Improvement In Numerical Efficiency Research Articles

On accelerating a multilevel correction adaptive finite element method for Kohn-Sham equation

Based on the numerical method proposed in Hu et al. (2018) [22] for Kohn-Sham equation, further improvement on the efficiency is obtained in this paper by i). designing a numerical method with the strategy of separately handling the nonlinear Hartree potential and exchange-correlation potential, and ii). parallelizing the algorithm in an eigenpairwise approach. The feasibility of two approaches is analyzed in detail, and the new algorithm is described completely. Compared with previous results, a significant improvement of numerical efficiency can be observed from plenty of numerical experiments, which make the new method more suitable for the practical problems.

A local to global (L2G) finite element method for efficient and robust analysis of arbitrary cracking in 2D solids

This paper presents and validates a new local to global (L2G) FEM approach that can analyze multiple, interactive fracture processes in 2D solids with improved numerical efficiency and robustness. The method features: 1) forming local problems for individual and interactive cracks; and 2) parallel solving local problems and returning local solutions as part of the trial solution for global iteration. It has been demonstrated analytically (through a simple 1D problem) and numerically (through several benchmarking examples) that, the proposed method can substantially improve the robustness of the global solution process and significantly reduce the costly global iteration for convergence. The demonstrated improvement in numerical efficiency is up to 20∼40% for mildly unstable problems. For problems with severely unstable crack initiation and propagation, the improvement can be more significant. This new method is readily applicable to other popular methods such as the extended FEM (X-FEM), Augmented FEM (A-FEM) and Phantom-node method (PNM).

A hybrid shallow water solver for overland flow modelling in rural and urban areas

This study aims to present an accurate and efficient finite volume approach for overland flow modelling in rural and urban areas through solving the two-dimensional shallow water equations. The proposed approach introduces a hybrid procedure that utilizes the sharpness of discontinuity to identify flow conditions in the entire computational domain, and then a low-accuracy/high-efficiency scheme (the Rusanov scheme) is used in regular flows, whereas a high-accuracy/low-efficiency scheme (the HLLC scheme) is adopted in strong discontinuous flows. Regions that simultaneously adopt the two schemes are artificially specified to diminish numerical unbalances between the two schemes. Model calibration is carried out through three strong discontinuous flow cases with the exact solutions. Model verification is next described by three benchmark cases, including rainfall-runoff around buildings, flash floods towards buildings, and street junction flows. Model efficiency assessment is also conducted to present the numerical efficiency improvement of the proposed approach for various flow conditions. Technical attention is devoted to the numerical performances on local accuracy and global efficiency of the proposed approach. The simulated results indicate that the proposed approach can simulate as accurate as the HLLC scheme with significant reduction on its computational time. How efficient the proposed hybrid approach can reach depends on flow conditions involved. It is more efficient than the HLLC scheme as the portion of strong discontinuous flows in the computational domain is relatively smaller. The proposed approach has proved its accuracy and efficiency for overland flow modeling, and it can also be used together with other speed-up techniques, such as local time stepping and parallelization, to improve its efficiency. Other finite volume schemes can also be utilized to improve the efficiency and accuracy of the proposed approach. Therefore, the solver has considerable potentials as a useful tool in flood inundation simulations.

Toward efficient shipping noise probability density function estimation using sea-lane source decomposition and probability theory

One goal of the Canadian Ocean Protection Plan (OPP) is to understand the potential effects of shipping noise on endangered whale species in order to mitigate them. Shipping noise environmental impact risk assessment requires the understanding of large scale, high-resolution time-space shipping noise distributions. The computation of such shipping noise probability density functions (pdf) requests considerable computing resources, especially when propagation occurs in complex and varying environments like shallow waters, canyons, or fjords. Besides, input parameters variability and uncertainties analyses require multiple hindcast, nowcast or forecast scenarios to be run when using a direct Monte-Carlo approach. In order to reduce the computation effort, sea-lane shipping traffic decomposition and probability theory are jointly used to derive shipping noise probability density functions with a logarithmic complexity algorithm, as opposed to the linear complexity of direct Monte-Carlo methods. First, a theoretical model is derived for straight shipping routes using simplified logarithmic propagation, validated with numerical examples, and used to perform a sensitivity analysis of shipping noise pdf to speed and route closest point of approach. The improvement in numerical efficiency is shown on a more realistic four sea-lane case scenario mimicking part of the summertime St. Lawrence estuary traffic. Eventually, in situ measurements will be available for comparison.

