We present the application of adjoint analysis to 3-D finite-element method scattering problems for a posteriori error estimation and adaptive refinement. Adjoint-based methodologies, though ...underutilized in computational electromagnetics (CEM), enable significant improvements for both efficiency and accuracy. We first formulate the adjoint problem of the 3-D double-curl wave equation and the error estimates for the construction of novel accelerated adaptive refinement algorithms. We demonstrate adaptive error control for a customizable quantity of interest (QoI) resulting in targeted refinement and improved resource allocation through the application of automatic global and local error tolerance heuristics that accelerate the refinement process. The proposed refinement algorithms rapidly refine even extremely coarse initial discretizations to high accuracy, eliminating or substantially reducing manual intervention in the generation of computationally efficient and accurate simulations. Moreover, comparisons with analytical results validate our approach to accelerating automatic refinement to fine tolerances.
We use the ideas of goal-oriented error estimation and adaptivity to design and implement an efficient adaptive algorithm for approximating linear quantities of interest derived from solutions to ...elliptic partial differential equations (PDEs) with parametric or uncertain inputs. In the algorithm, the stochastic Galerkin finite element method (sGFEM) is used to approximate the solutions to primal and dual problems that depend on a countably infinite number of uncertain parameters. Adaptive refinement is guided by an innovative strategy that combines the error reduction indicators computed for spatial and parametric components of the primal and dual solutions. The key theoretical ingredient is a novel two-level a posteriori estimate of the energy error in sGFEM approximations. We prove that this error estimate is reliable and efficient. The effectiveness of the goal-oriented error estimation strategy and the performance of the goal-oriented adaptive algorithm are tested numerically for three representative model problems with parametric coefficients and for three quantities of interest (including the approximation of pointwise values).
•Novel two-level a posteriori error estimates for stochastic Galerkin approximations.•Effective goal-oriented error estimation strategy for stochastic Galerkin FEM.•Efficient goal-oriented adaptive sGFEM algorithm driven by error reduction indicators.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Abstract
The three-component magnetic sensor is used to measure the heading of the vehicle. Under working, the magnetic sensor be rotated to the horizontal plane according to the attitude angle of ...the vehicle, and then the heading estimation is performed. However, the vehicle’s attitude angle measurement errors affect the accuracy of the magnetic sensor measurement’s east and north components and then lead to a false heading result. Based on the relation of magnetic field measurement error and magnetic heading error, the effect model of geomagnetic measurement error on magnetic heading error is derived in this paper. Finally, the characteristics of attitude angle errors on magnetic heading are verified by experiments, and the results show that particular angles can avoid the magnetic compass’s effect by the vehicle’s attitude angle error.
Abstract
Geotechnical site investigations represent an imperative prerequisite in the pursuit of reliable foundation designs. However, site investigations are frequently restricted to a limited ...number of locations owing to the constraints imposed by budget and time considerations, thereby potentially yielding a range of adverse consequences. Hence, the development of an efficient site investigation plan — one that optimally selects the number and location of tests, is important to gain adequate information for a given cost. This paper proposes a framework to identify optimal investigation locations by minimizing the probability of erroneous decisions (i.e., error types I and II). A pile group was adopted for the demonstration. The best locations corresponding to various numbers of tests were identified based on the derived probabilities of type I and II errors.
We clarify differences among moderation, partial mediation, and full mediation and identify methodological problems related to moderation and mediation from a review of articles in Strategic ...Management Journal and Organization Science published from 2005 to 2014. Regarding moderation, we discuss measurement error, range restriction, and unequal sample sizes across moderator-based subgroups; insufficient statistical power; the artificial categorization of continuous variables; assumed negative consequences of correlations between product terms and its components (i.e., multicollinearity); and interpretation of first-order effects based on models excluding product terms. Regarding mediation, we discuss problems with the causal-steps procedure, inferences about mediation based on cross-sectional designs, whether a relation between the antecedent and the outcome is necessary for testing mediation, the routine inclusion of a direct path from the antecedent to the outcome, and consequences of measurement error. We also explain how integrating moderation and mediation can lead to important and useful insights for strategic management theory and practice. Finally, we offer specific and actionable recommendations for improving the appropriateness and accuracy of tests of moderation and mediation in strategic management research. Our recommendations can also be used as a checklist for editors and reviewers who evaluate manuscripts reporting tests of moderation and mediation.
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NUK, OILJ, SAZU, UKNU, UL, UM, UPUK
Abstract
In solar photovoltaic power generation, the prediction of solar irradiance is essential for minimizing energy costs and ensuring the provision of high-quality electricity. Deep learning ...models have recently gained popularity in the field, as numerous scholars have successfully employed them to predict solar irradiance. In line with this, this paper proposes three distinct methods for dividing the training dataset. Subsequently, these methods are employed in predicting solar irradiance using the LSTM-based model. Furthermore, an error analysis of the prediction results is conducted for each of the three models. The optimal training dataset division method is determined and proposed based on a comparison of the sizes of the three models using six error evaluation indexes.
We present the complete calculation of W-boson production in association with a jet in hadronic collisions through next-to-next-to-leading order (NNLO) in perturbative QCD. To cancel infrared ...divergences, we discuss a new subtraction method that exploits the fact that the N-jettiness event-shape variable fully captures the singularity structure of QCD amplitudes with final-state partons. This method holds for processes with an arbitrary number of jets and is easily implemented into existing frameworks for higher-order calculations. We present initial phenomenological results for W+jet production at the LHC. The NNLO corrections are small and lead to a significantly reduced theoretical error, opening the door to precision measurements in the W+jet channel at the LHC.
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We consider simulating an n-qubit Hamiltonian with nearest-neighbor interactions evolving for time t on a quantum computer. We show that this simulation has gate complexity (nt)^{1+o(1)} using ...product formulas, a straightforward approach that has been demonstrated by several experimental groups. While it is reasonable to expect this complexity-in particular, this was claimed without rigorous justification by Jordan, Lee, and Preskill-we are not aware of a straightforward proof. Our approach is based on an analysis of the local error structure of product formulas, as introduced by Descombes and Thalhammer and significantly simplified here. We prove error bounds for canonical product formulas, which include well-known constructions such as the Lie-Trotter-Suzuki formulas. We also develop a local error representation for time-dependent Hamiltonian simulation, and we discuss generalizations to periodic boundary conditions, constant-range interactions, and higher dimensions. Combined with a previous lower bound, our result implies that product formulas can simulate lattice Hamiltonians with nearly optimal gate complexity.
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