Point Interpolation Research Articles

An explicit velocity correction-based immersed boundary-hybrid lattice Boltzmann flux solver for fluid-structure interaction with large solid deformation

In this work, an explicit velocity correction-based Immersed Boundary-Hybrid Lattice Boltzmann Flux Solver (IB-HLBFS) is developed for Fluid-Structure Interaction (FSI) problems with large solid deformation in two-dimensional. The fluid domain is solved by the Lattice Boltzmann Flux Solver (LBFS) while the solid domain is solved by the Smoothed Point Interpolation Method (S-PIM). For coupling the two methods, the Explicit Velocity Correction (EVC) is developed and applied to both the fluid and the solid by implementing the Immersed Boundary Method (IBM). The fluid domain in IB-HLBFS can be discretized with non-uniform mesh so that the efficiency is improved meanwhile the accuracy is ensured compared with the original Lattice Boltzmann Method (LBM). Moreover, the explicit velocity correction simplifies the matrix inversion in the Implicit Velocity Correction (IVC) hence the efficiency is further improved. To show the advantages and the reliability of the present IB-HLBFS, the numerical simulations of flow past the elastic beam, flow past a circular cylinder with a flexible beam behind, and swimming of a self-propelled fishlike body are given to show the application of IB-HLBFS in FSI with complex fluid dynamics and large solid deformation. The results indicate that the present method is advantageous in terms of efficiency and accuracy, and has a wide prospect in engineering applications as well.

Solvability of the Nevanlinna-Pick interpolation problem

A solvability theorem is proved for the Nevanlinna-Pick interpolation problem. Its extreme cases are Carathéodory's and Sсhur's criteria on the one hand (when all interpolation points coincide) and the Krein-Rekhtman theorem on the other (when the interpolation points are pairwise distinct). Bibliography: 19 titles.

Soil parameters in terms of entropy coordinates

In the ongoing research, an approximate, grading entropy based, advanced interpolation method is applied to establish empirical functions between the grading curves and the model parameters of sands. The space of the grain size distribution curves withNfractions is isomorphic to the space of the unit-sided simplex with dimensionN-1. The traditional interpolation over the simplex with dimensionN-1 is problematic since the number of the sub-simplexes (and the interpolation points) may increase exponentially withN. To overcome this difficulty, the function is approximately interpolated, which means that the interpolation is made on some 2-dimensional sections of the simplex and is extended to the whole simplex, using the grading entropy map. Two kinds of 2-dimensional sections can be used based on either fractal distributions or partly fractal partly on some maximal gap-graded distributions. In this paper the experiments were made on the artificial mixtures of natural sand grains earlier. Two kinds of functions were approximately interpolated for the minimum dry density using the measured data. One kind of function was determined for the parameters of an SWCC model directly from the level lines previously graphically interpolated from fractal distribution data.

A new approach for the generation of real-time GNSS low-latitude ionospheric scintillation maps

Ionospheric scintillation disturbs radio frequency signals affecting navigation based on Global Navigation System (GNSS), especially in Brazil, due to the large magnetic declination. The generation of real-time scintillation maps is an important way to provide scintillation monitoring. This work considers amplitude scintillation, given by the S4 index. Some existing and some proposed approaches for generating these maps are presented and tested, being each one a combination of an interpolation method with some existing and/or proposed sets of pre-processing options. These approaches are named after the related interpolation method as GRIDDATA, Inverse Distance Weighting, Radial Basis Functions and Gaussian Process Regression. The making of scintillation maps requires the interpolation of Ionospheric Pierce Point (IPP) samples, given by the S4 values for each IPP of each satellite-station link considering the set of GNSS stations of the given area and time interval. Some intervals of time that presented strong scintillation over Brazil were selected and the corresponding sets of IPP samples were used to obtain sequences of maps using all possible combinations of interpolation and pre-processing options. Furthermore, a fifth, more recent, approach was also included in the comparison. The quality of the resulting maps was assessed, concluding that the Gaussian Process Regression approach, with a specific set of pre-processing options, allows to generate the most accurate scintillation maps. The proposed map generation approach is part of a broader proposal being implemented to provide real-time scintillation maps covering the Brazilian territory.