Adaptive Thermostats for Noisy Gradient Systems

We study numerical methods for sampling probability measures in high dimension where the underlying model is only approximately identified with a gradient system. Extended stochastic dynamical methods are discussed which have application to multiscale models, nonequilibrium molecular dynamics, and Bayesian sampling techniques arising in emerging machine learning applications. In addition to providing a more comprehensive discussion of the foundations of these methods, we propose a new numerical method for the adaptive Langevin/stochastic gradient Nos\'{e}--Hoover thermostat that achieves a dramatic improvement in numerical efficiency over the most popular stochastic gradient methods reported in the literature. We also demonstrate that the newly established method inherits a superconvergence property (fourth order convergence to the invariant measure for configurational quantities) recently demonstrated in the setting of Langevin dynamics. Our findings are verified by numerical experiments.

A consistency-check based algorithm for element condensation in augmented finite element methods for fracture analysis

This paper reports a new algorithm that provides analytic solution to the equilibrium equation in A-FEM. It utilizes a consistency check between trial cohesive stiffness and resulting displacements to differentiate crack displacements from nodal displacements. Benchmark numerical tests demonstrate that the algorithm yields superior numerical accuracy, efficiency, and robustness to other methods. The overall improvement in numerical efficiency is ∼50 times that of the phantom-node based A-FEM in modeling a 4-point shear beam test. For mixed-mode composite delamination problems, the A-FEM with the algorithm is 20–30% faster than standard CZM despite that in the CZM delamination paths are pre-defined.

Direct analysis by an arbitrarily-located-plastic-hinge element — Part 2: Spatial analysis

This is the part two of the two companion papers, which extends the element formulations and the applications of the curved ALH (Arbitrarily Located Hinge) element to three-dimensional space for direct analysis of the steel frames considering large deflection and inelastic behaviors. A simplified approach assuming the space frame to deform with finite but small rotations is adopted for extending the planar element to the three-dimensional space. The updated Lagrangian description and the incremental secant stiffness method are introduced for considering large deflection in the analysis, which is proven to be accurate and efficient in the convergence in iterations for equilibrium. Since the internal degrees of freedom of the proposed element are condensed, a significant reduction on the size of the global stiffness matrix can be achieved with improvement in numerical efficiency. Finally, examples are given for the verification of the proposed numerical method.

Analysis of efficient preconditioned defect correction methods for nonlinear water waves

SUMMARYRobust computational procedures for the solution of non‐hydrostatic, free surface, irrotational and inviscid free‐surface water waves in three space dimensions can be based on iterative preconditioned defect correction (PDC) methods. Such methods can be made efficient and scalable to enable prediction of free‐surface wave transformation and accurate wave kinematics in both deep and shallow waters in large marine areas or for predicting the outcome of experiments in large numerical wave tanks. We revisit the classical governing equations are fully nonlinear and dispersive potential flow equations. We present new detailed fundamental analysis using finite‐amplitude wave solutions for iterative solvers. We demonstrate that the PDC method in combination with a high‐order discretization method enables efficient and scalable solution of the linear system of equations arising in potential flow models. Our study is particularly relevant for fast and efficient simulation of non‐breaking fully nonlinear water waves over varying bottom topography that may be limited by computational resources or requirements. To gain insight into algorithmic properties and proper choices of discretization parameters for different PDC strategies, we study systematically limits of accuracy, convergence rate, algorithmic and numerical efficiency and scalability of the most efficient known PDC methods. These strategies are of interest, because they enable generalization of geometric multigrid methods to high‐order accurate discretizations and enable significant improvement in numerical efficiency while incuring minimal storage requirements. We demonstrate robustness using such PDC methods for practical ranges of interest for coastal and maritime engineering, that is, from shallow to deep water, and report details of numerical experiments that can be used for benchmarking purposes. Copyright © 2014 John Wiley & Sons, Ltd.

