Super Accuracy Research Articles

An Element Decomposition Method for Three-Dimensional Solid Mechanics

This paper proposes an element decomposition method (EDM) for elastic-static, free vibration and forced vibration analyses of three-dimensional solid mechanics. The problem domain is first discretized using eight-node hexahedral elements. Then, each hexahedron is further subdivided into a set of sub-tetrahedral cells, and the local strains in each sub-tetrahedron are obtained using linear interpolation functions. For each hexahedron, the strain of the whole element is the weighted average value of the local strains, which means only one integration point is adopted to establish the stiffness matrix. To cure the numerical instability of one-point quadrature and improve the accuracy, a variation gradient item is complemented by variance of the local strains. Numerical examples, including both benchmark and practical engineering cases, demonstrate that the present method possesses the following interesting properties compared with the traditional finite element method using the same mesh discretization (1) super accuracy and faster convergence rate; (2) higher computational efficiency; (3) more immune to mesh distortion.

Nanopore-only assemblies for genomic surveillance of the global priority drug-resistant pathogen, Klebsiella pneumoniae.

Oxford Nanopore Technologies (ONT) sequencing has rich potential for genomic epidemiology and public health investigations of bacterial pathogens, particularly in low-resource settings and at the point of care, due to its portability and affordability. However, low base-call accuracy has limited the reliability of ONT data for critical tasks such as antimicrobial resistance (AMR) and virulence gene detection and typing, serotype prediction, and cluster identification. Thus, Illumina sequencing remains the standard for genomic surveillance despite higher capital and running costs. We tested the accuracy of ONT-only assemblies for common applied bacterial genomics tasks (genotyping and cluster detection, implemented via Kleborate, Kaptive and Pathogenwatch), using data from 54 unique Klebsiella pneumoniae isolates. ONT reads generated via MinION with R9.4.1 flowcells were basecalled using three alternative models [Fast, High-accuracy (HAC) and Super-accuracy (SUP), available within ONT's Guppy software], assembled with Flye and polished using Medaka. Accuracy of typing using ONT-only assemblies was compared with that of Illumina-only and hybrid ONT+Illumina assemblies, constructed from the same isolates as reference standards. The most resource-intensive ONT-assembly approach (SUP basecalling, with or without Medaka polishing) performed best, yielding reliable capsule (K) type calls for all strains (100 % exact or best matching locus), reliable multi-locus sequence type (MLST) assignment (98.3 % exact match or single-locus variants), and good detection of acquired AMR genes and mutations (88-100 % correct identification across the various drug classes). Distance-based trees generated from SUP+Medaka assemblies accurately reflected overall genetic relationships between isolates. The definition of outbreak clusters from ONT-only assemblies was problematic due to inflation of SNP counts by high base-call errors. However, ONT data could be reliably used to 'rule out' isolates of distinct lineages from suspected transmission clusters. HAC basecalling + Medaka polishing performed similarly to SUP basecalling without polishing. Therefore, we recommend investing compute resources into basecalling (SUP model), wherever compute resources and time allow, and note that polishing is also worthwhile for improved performance. Overall, our results show that MLST, K type and AMR determinants can be reliably identified with ONT-only R9.4.1 flowcell data. However, cluster detection remains challenging with this technology.

Comparison of R9.4.1/Kit10 and R10/Kit12 Oxford Nanopore flowcells and chemistries in bacterial genome reconstruction.

