method to relate parts of an already computed swept volume boundary to those triangles of the generator, that come closest during the sweep. We use this to verify as well as to colorize meshes resulting from our implementations.

Manual pumping test method for characterizing the productivity of drilled wells equipped with rope pumps

Since the introduction of the rope-pump in Nicaragua in the 1990s, the dependence on wells in rural areas has grown steadily. However, little or no attention is paid to rope-pump well performance after installation. Due to financial restraints, groundwater resource monitoring using conventional testing methods is too costly and out of reach of rural municipalities. Nonetheless, there is widespread agreement that without a way to quantify the changes in well performance over time, prioritizing regulatory actions is impossible. A manual pumping test method is presented, which at a fraction of the cost of a conventional pumping test, measures the specific capacity of rope-pump wells. The method requires only sight modifcations to the well and reasonable limitations on well useage prior to testing. The pumping test was performed a minimum of 33 times in three wells over an eight-month period in a small rural community in Chontales, Nicaragua. Data was used to measure seasonal variations in specific well capacity for three rope-pump wells completed in fractured crystalline basalt. Data collected from the tests were analyzed using four methods (equilibrium approximation, time-drawdown during pumping, time-drawdown during recovery, and time-drawdown during late-time recovery) to determine the best data-analyzing method. One conventional pumping test was performed to aid in evaluating the manual method. The equilibrim approximation can be performed while in the field with only a calculator and is the most technologically appropriate method for analyzing data. Results from this method overestimate specific capacity by 41% when compared to results from the conventional pumping test. The other analyes methods, requiring more sophisticated tools and higher-level interpretation skills, yielded results that agree to within 14% (pumping phase), 31% (recovery phase) and 133% (late-time recovery) of the conventional test productivity value. The wide variability in accuracy results principally from difficulties in achieving equilibrated pumping level and casing storage effects in the puping/recovery data. Decreases in well productivity resulting from naturally occuring seasonal water-table drops varied from insignificant in two wells to 80% in the third. Despite practical and theoretical limitations on the method, the collected data may be useful for municipal institutions to track changes in well behavior, eventually developing a database for planning future ground water development projects. Furthermore, the data could improve well-users’ abilities to self regulate well usage without expensive aquifer characterization.

Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows

In this article, we develop the a priori and a posteriori error analysis of hp-version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ ℝd, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp-adaptive refinement algorithm.

Analytical Models of Exoplanetary Atmospheres. II. Radiative Transfer via the Two-Stream Approximation

We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and solutions describing two-stream radiative transfer (which approximates the passage of radiation as a pair of outgoing and incoming fluxes), flux-limited diffusion (which describes radiative transfer in the deep interior) and solutions for the temperature-pressure profiles. Generally, the problem is mathematically under-determined unless a set of closures (Eddington coefficients) is specified. We demonstrate that the hemispheric (or hemi-isotropic) closure naturally derives from the radiative transfer equation if energy conservation is obeyed, while the Eddington closure produces spurious enhancements of both reflected light and thermal emission. We concoct recipes for implementing two-stream radiative transfer in stand-alone numerical calculations and general circulation models. We use our two-stream solutions to construct toy models of the runaway greenhouse effect. We present a new solution for temperature-pressure profiles with a non-constant optical opacity and elucidate the effects of non-isotropic scattering in the optical and infrared. We derive generalized expressions for the spherical and Bond albedos and the photon deposition depth. We demonstrate that the value of the optical depth corresponding to the photosphere is not always 2/3 (Milne's solution) and depends on a combination of stellar irradiation, internal heat and the properties of scattering both in optical and infrared. Finally, we derive generalized expressions for the total, net, outgoing and incoming fluxes in the convective regime.

New method for analytical photovoltaic parameter extraction

Correct modeling of the equivalent circuits regarding solar cell and panels is today an essential tool for power optimization. However, the parameter extraction of those circuits is still a quite difficult task that normally requires both experimental data and calculation procedures, generally not available to the normal user. This paper presents a new analytical method that easily calculates the equivalent circuit parameters from the data that manufacturers usually provide. The analytical approximation is based on a new methodology, since methods developed until now to obtain the aforementioned equivalent circuit parameters from manufacturer's data have always been numerical or heuristic. Results from the present method are as accurate as the ones resulting from other more complex (numerical) existing methods in terms of calculation process and resources.