An Accurate and Efficient Augmented Finite Element Method for Arbitrary Crack Interactions

This paper presents a new augmented finite element method (A-FEM) that can account for path-arbitrary, multiple intraelemental discontinuities with a demonstrated improvement in numerical efficiency by two orders of magnitude when compared to the extended finite element method (X-FEM). We show that the new formulation enables the derivation of explicit, fully condensed elemental equilibrium equations that are mathematically exact within the finite element context. More importantly, it allows for repeated elemental augmentation to include multiple interactive cracks within a single element without additional external nodes or degrees of freedom (DoFs). A novel algorithm that can rapidly and accurately solve the nonlinear equilibrium equations at the elemental level has also been developed for cohesive cracks with piecewise linear traction-separation laws. This efficient new solving algorithm, coupled with the mathematically exact elemental equilibrium equation, leads to dramatic improvement in numerical accuracy, efficiency, and stability when dealing with arbitrary cracking problems. The A-FEM's excellent capability in high-fidelity simulation of interactive cohesive cracks in homogeneous and heterogeneous solids has been demonstrated through several numerical examples.

Regularization in retrieval-driven classification of clustered microcalcifications for breast cancer.

We propose a regularization based approach for case-adaptive classification in computer-aided diagnosis (CAD) of breast cancer. The goal is to improve the classification accuracy on a query case by making use of a set of similar cases retrieved from an existing library of known cases. In the proposed approach, a prior is first derived from a traditional CAD classifier (which is typically pre-trained offline on a set of training cases). It is then used together with the retrieved similar cases to obtain an adaptive classifier on the query case. We consider two different forms for the regularization prior: one is fixed for all query cases and the other is allowed to vary with different query cases. In the experiments the proposed approach is demonstrated on a dataset of 1,006 clinical cases. The results show that it could achieve significant improvement in numerical efficiency compared with a previously proposed case adaptive approach (by about an order of magnitude) while maintaining similar (or better) improvement in classification accuracy; it could also adapt faster in performance with a small number of retrieved cases. Measured by the area of under the ROC curve (AUC), the regularization based approach achieved AUC = 0.8215, compared with AUC = 0.7329 for the baseline classifier (P-value = 0.001).

A Spectral Coupled-Mode Formulation for Sound Propagation around Axisymmetric Seamounts

A spectral coupled-mode solution of the three-dimensional (3D) acoustic field generated by a point source in the presence of an axisymmetric seamount is developed. Based on the same theoretical foundation as the formulation presented by Taroudakis [J. Comput. Acoust. 4 (1996) 101], the present approach combines a spectral decomposition in azimuth with a coupled-mode theory for two-way range-dependent propagation. However, the earlier formulations are severely limited in terms of frequency, size and geometry of the seamount, the seabed composition, and the distance between the source and the seamount, and are therefore severely limited in regard to realistic seamount problems. Without changing the fundamental theoretical foundation, the present approach applies a number of modifications to the formulation, leading to orders of magnitude improvement in numerical efficiency for realistic problems. Therefore, realistic propagation and scattering scenarios can be modeled, including effects of seamount roughness and realistic sedimentary structure.

The comparison of incomplete sensitivities and Genetic algorithms applications in 3D radial turbomachinery blade optimization

In the present work, a centrifugal pump impeller’s blades shape was redesigned to reach a higher efficiency in turbine mode using two different optimization algorithms: one is a local method as incomplete sensitivities–gradient based optimization algorithm coupled by 3D Navier–Stokes flow solver, and another is a global method as Genetic algorithms and artificial neural network coupled by 3D Navier–Stokes flow solver. New impeller was manufactured and tested in the test rig. Comparison of the local optimization method results with the global optimization method results showed that the gradient based method has detected the global optimum point. Experimental results confirmed the numerical efficiency improvement in all measured points. This study illustrated that the developed gradient based optimization method is efficient for 3D radial turbomachinery blade optimization.

Efficiency Improvement of Centrifugal Reverse Pumps

Pumps as turbines have been successfully applied in a wide range of small hydrosites in the world. Since the overall efficiency of these machines is lower than the overall efficiency of conventional turbines, their application in larger hydrosites is not economical. Therefore, the efficiency improvement of reverse pumps is essential. In this study, by focusing on a pump impeller, the shape of blades was redesigned to reach a higher efficiency in turbine mode using a gradient based optimization algorithm coupled by a 3D Navier–Stokes flow solver. Also, another modification was done by rounding the blades’ leading edges and hub/shroud interface in turbine mode. After each modification, a new impeller was manufactured and tested in the test rig. The efficiency was improved in all measured points by the optimal design of the blade and additional modification as the rounding of the blade’s profile in the impeller inlet and hub/shroud inlet edges in turbine mode. Experimental results confirmed the numerical efficiency improvement in all measured points. This study illustrated that the efficiency of the pump in reverse operation can be improved just by impeller modification.