Interactive Restoration of Three-Dimensional Implicit Surface with營rregular燩arts

Implicit surface generation based on the interpolation of surface points is one of the well-known modeling methods in the area of computer graphics. Several methods for the implicit surface reconstruction from surface points have been proposed on the basis of radial basis functions, a weighted sum of local functions, splines, wavelets, and combinations of them. However, if the surface points contain errors or are sparsely distributed, irregular components, such as curvature-shaped redundant bulges and unexpectedly generated high-frequency components, are commonly seen. This paper presents a framework for restoring irregular components generated on and around surfaces. Users are assumed to specify local masks that cover irregular components and parameters that determine the degree of restoration. The algorithm in this paper removes the defects based on the user-specific masks and parameters. Experiments have shown that the proposed methods can effectively remove redundant protrusions and jaggy noise.

Crack Analysis by Using An Extended Meshfree Method and Cartesian Transformation Method without Creating Subdomains

This paper investigates the fracture behavior of plates with through-thickness crack by using the extended concept of the Radial Point Interpolation Method (RPIM). The attractiveness of the RPIM shape functions is the satisfaction of the Kronecker delta property providing direct imposition of essential boundary conditions. In the extended concept, the jump in deflection and rotation fields caused by crack, also the stress singularity near the crack tip are described by adding enriched functions to the interpolation equation. Particularly, Heaviside function and asymptotic enriched function. For numerical integration, the Cartesian Transformation Method (CTM) is employed. No integration background cell is required in CTM, this technique transforms a domain integral into a boundary integral and a 1D integral. For analysis of discontinuous problems, in this study, the distribution of integration points is manipulated to avoid the discontinuity caused by crack segmentation. Therefore, no subdomains are required, unlike other reference CTM studies. To achieve that, a virtual boundary is introduced that represents the discontinuity such as holes or cracks. This also matches the concept of the extended approach that no explicit discontinuity exists in the geometry, instead, the discontinuity is modelled by mathematics equation. The Stress Intensity Factors (SIFs) of the cracked plate are evaluated through the interaction integral technique. The efficiency of the proposed method is illustrated through various numerical examples. The accuracy of the obtained results are compared with other available numerical solutions and analytical solutions.

Analysis of cracked Reissner-Mindlin plate using an extended meshfree method

An extended meshfree method for analyzing cracked plates based on Reissner-Mindlin theory is presented in this paper. Among a variety of meshfree formulations, the radial point interpolation method (RPIM) is chosen in this study due to the satisfaction of the Kronecker delta property. The essential boundary conditions, therefore, are easily imposed in the RPIM. The shape function derived from RPIM is employed to interpolate the field variables. An extended RPIM formulation is used to model the crack segment without explicitly defining it in the discretized domain. The discontinuity due to the crack is defined by extrinsic enriched functions, particularly, the jump in the displacement field on two sides of the crack is modelled by the Heaviside function, and the stress singularity near the crack tip is described by the asymptotic enriched function. In this study, the stress resultant intensity factors (SRIFs) are evaluated through the interaction integral approach. The obtained SRIFs are shown in the paper through many numerical examples for comparison purposes. The trending variation of SRIFs is also observed from the numerical results. It can be remarked that the SRIFs depend on many factors: the number of cracks, crack orientation, load type and boundary conditions. The numerical examples show the accuracy of the present approach. The obtained results are compared with analytical solutions and other numerical methods.

Application of Random Radial Point Interpolation Method to Foundations Bearing Capacity Considering Progressive Failure