Optimal Piecewise Linear Function Approximation for GPU-based Applications

Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind of functions often implies a very high computational cost, unacceptable in real-time applications. To alleviate this problem, functions are commonly approximated by simpler piecewise-polynomial representations. Following this idea, we propose a novel, efficient, and practical technique to evaluate complex and continuous functions using a nearly optimal design of two types of piecewise linear approximations in the case of a large budget of evaluation subintervals. To this end, we develop a thorough error analysis that yields asymptotically tight bounds to accurately quantify the approximation performance of both representations. It provides an improvement upon previous error estimates and allows the user to control the trade-off between the approximation error and the number of evaluation subintervals. To guarantee real-time operation, the method is suitable for, but not limited to, an efficient implementation in modern Graphics Processing Units (GPUs), where it outperforms previous alternative approaches by exploiting the fixed-function interpolation routines present in their texture units. The proposed technique is a perfect match for any application requiring the evaluation of continuous functions, we have measured in detail its quality and efficiency on several functions, and, in particular, the Gaussian function because it is extensively used in many areas of computer vision and cybernetics, and it is expensive to evaluate.

The segmental approximation in multijunction solar cells

The segmental approach has been considered to analyze dark and light I-V curves. The photovoltaic (PV) dependence of the open-circuit voltage (Voc), the maximum power point voltage (Vm), the efficiency (?) on the photogenerated current (Jg), or on the sunlight concentration ratio (X), are analyzed, as well as other photovoltaic characteristics of multijunction solar cells. The characteristics being analyzed are split into monoexponential (linear in the semilogarithmic scale) portions, each of which is characterized by a definite value of the ideality factor A and preexponential current J0. The monoexponentiality ensures advantages, since at many steps of the analysis, one can use the analytical dependences instead of numerical methods. In this work, an experimental procedure for obtaining the necessary parameters has been proposed, and an analysis of GaInP/GaInAs/Ge triple-junction solar cell characteristics has been carried out. It has been shown that up to the sunlight concentration ratios, at which the efficiency maximum is achieved, the results of calculation of dark and light I-V curves by the segmental method fit well with the experimental data. An important consequence of this work is the feasibility of acquiring the resistanceless dark and light I-V curves, which can be used for obtaining the I-V curves characterizing the losses in the transport part of a solar cell.

Approximation algorithms

Increasing global competition, rapidly changing markets, and greater consumer awareness have altered the way in which corporations do business. To become more efficient, many industries have sought to model some operational aspects by gigantic optimization problems. It is not atypical to encounter models that capture 106 separate “yes” or “no” decisions to be made. Although one could, in principle, try all 2106 possible solutions to find the optimal one, such a method would be impractically slow. Unfortunately, for most of these models, no algorithms are known that find optimal solutions with reasonable computation times. Typically, industry must rely on solutions of unguaranteed quality that are constructed in an ad hoc manner. Fortunately, for some of these models there are good approximation algorithms: algorithms that produce solutions quickly that are provably close to optimal. Over the past 6 years, there has been a sequence of major breakthroughs in our understanding of the design of approximation algorithms and of limits to obtaining such performance guarantees; this area has been one of the most flourishing areas of discrete mathematics and theoretical computer science.

A novel information theory method for filter feature selection

In this paper, we propose a novel filter for feature selection. Such filter relies on the estimation of the mutual information between features and classes. We bypass the estimation of the probability density function with the aid of the entropic-graphs approximation of Rényi entropy, and the subsequent approximation of the Shannon one. The complexity of such bypassing process does not depend on the number of dimensions but on the number of patterns/samples, and thus the curse of dimensionality is circumvented. We show that it is then possible to outperform a greedy algorithm based on the maximal relevance and minimal redundancy criterion. We successfully test our method both in the contexts of image classification and microarray data classification.

Evaluating approximations generated by the GNG3D method for mesh simplification

In this paper we present different error measurements with the aim to evaluate the quality of the approximations generated by the GNG3D method for mesh simplification. The first phase of this method consists on the execution of the GNG3D algorithm, described in the paper. The primary goal of this phase is to obtain a simplified set of vertices representing the best approximation of the original 3D object. In the reconstruction phase we use the information provided by the optimization algorithm to reconstruct the faces thus obtaining the optimized mesh. The implementation of three error functions, named Eavg, Emax, Esur, permitts us to control the error of the simplified model, as it is shown in the examples studied.