Discrete polynomial moments for real-time geometric surface inspection

A thorough analysis of discrete polynomial moments and their suitability for application to geometric surface inspection is presented. A new approach is taken to the analysis based on matrix algebra, revealing some formerly unknown fundamental properties. It is proven that there is one and only one unitary polynomial basis that is complete, i.e., the polynomial basis for a Chebychev system. Furthermore, it is proven that the errors in the computation of moments are almost exclusively associated with the application of the recurrence relationship, and it is shown that QR decomposition can be used to eliminate the systematic propagation of errors. It is also shown that QR decomposition produces a truly orthogonal basis set despite the presence of stochastic errors. Fourier analysis is applied to the polynomial bases to determine the spectral distribution of the numerical errors. The new unitary basis offers almost perfect numerical behavior, enabling the modeling of larger images with higher-degree polynomials for the first time. The application of a unitary polynomial basis eliminates the need to compute pseudo-inverses. This improvement in numerical efficiency enables real-time modeling of surfaces in industrial surface inspection. Two applications in industrial quality control via artificial vision are demonstrated.

Structural collapse simulation under consideration of uncertainty – Improvement of numerical efficiency

The focus in this paper is set on the improvement of the numerical efficiency of a fuzzy stochastic structural collapse simulation. The deterministic computation is performed with an FE-model taking into account large deformations, contact phenomena and non-linear behavior of the material. Structural parameters have to be specified on the basis of rare, vague and imprecise information. This is taken into account with the aid of uncertainty model fuzzy randomness. A substantial reduction of the computational effort is achieved by approximating structural responses with a neural network following the response surface methodology. The improved fuzzy stochastic analysis of a structural collapse is demonstrated by a moderate complex structural collapse example.

PRICING PATH-DEPENDENT OPTIONS ON STATE DEPENDENT VOLATILITY MODELS WITH A BESSEL BRIDGE

This paper develops bridge sampling path integral algorithms for pricing path-dependent options under a new class of nonlinear state dependent volatility models. Path-dependent option pricing is considered within a new (dual) Bessel family of semimartingale diffusion models, as well as the constant elasticity of variance (CEV) diffusion model, arising as a particular case of these models. The transition p.d.f.s or pricing kernels are mapped onto an underlying simpler squared Bessel process and are expressed analytically in terms of modified Bessel functions. We establish precise links between pricing kernels of such models and the randomized gamma distributions, and thereby demonstrate how a squared Bessel bridge process can be used for exact sampling of the Bessel family of paths. A Bessel bridge algorithm is presented which is based on explicit conditional distributions for the Bessel family of volatility models and is similar in spirit to the Brownian bridge algorithm. A special rearrangement and splitting of the path integral variables allows us to combine the Bessel bridge sampling algorithm with either adaptive Monte Carlo algorithms, or quasi-Monte Carlo techniques for significant numerical efficiency improvement. The algorithms are illustrated by pricing Asian-style and lookback options under the Bessel family of volatility models as well as the CEV diffusion model.

Subspace Projection Extrapolation Scheme for Transient Field Simulations

A subspace projection extrapolation (SPE) scheme is introduced for the start vector generation for the iterative solution of the algebraic systems of equations resulting from implicit time integration schemes for electromagnetic discrete field formulations. The SPE scheme yields optimal linear combinations from multiple available start vectors. Spectral components of the exact solution contained therein are optimally resolved which causes subsequently started conjugate gradient (CG) methods to converge according to a reduced effective condition number similar to deflated CG methods. Numerical tests show a significant improvement in numerical efficiency with the SPE scheme in comparison to established extrapolation methods.

A hybrid method for combining quasi-static and full-wave techniques for electromagnetic scattering problems

Electromagnetic scattering problems containing subregions which are electrically small but geometrically complex are examined. By utilizing quasi-static methods for the small regions, full-wave methods in the remaining region, and determining necessary coupling relations between the small regions and the overall geometry, a considerable improvement in numerical efficiency is realized. The particular method developed here is valid for quasi-static regions in which magnetic induction can be ignored. Results using the proposed method have been obtained for a pair of closely spaced collinear wires. A comparison of these results with the wire antenna code, MININEC, showed excellent agreement.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>