In conventional analyzes of foundations failure, strengh parameters are assumed constant. However, during the failure, soil resistance exhibits maximum and residual amounts, and its strength decreases prematurely by increasing the plastic strain. In addition to change soil strengh parameters in the progressive mechanism, the non-uniform nature of the soil also causes spatial variations of these parameters. Therefore, geotechnical systems should be considered in terms of the uncertainty of soil parameters values, uncertainly using the concepts of statistics and probabilities. The purpose of this study is to investigate foundations in meshless method. In this article, radial point interpolation method (RPIM), a meshless method is proposed for simulation of soil foundation. Difficulties of methods related to mesh are solved by using this method. A code has been developed based on this method and some examples are solved for analyzing the code. In this research, a RPIM in combination with a random field was used to model the spatial variations of soil strengh properties and foundation bearing capacity analysis. For probabilistic analysis, random field is also used to determine the cohesion and the friction angle as well as the dilation angle based on their mean values and standard deviation. In order to investigate the application of the point interpolation method with randomized radial functions, a foundation with definite geometry has been analyzed deterministic and probabilistic and its safety factor has been investigated. Based on the analysis of the progressive failure modeling, it is concluded that the actual failure of the soil and the occurrence of continuous displacements occur simultaneously with the formation of a progressive mechanism of soil failure and the arrival of the slipping path to the ground. In the following, probabilistic distribution functions of the safety factor were determined by probabilistic analysis and the production of random fields, and then the statistical parameters are calculated.

Free Vibration Analysis of Curved Shell Structures with Various Boundary Conditions by Using A Meshfree Method

In this paper, the free vibration of curved shell structures with various boundary conditions is examined by using a meshfree method. The meshfree method in this study is based on the radial point interpolation method (RPIM). The RPIM shape function is chosen because it satisfies the Kronecker delta property allowing for the direct imposition of essential boundary conditions. The field variables and the geometry of the curved shell are interpolated through the RPIM shape function. The curved shell formulation is constructed based on the first-order shear deformation theory (FSDT), which considers the transverse shear strain. In a meshfree approach to investigate curved shell structures, a convected coordinate system is employed. This convected coordinate system is tied to the curved surface and used to map an arbitrary curved shell in 3D space into 2D space. To obtain the numerical solution, the calculation is performed first in this convected coordinate system and then mapped back to the global coordinate system. The accuracy and ability of the meshfree method have been shown through many numerical examples. The natural frequencies of curved shells with different geometry and boundary conditions are in good agreement with other available reference solutions.

The Ogden model and the natural neighbour radial point interpolation method for hyperelastic analyses

The Ogden model and the natural neighbour radial point interpolation method for hyperelastic analyses

Adaptive Anisotropy Optimization Method for the Radial Point Interpolation Method in Lossy Media

Adaptive Anisotropy Optimization Method for the Radial Point Interpolation Method in Lossy Media

Optimization technique for increasing resolution in computed tomography imaging

Starting from the importance of conforming to biological reality in medicine, in this paper we propose an optimization technique for increasing resolution of computed tomography (CT) images acquired using various existing scanners. Considering a three-dimensional Hounsfield Units (HU) array, together with the corresponding spatial metadata of interest (pixel sizes and slice thickness), the procedure is based on halving each voxel along the directions of the device's Cartesian frame of reference and find those values which are both satisfying the X-Rays attenuation coefficient average requirement and minimizing the HU distance to classical interpolation points. The discussed method was tested by implementing a C# .Net 6, cross-platform library containing two algorithm flavors that could be independently applied: “Z” for doubling the number of slices, and “XY” for doubling the resolution of individual slices. This design allows also chaining (e.g. one could apply the “Z,XY,Z” sequence in order to reduce four times slice thickness). In the context of existing unavoidable limitations, the first results are suggesting the “CT compatible” interpolation technique could provide a reasonable approximation of reality. However, the main advantage comes from satisfying mass conservation, which is of high importance in medical diagnosis and treatment.•The Hounsfield Units scale is defined as a linear transformation of the X-Rays attenuation coefficients. Thus, splitting a computed tomography voxel into two congruent volumes must satisfy the HU average requirement (the initial value must equal the average of the two output HU values).•Existing interpolation methods (linear, spline, etc.) are not compatible with the computed tomography HU average requirement. This could also result in mass estimate anomalies with significant impact in medical diagnosis.•The proposed “CT compatible” interpolation method is based on finding those values which are both satisfying the X-Rays attenuation coefficient average requirement and minimizing the Hounsfield Units distance to classical interpolation points.