Complete, accurate, cost-effective, and high-throughput reconstruction of bacterial genomes for large-scale genomic epidemiological studies is currently only possible with hybrid assembly, combining long- (typically using nanopore sequencing) and short-read (Illumina) datasets. Being able to use nanopore-only data would be a significant advance. Oxford Nanopore Technologies (ONT) have recently released a new flowcell (R10.4) and chemistry (Kit12), which reportedly generate per-read accuracies rivalling those of Illumina data. To evaluate this, we sequenced DNA extracts from four commonly studied bacterial pathogens, namely Escherichia coli, Klebsiella pneumoniae, Pseudomonas aeruginosa and Staphylococcus aureus, using Illumina and ONT's R9.4.1/Kit10, R10.3/Kit12, R10.4/Kit12 flowcells/chemistries. We compared raw read accuracy and assembly accuracy for each modality, considering the impact of different nanopore basecalling models, commonly used assemblers, sequencing depth, and the use of duplex versus simplex reads. 'Super accuracy' (sup) basecalled R10.4 reads - in particular duplex reads - have high per-read accuracies and could be used to robustly reconstruct bacterial genomes without the use of Illumina data. However, the per-run yield of duplex reads generated in our hands with standard sequencing protocols was low (typically <10 %), with substantial implications for cost and throughput if relying on nanopore data only to enable bacterial genome reconstruction. In addition, recovery of small plasmids with the best-performing long-read assembler (Flye) was inconsistent. R10.4/Kit12 combined with sup basecalling holds promise as a singular sequencing technology in the reconstruction of commonly studied bacterial genomes, but hybrid assembly (Illumina+R9.4.1 hac) currently remains the highest throughput, most robust, and cost-effective approach to fully reconstruct these bacterial genomes.

Barycentric Lagrange Interpolation Methods for Evaluating Singular Integrals

We investigate new, straightforward methods for interpolating and integrating discontinuous single and two-variable real valued functions. The method is based on some modified matrix–vector barycentric Lagrange interpolation formulas. We developed seven rules for the optimum distribution of nodes inside the domain of integration: five for single-valued discontinuous functions, and two rules for the two independent variables of discontinuous functions. We designed these rules to depend on the length of the integration domain and the degree of the interpolant polynomials. Thus, we obtained uniform interpolation and minimum roundoff errors. Based on these rules with the application of the modified matrix–vector barycentric formulas, we easily isolated the singularities of the interpolant integrands and evaluated the corresponding interpolant integral values with super accuracy. The obtained numerical solutions of the five given examples show the high accuracy and efficiency of the presented method compared with the exact solutions and with the cited method.

HIV-Quasipore: A Suite of HIV-1-Specific Nanopore Basecallers Designed to Enhance Viral Quasispecies Detection

Accounting for genetic variation is an essential consideration during human immunodeficiency virus type 1 (HIV-1) investigation. Nanopore sequencing preserves proviral integrity by passing long genomic fragments through ionic channels, allowing reads that span the entire genome of different viral quasispecies (vQS). However, this sequencing method has suffered from high error rates, limiting its utility. This was the inspiration behind HIV-Quasipore: an HIV-1-specific Nanopore basecaller suite designed to overcome these error rates through training with gold-standard data. It comprises three deep learning-based R9.4.1 basecallers: fast, high accuracy (HAC), super accuracy (SUP), and two R10.3 deep learning-based basecallers: HAC and SUP. This was accomplished by sequencing the HIV-1 J-Lat 10.6 cell line using Nanopore and high-quality Sanger techniques. Training significantly reduced basecaller error rates across all models (Student’s one-sided t-test; p = 0.0) where median error rates were 0.0189, 0.0018, 0.0008, for R9.4.1 HIV-Quasipore-fast, HAC, SUP, and 0.0007, 0.0011 for R10.3 HIV-Quasipore-HAC, and SUP, respectively. This improved quality reduces the resolution needed to accurately detect a vQS from 22.4 to 2.6% of total positional coverage for R9.4.1 HIV-Quasipore-fast, 6.9 to 0.5% for R9.4.1 HIV-Quasipore-HAC, 4.5 to 0.3% for R9.4.1 HIV-Quasipore-SUP, 8.0 to 0.3% for R10.3 HIV-Quasipore-HAC, and 5.4 to 0.3% for R10.3 HIV-Quasipore-SUP. This was consistently observed across the entire J-Lat 10.6 genome and maintained across longer reads. Reads with greater than 8,000 nucleotides display a median nucleotide identity of 0.9819, 0.9982, and 0.9991, for R9.4.1 HIV-Quasipore-fast, HAC, SUP, and 0.9993, 0.9988 for R10.3 HIV-Quasipore-HAC, and SUP, respectively. To evaluate the robustness of this tool against unseen data, HIV-Quasipore and their corresponding pretrained basecallers were used to sequence the J-Lat 9.2 cell line and a clinical isolate acquired from the Drexel Medicine CARES cohort. When sample reads were compared against their corresponding consensus sequence, all HIV-Quasipore basecallers displayed higher median alignment accuracies than their pretrained counterparts for both the J-Lat 9.2 cell line and clinical isolate. Using Nanopore sequencing can allow investigators to explore topics, such as vQS profile detection, HIV-1 integration site analysis, whole genome amplification, gene coevolution, and CRISPR-induced indel detection, among others. HIV-Quasipore basecallers can be acquired here: https://github.com/DamLabResources/HIV-Quasipore-basecallers.

