Image interpolation allows accurate quantitative bone morphometry in registered micro-computed tomography scans.

PubMed

Schulte, Friederike A; Lambers, Floor M; Mueller, Thomas L; Stauber, Martin; Müller, Ralph

2014-04-01

Time-lapsed in vivo micro-computed tomography is a powerful tool to analyse longitudinal changes in the bone micro-architecture. Registration can overcome problems associated with spatial misalignment between scans; however, it requires image interpolation which might affect the outcome of a subsequent bone morphometric analysis. The impact of the interpolation error itself, though, has not been quantified to date. Therefore, the purpose of this ex vivo study was to elaborate the effect of different interpolator schemes [nearest neighbour, tri-linear and B-spline (BSP)] on bone morphometric indices. None of the interpolator schemes led to significant differences between interpolated and non-interpolated images, with the lowest interpolation error found for BSPs (1.4%). Furthermore, depending on the interpolator, the processing order of registration, Gaussian filtration and binarisation played a role. Independent from the interpolator, the present findings suggest that the evaluation of bone morphometry should be done with images registered using greyscale information.

Topology optimization for design of segmented permanent magnet arrays with ferromagnetic materials

NASA Astrophysics Data System (ADS)

Lee, Jaewook; Yoon, Minho; Nomura, Tsuyoshi; Dede, Ercan M.

2018-03-01

This paper presents multi-material topology optimization for the co-design of permanent magnet segments and iron material. Specifically, a co-design methodology is proposed to find an optimal border of permanent magnet segments, a pattern of magnetization directions, and an iron shape. A material interpolation scheme is proposed for material property representation among air, permanent magnet, and iron materials. In this scheme, the permanent magnet strength and permeability are controlled by density design variables, and permanent magnet magnetization directions are controlled by angle design variables. In addition, a scheme to penalize intermediate magnetization direction is proposed to achieve segmented permanent magnet arrays with discrete magnetization directions. In this scheme, permanent magnet strength is controlled depending on magnetization direction, and consequently the final permanent magnet design converges into permanent magnet segments having target discrete directions. To validate the effectiveness of the proposed approach, three design examples are provided. The examples include the design of a dipole Halbach cylinder, magnetic system with arbitrarily-shaped cavity, and multi-objective problem resembling a magnetic refrigeration device.

On-chip frame memory reduction using a high-compression-ratio codec in the overdrives of liquid-crystal displays

NASA Astrophysics Data System (ADS)

Wang, Jun; Min, Kyeong-Yuk; Chong, Jong-Wha

2010-11-01

Overdrive is commonly used to reduce the liquid-crystal response time and motion blur in liquid-crystal displays (LCDs). However, overdrive requires a large frame memory in order to store the previous frame for reference. In this paper, a high-compression-ratio codec is presented to compress the image data stored in the on-chip frame memory so that only 1 Mbit of on-chip memory is required in the LCD overdrives of mobile devices. The proposed algorithm further compresses the color bitmaps and representative values (RVs) resulting from the block truncation coding (BTC). The color bitmaps are represented by a luminance bitmap, which is further reduced and reconstructed using median filter interpolation in the decoder, while the RVs are compressed using adaptive quantization coding (AQC). Interpolation and AQC can provide three-level compression, which leads to 16 combinations. Using a rate-distortion analysis, we select the three optimal schemes to compress the image data for video graphics array (VGA), wide-VGA LCD, and standard-definitionTV applications. Our simulation results demonstrate that the proposed schemes outperform interpolation BTC both in PSNR (by 1.479 to 2.205 dB) and in subjective visual quality.

A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models

NASA Technical Reports Server (NTRS)

Giunta, Anthony A.; Watson, Layne T.