On trigonometric interpolation in an even number of points

In contrast to odd-length trigonometric interpolants, even-length trigonometric interpolants need not be unique; this is apparent from the representation of the interpolant in the (real or complex) Fourier basis, which possesses an extra degree of freedom in the choice of the highest-order basis function in the even case. One can eliminate this degree of freedom by imposing a constraint, but then the interpolant may cease to exist for certain choices of the interpolation points. On the other hand, the Lagrange representation developed by Gauss always produces an interpolant despite having no free parameters. We discuss the choice Gauss's formula makes for the extra degree of freedom and show that, when the points are equispaced, its choice is optimal in the sense that it minimizes both the standard and 2-norm Lebesgue constants for the interpolation problem. For non-equispaced points, we give numerical evidence that Gauss's formula is no longer optimal and consider interpolants of minimal 2-norm instead. We show how to modify Gauss's formula to produce a minimal-norm interpolant and that, if the points are equispaced, no modification is necessary.

Conical Differential Range Based Back-Projection Algorithm for Concealed Object Detection with Three-Dimensional mmW Imaging

Millimeter wave(mmW) imaging has spread to a wide range of applications in the last quarter. One of the most important research areas of mmW is three-dimensional (3D) imaging systems. In this study, conical differential range-based back-projection (BP) algorithm is proposed for three-dimensional mmW imaging. In the algorithm, the differential range is created using points inside a conical volume, thus the number of interpolation points is considerably reduced. The performance of the algorithm is demonstrated by simulation and experimental studies. Cylindrical scanning is carried out by means of the experimental setup. Experiments are carried out at frequencies of 26.5-40 GHz. The traditional BP algorithm (BPA) and the proposed algorithm are used to reconstruct the images. With the proposed method, it is observed that ISLR for the point target increased by about 5 dB compared to the traditional method. Moreover, the computational complexity is reduced by up to 10 times, depending on the imaging area. Thanks to the proposed method, the image of the concealed weapon under the cloth in an experimental study is more clearly focused compared to the traditional method. Therefore, it can provide images that give more accurate results for applications such as automatic target detection methods.

Bending analysis of antisymmetric angle-ply laminates using HSDTs and the radial point interpolation method – Part I: Literature review and formulation

Bending analysis of antisymmetric angle-ply laminates using HSDTs and the radial point interpolation method – Part I: Literature review and formulation

ClevRvis: visualization techniques for clonal evolution.

A thorough analysis of clonal evolution commonly requires integration of diverse sources of data (e.g., karyotyping, next-generation sequencing, and clinical information). Subsequent to actual reconstruction of clonal evolution, detailed analysis and interpretation of the results are essential. Often, however, only few tumor samples per patient are available. Thus, information on clonal development and therapy effect may be incomplete. Furthermore, analysis of biallelic events-considered of high relevance with respect to disease course-can commonly only be realized by time-consuming analysis of the raw results and even raw sequencing data. We developed clevRvis, an R/Bioconductor package providing an extensive set of visualization techniques for clonal evolution. In addition to common approaches for visualization, clevRvis offers a unique option for allele-aware representation: plaice plots. Biallelic events may be visualized and inspected at a glance. Analyzing 4 public datasets, we show that plaice plots help to gain new insights into tumor development and investigate hypotheses on disease progression and therapy resistance. In addition to a graphical user interface, automatic phylogeny-aware color coding of the plots, and an approach to explore alternative trees, clevRvis provides 2 algorithms for fully automatic time point interpolation and therapy effect estimation. Analyzing 2 public datasets, we show that both approaches allow for valid approximation of a tumor's development in between measured time points. clevRvis represents a novel option for user-friendly analysis of clonal evolution, contributing to gaining new insights into tumor development.

Can global longitudinal strain (GLS) with magnetic resonance prognosticate early cancer therapy-related cardiac dysfunction (CTRCD) in breast cancer patients, a prospective study?