On explicit discontinuous Galerkin methods for conservation laws

The concept of projection applied to explicit discontinuous Galerkin (DG) schemes is investigated. The two explicit DG methods in this study are based on a ‘predictor-corrector’ formulation, the first introduced by Lörcher, Gassner, and Munz called space–time expansion discontinuous Galerkin or STE-DG scheme (Lörcher et al. 2007, Gassner et al. 2008), and the second, introduced independently by the author (Huynh 2006, 2013) called the upwind moment scheme. The predictor step of the two methods is essentially identical using a Cauchy-Kovalevsky procedure, which involves no interaction of the data among neighboring cells. The corrector step also shares the same space-time integration formulation and is where interaction takes place; the two methods differ, however, in the evaluation of the projections in the space-time volume integrals. The STE-DG scheme evaluates these in a straightforward manner, whereas the moment scheme employs a successive procedure with each moment update uses the results by the lower-order updates. The trade-off is that the moment scheme has the disadvantage of a more elaborate corrector step and the significant advantage of a CFL (Courant-Friedrichs-Lewy) condition of 1 for all (degree) p and accuracy order of 2p+1 (super accuracy property) for one-dimensional (1D) advection. In contrast, the STE-DG method is accurate to only the expected order of p+1 and has a more restrictive CFL condition. Due to the predictor-corrector formulation that does not involve methods of characteristics, these schemes extend easily to systems of equations in multiple dimensions. Concerning the case of two spatial dimensions (2D), for an advection using a Cartesian grid, when the flow does not align with the axes, especially when it is along a diagonal direction, the CFL conditions for the moment schemes also become restrictive and need improvement as will be shown by Fourier (von Neumann) analyses.

Flux reconstruction using Jacobi correction functions in discontinuous spectral element method

A flux reconstruction approach is implemented in the spectral difference (SD) framework, which we refer to it as discontinuous spectral element method (DSEM), to improve the accuracy and stability of numerical simulations. A new class of correction functions is developed based on a weighted orthogonality condition, which leads to the introduction of Jacobi correction functions. Jacobi correction functions can construct the well-known DSEM and staggered-grid version of nodal discontinuous Galerkin spectral element method (DGSEM) as well as a broad range of other high-order numerical schemes with a variety of numerical characteristics, such as high numerical dissipation to suppress aliasing-driven errors, super accuracy, and solution boundedness in shock prediction. Three single-parameter families of Jacobi correction functions are recognized, and a von Neumann analysis is performed to acquire their wave propagation properties. The order of accuracy and stability criterion of a broad range of schemes are calculated, and the most super-accurate and stable numerical schemes are identified and later validated through a set of numerical experiments on a one-dimensional advection equation. The solution unboundedness issue of the high-order DSEM scheme is discussed through simulating the Burgers equation. An accuracy test performed on the Burgers equation revealed that the new staggered-grid flux reconstruction approach could acquire a higher accuracy than that of the energy stable flux reconstruction framework on a collocated grid. The two-dimensional extension of the new framework is also examined by simulation of a non-linear Euler system of equations for the isentropic vortex in free-stream flow. The staggered-grid flux reconstruction using the Jacobi correction function can precisely reconstruct the DSEM approach for non-linear two-dimensional hyperbolic equations for all polynomial orders.

An edge-based smoothed finite element method for the assessment of human exposure to extremely low frequency electric fields

This paper presents an edge-based smoothed finite element method (ES-FEM) for the assessment of human exposure to extremely low frequency (ELF) electric fields. The problem domain is first discretized into a set of four-node tetrahedral elements, and linear shape functions are employed to interpolate the field variables. Then, the smoothing domains are further formed with respect to the edges of elements. In order to improve the accuracy of lower order interpolation, a gradient smoothing technique (GST) is introduced to perform the electric potential gradient smoothing operation over each smoothing domain. Based on the generalized smoothed Galerkin weakform, the discretized system equations are finally obtained. Numerical examples, including both benchmark and practical complex cases, demonstrate that the present method possesses the following interesting properties in assessing human exposure to ELF electric fields: (1) super accuracy and faster convergence rate; (2) higher computational efficiency; (3) insensitive to mesh distortion.