Logic-Based Outer Approximation for the Design of Discrete-Continuous Dynamic Systems with Implicit Discontinuities

We address the optimization of discrete-continuous dynamic optimization problems using a disjunctive multistage modeling framework, with implicit discontinuities, which increases the problem complexity since the number of continuous phases and discrete events is not known a-priori. After setting a fixed alternative sequence of modes, we convert the infinite-dimensional continuous mixed-logic dynamic (MLDO) problem into a finite dimensional discretized GDP problem by orthogonal collocation on finite elements. We use the Logic-based Outer Approximation algorithm to fully exploit the structure of the GDP representation of the problem. This modelling framework is illustrated with an optimization problem with implicit discontinuities (diver problem).

An empirical study of three stochastic approximation techniques applicable to sensitivity testing (U)

Photocopy.

Theory of strongly correlated electron systems. I. Intersite coulomb interaction and the approximation of renormalized fermions in total energy calculations

The diagrammatic strong-coupling perturbation theory (SCPT) for correlated electron systems is developed for intersite Coulomb interaction and for a nonorthogonal basis set. The construction is based on iterations of exact closed equations for many - electron Green functions (GFs) for Hubbard operators in terms of functional derivatives with respect to external sources. The graphs, which do not contain the contributions from the fluctuations of the local population numbers of the ion states, play a special role: a one-to-one correspondence is found between the subset of such graphs for the many - electron GFs and the complete set of Feynman graphs of weak-coupling perturbation theory (WCPT) for single-electron GFs. This fact is used for formulation of the approximation of renormalized Fermions (ARF) in which the many-electron quasi-particles behave analogously to normal Fermions. Then, by analyzing: (a) Sham's equation, which connects the self-energy and the exchange- correlation potential in density functional theory (DFT); and (b) the Galitskii and Migdal expressions for the total energy, written within WCPT and within ARF SCPT, a way we suggest a method to improve the description of the systems with correlated electrons within the local density approximation (LDA) to DFT. The formulation, in terms of renormalized Fermions LIDA (RF LDA), is obtained by introducing the spectral weights of the many electron GFs into the definitions of the charge density, the overlap matrices, effective mixing and hopping matrix elements, into existing electronic structure codes, whereas the weights themselves have to be found from an additional set of equations. Compared with LDA+U and self-interaction correction (SIC) methods, RF LDA has the advantage of taking into account the transfer of spectral weights, and, when formulated in terms of GFs, also allows for consideration of excitations and nonzero temperature. Going beyond the ARF SCPT, as well as RF LIDA, and taking into account the fluctuations of ion population numbers would require writing completely new codes for ab initio calculations. The application of RF LDA for ab initio band structure calculations for rare earth metals is presented in part 11 of this study (this issue). (c) 2005 Wiley Periodicals, Inc.

A tutorial on the cross-entropy method

The cross-entropy (CE) method is a new generic approach to combinatorial and multi-extremal optimization and rare event simulation. The purpose of this tutorial is to give a gentle introduction to the CE method. We present the CE methodology, the basic algorithm and its modifications, and discuss applications in combinatorial optimization and machine learning. combinatorial optimization

Time complexity and convergence analysis of domain theoretic Picard method

We present an implementation of the domain-theoretic Picard method for solving initial value problems (IVPs) introduced by Edalat and Pattinson [1]. Compared to Edalat and Pattinson's implementation, our algorithm uses a more efficient arithmetic based on an arbitrary precision floating-point library. Despite the additional overestimations due to floating-point rounding, we obtain a similar bound on the convergence rate of the produced approximations. Moreover, our convergence analysis is detailed enough to allow a static optimisation in the growth of the precision used in successive Picard iterations. Such optimisation greatly improves the efficiency of the solving process. Although a similar optimisation could be performed dynamically without our analysis, a static one gives us a significant advantage: we are able to predict the time it will take the solver to obtain an approximation of a certain (arbitrarily high) quality.