PurposeTo determine if Artificial Intelligence-based computation of global longitudinal strain (GLS) from left ventricular (LV) MRI is an early prognostic factor of cancer therapy-related cardiac dysfunction (CTRCD) in breast cancer patients. The main hypothesis based on the patients receiving antineoplastic chemotherapy treatment was CTRCD risk analysis with GLS that was independent of LV ejection fraction (LVEF). MethodsDisplacement Encoding with Stimulated Echoes (DENSE) MRI was acquired on 32 breast cancer patients at baseline and 3- and 6-month follow-ups after chemotherapy. Two DeepLabV3+ Fully Convolutional Networks (FCNs) were deployed to automate image segmentation for LV chamber quantification and phase-unwrapping for 3D strains, computed with the Radial Point Interpolation Method. CTRCD risk (cardiotoxicity and adverse cardiac events) was analyzed with Cox Proportional Hazards (PH) models with clinical and contractile prognostic factors. ResultsGLS worsened from baseline to the 3- and 6-month follow-ups (−19.1 ± 2.1%, −16.0 ± 3.1%, −16.1 ± 3.0%; P < 0.001). Univariable Cox regression showed the 3-month GLS significantly associated as an agonist (hazard ratio [HR]-per-SD: 2.1; 95% CI: 1.4–3.1; P < 0.001) and LVEF as a protector (HR-per-SD: 0.8; 95% CI: 0.7–0.9; P = 0.001) for CTRCD occurrence. Bivariable regression showed the 3-month GLS (HR-per-SD: 2.0; 95% CI: 1.2–3.4; P = 0.01) as a CTRCD prognostic factor independent of other covariates, including LVEF (HR-per-SD: 1.0; 95% CI: 0.9–1.2; P = 0.9). ConclusionsThe end-point analyses proved the hypothesis that GLS is an early, independent prognosticator of incident CTRCD risk. This novel GLS-guided approach to CTRCD risk analysis could improve antineoplastic treatment with further validation in a larger clinical trial.

Characterization of a cubic interpolation scheme dependent on two parameters and applications

"The aim of this paper is to provide a characterization diagram for a family of B\'{e}zier flexible interpolation curves as well as to present an application of our results in cryptography. In our interpolation scheme, two parameters, $t_1,\ t_2\in (0,1)$ determine the position of the interpolation points on the B\'{e}zier curve. Consequently we obtain a family of B\'{e}zier interpolation curves depending on two parameters. Altering the values of the parameters we modify the intermediary control points and implicitly the shape of the interpolation curve. In order to control the shape of the interpolation curves from this family, we provide a partition of the domain $T=(0,1)\times (0,1)$ where the parameters lie according to the geometric characterization of these curves: with zero, one or two inflexion points; with loop; with cusp and degenerated in quadratic curves. The characterization diagram can be used as a tool for the choice of parameters, with possible applications in different fields. We present one of its application in cryptography, for finding certain subspaces over which particular elliptic sub-curves are defined. Computation, implementation and graphics are made using MATLAB."

Elastoplastic Analysis of Plates with Radial Point Interpolation Meshless Methods

For both linear and nonlinear analysis, finite element method (FEM) software packages, whether commercial or in-house, have contributed significantly to ease the analysis of simple and complex structures with various working conditions. However, the literature offers other discretization techniques equally accurate, which show a higher meshing flexibility, such as meshless methods. Thus, in this work, the radial point interpolation meshless method (RPIM) is used to obtain the required variable fields for a nonlinear elastostatic analysis. This work focuses its attention on the nonlinear analysis of two benchmark plate-bending problems. The plate is analysed as a 3D solid and, in order to obtain the nonlinear solution, modified versions of the Newton–Raphson method are revisited and applied. The material elastoplastic behaviour is predicted assuming the von Mises yield surface and isotropic hardening. The nonlinear algorithm is discussed in detail. The analysis of the two benchmark plate examples allows us to understand that the RPIM version explored is accurate and allows to achieve smooth variable fields, being a solid alternative to FEM.

Multivariate moment-matching for model order reduction of quadratic-bilinear systems using error bounds

We propose an adaptive moment-matching framework for model order reduction of quadratic-bilinear systems. In this framework, an important issue is the selection of those shift frequencies where moment-matching is to be achieved. So far, the choice often has been random or linked to the linear part of the nonlinear system. In this paper, we extend the use of an existing a posteriori error bound for general linear time invariant systems to quadratic-bilinear systems and develop a greedy-type framework to select a good choice of interpolation points for the construction of the projection matrices. The results are compared with standard quadratic-bilinear projection methods and we observe that the approximations obtained by the proposed method yield high accuracy.