Isogeometric indirect boundary element method for solving the 3D acoustic problems

This paper provides an Isogeometric Indirect Boundary Element Method (IGIBEM) based on NURBS (Non-Uniform Rational B-Splines) and PHT-splines (polynomial splines over hierarchical T-meshes) for analyzing the three-dimensional (3D) acoustic problems. In the classical procedure, the geometries are discretized by Lagrange polynomials elements, which leads to both substantial geometrical error and time-consuming meshing steps. However, these deficiencies can be eliminated by the isogeometric analysis (IGA) directly incorporating the geometry description generated from the CAD (Computer Aided Design) software into CAE (Computer Aided Engineering) analysis. Unlike the DBEM (direct boundary element method), the IBEM (indirect boundary element method) allows different types of boundary conditions on the two sides of a surface. Moreover, the hypersingular integrals in IBEM can be transformed to a weakly singular form. In addition, the PHT-based IBEM is used to investigate the influence of local refinement on the accuracy of solutions. Finally, the non-uniqueness problem is solved, which is a fatal defect in the acoustic BEM for the exterior problem. Four different methods to handle the non-uniqueness problem are discussed and compared. The results obtained by the proposed method were compared with analytical solutions and the results computed by Lagrange-based IBEM. Several benchmark examples demonstrate: (1) the present method, i.e. IGIBEM, has super accuracy over conventional IBEM for the acoustic problems; (2) local refinement has a significant influence on the convergence rate of the solutions, and the numerical accuracy is relevant to the distance to the boundary where the local refinement acted; (3) as for the non-uniqueness problem, the imposition of specific interior boundary conditions not only obtains the best calculation result over the entire range of frequencies, but also has a simple integral formulation. • We implement an IGIBEM based on NURBS and PHT-splines for 3D acoustic problems. • The NURBS-based IBEM has super accuracy over the Lagrange-based IBEM. • The PHT-based IBEM was proposed to investigate the effect of local refinement on solution domain. • We investigated four indirect boundary integral equations to overcome the non-uniqueness problem. • The imposition of specific interior boundary conditions has simple integral formulation and the best calculation result.

Phenomenological model for mixed multiphoton absorption in bialkali photocathode and application to ultrafast pulse characterization

We propose a phenomenological model composed of concise formulas to describe mixed multiphoton absorption (MPA), revealing its quasi-exponent-function in relation to intensity, complicated spectral features, and polarization dependence, and then demonstrate it perfectly by experiments on a bialkali-cathode photomultiplier-tube (PMT) single-photon detector. The dichroism parameter is obtained based on polarization dependent visibility. Accomplishing MPA-based autocorrelation, we manifest that the peak-to-baseline contrast ratio is determined by the mixture exponent. After extracting the pure two-photon absorption, we obtain the ultrafast pulse width which agrees well with that of the standard autocorrelator. Furthermore, we put forward the mutual-correlation scheme and acquire accurately the time jitter of a femtosecond-pulse train. Our results pave the way for analyzing high-order complex MPAs and characterization of ultrafast pulses with super accuracy by a widely used bialkali PMT.

The stable node-based smoothed finite element method for analyzing acoustic radiation problems

In this paper, the stable node-based smoothed finite element method (SNS-FEM) and the well-known Dirichlet-to-Neumann (DtN) boundary condition are coupled together to reduce the dispersion error in analyzing acoustic radiation problems. An artificial boundary is introduced to truncate the infinite domain and the DtN boundary condition is imposed on the artificial boundary to guarantee the uniqueness of the solution. In the SNS-FEM formulation, a stable item which contains the gradient variance items is constructed without any uncertain parameter to strengthen the system stiffness. Through this operation, a perfect balance between the stiffness and mass matrices is established and the dispersion error is reduced significantly. Two benchmark cases and two practical engineering problems are employed to investigate the performance of the SNS-FEM. The results demonstrate that the SNS-FEM achieves super accuracy and super convergence. Additionally, the SNS-FEM is less sensitive to the wave number and high-efficiency.

Speckle-based at-wavelength metrology of X-ray mirrors with super accuracy

X-ray active mirrors, such as bimorph and mechanically bendable mirrors, are increasingly being used on beamlines at modern synchrotron source facilities to generate either focused or "tophat" beams. As well as optical tests in the metrology lab, it is becoming increasingly important to optimise and characterise active optics under actual beamline operating conditions. Recently developed X-ray speckle-based at-wavelength metrology technique has shown great potential. The technique has been established and further developed at the Diamond Light Source and is increasingly being used to optimise active mirrors. Details of the X-ray speckle-based at-wavelength metrology technique and an example of its applicability in characterising and optimising a micro-focusing bimorph X-ray mirror are presented. Importantly, an unprecedented angular sensitivity in the range of two nanoradians for measuring the slope error of an optical surface has been demonstrated. Such a super precision metrology technique will be beneficial to the manufacturers of polished mirrors and also in optimization of beam shaping during experiments.

A stable node-based smoothed finite element method for acoustic problems

It is well-known that the classical “overly-soft” node-based smoothed finite element method (NS-FEM) fails to provide reliable results to the Helmholtz equation due to the “temporal instability”. To cure the fatal drawback of NS-FEM and reduce the dispersion error in computational acoustics, this paper proposed a stable node-based smoothed finite element method (SNS-FEM) for analyzing acoustic problems using linear triangular (for 2D space) and tetrahedral (for 3D space) elements that can be generated automatically for any complicated configurations. In the present formulation, the system stiffness matrix is computed using the smoothed acoustic pressure gradients together with the gradient variance items over the smoothing domains associated with nodes of element mesh. It turns out the addition of stabilization term makes the SNS-FEM possess an ideal stiffness, thus successfully cures the temporal instability and significantly reduces the dispersion error in acoustic problems. Numerical examples, including both benchmark cases and practical engineering problems, demonstrate that the SNS-FEM possesses the following important properties: (1) temporal stability; (2) super accuracy and super convergence; (3) higher computational efficiency; (4) insensitive to mesh distortion.

ADDITIONAL PROPERTIES OF THE NODE-BASED SMOOTHED FINITE ELEMENT METHOD (NS-FEM) FOR SOLID MECHANICS PROBLEMS

A node-based smoothed finite element method (NS-FEM) for solving solid mechanics problems using a mesh of general polygonal elements was recently proposed. In the NS-FEM, the system stiffness matrix is computed using the smoothed strains over the smoothing domains associated with nodes of element mesh, and a number of important properties have been found, such as the upper bound property and free from the volumetric locking. The examination was performed only for two-dimensional (2D) problems. In this paper, we (1) extend the NS-FEM to three-dimensional (3D) problems using tetrahedral elements (NS-FEM-T4), (2) reconfirm the upper bound and free from the volumetric locking properties for 3D problems, and (3) explore further other properties of NS-FEM for both 2D and 3D problems. In addition, our examinations will be thorough and performed fully using the error norms in both energy and displacement. The results in this work revealed that NS-FEM possesses two additional interesting properties that quite similar to the equilibrium FEM model such as: (1) super accuracy and super-convergence of stress solutions; (2) similar accuracy of displacement solutions compared to the standard FEM model.

Automatic Polishing of Super Accuracy Mirror Mold with Free-Form Surface by Curvature Analysis

This paper proposed a polishing path planning method of super accuracy mirror mold with free-form surface by curvature analysis. First, IGES files of free-form surfaces are read and the mold geometry is regenerated as B-spline surface by the Automatic Mold Polishing System (AMPS). By using the derivative properties of B-spline surface, normal vector and principal curvatures at any point of the surface are calculated. In addition, the effective contact width between polishing tool and mold surface based on the grain size and the principal radii of curvature is also determined. The minimum contact width in 3-D is mapped onto the (u, v) parameters of B-spline surface. Then a modified Peano fractal path with weaving function is calculated based on the effective contact width in the (u, v) coordinate. This Peano-weaving path was tested on an optical mold with free-form surface. The polishing result shows the method is very effective and achieves the level of mirror surface with roughness Ra 29nm.