1998-01-01

Two methods of creating approximation models are compared through the calculation of the modeling accuracy on test problems involving one, five, and ten independent variables. Here, the test problems are representative of the modeling challenges typically encountered in realistic engineering optimization problems. The first approximation model is a quadratic polynomial created using the method of least squares. This type of polynomial model has seen considerable use in recent engineering optimization studies due to its computational simplicity and ease of use. However, quadratic polynomial models may be of limited accuracy when the response data to be modeled have multiple local extrema. The second approximation model employs an interpolation scheme known as kriging developed in the fields of spatial statistics and geostatistics. This class of interpolating model has the flexibility to model response data with multiple local extrema. However, this flexibility is obtained at an increase in computational expense and a decrease in ease of use. The intent of this study is to provide an initial exploration of the accuracy and modeling capabilities of these two approximation methods.

Error Estimation in an Optimal Interpolation Scheme for High Spatial and Temporal Resolution SST Analyses

NASA Technical Reports Server (NTRS)

Rigney, Matt; Jedlovec, Gary; LaFontaine, Frank; Shafer, Jaclyn

2010-01-01

Heat and moisture exchange between ocean surface and atmosphere plays an integral role in short-term, regional NWP. Current SST products lack both spatial and temporal resolution to accurately capture small-scale features that affect heat and moisture flux. NASA satellite is used to produce high spatial and temporal resolution SST analysis using an OI technique.

On the Quality of Velocity Interpolation Schemes for Marker-in-Cell Method and Staggered Grids

NASA Astrophysics Data System (ADS)

Pusok, Adina E.; Kaus, Boris J. P.; Popov, Anton A.

2017-03-01

The marker-in-cell method is generally considered a flexible and robust method to model the advection of heterogenous non-diffusive properties (i.e., rock type or composition) in geodynamic problems. In this method, Lagrangian points carrying compositional information are advected with the ambient velocity field on an Eulerian grid. However, velocity interpolation from grid points to marker locations is often performed without considering the divergence of the velocity field at the interpolated locations (i.e., non-conservative). Such interpolation schemes can induce non-physical clustering of markers when strong velocity gradients are present (Journal of Computational Physics 166:218-252, 2001) and this may, eventually, result in empty grid cells, a serious numerical violation of the marker-in-cell method. To remedy this at low computational costs, Jenny et al. (Journal of Computational Physics 166:218-252, 2001) and Meyer and Jenny (Proceedings in Applied Mathematics and Mechanics 4:466-467, 2004) proposed a simple, conservative velocity interpolation scheme for 2-D staggered grid, while Wang et al. (Geochemistry, Geophysics, Geosystems 16(6):2015-2023, 2015) extended the formulation to 3-D finite element methods. Here, we adapt this formulation for 3-D staggered grids (correction interpolation) and we report on the quality of various velocity interpolation methods for 2-D and 3-D staggered grids. We test the interpolation schemes in combination with different advection schemes on incompressible Stokes problems with strong velocity gradients, which are discretized using a finite difference method. Our results suggest that a conservative formulation reduces the dispersion and clustering of markers, minimizing the need of unphysical marker control in geodynamic models.

Multilevel Green's function interpolation method for scattering from composite metallic and dielectric objects.

PubMed

Shi, Yan; Wang, Hao Gang; Li, Long; Chan, Chi Hou

2008-10-01

A multilevel Green's function interpolation method based on two kinds of multilevel partitioning schemes--the quasi-2D and the hybrid partitioning scheme--is proposed for analyzing electromagnetic scattering from objects comprising both conducting and dielectric parts. The problem is formulated using the surface integral equation for homogeneous dielectric and conducting bodies. A quasi-2D multilevel partitioning scheme is devised to improve the efficiency of the Green's function interpolation. In contrast to previous multilevel partitioning schemes, noncubic groups are introduced to discretize the whole EM structure in this quasi-2D multilevel partitioning scheme. Based on the detailed analysis of the dimension of the group in this partitioning scheme, a hybrid quasi-2D/3D multilevel partitioning scheme is proposed to effectively handle objects with fine local structures. Selection criteria for some key parameters relating to the interpolation technique are given. The proposed algorithm is ideal for the solution of problems involving objects such as missiles, microstrip antenna arrays, photonic bandgap structures, etc. Numerical examples are presented to show that CPU time is between O(N) and O(N log N) while the computer memory requirement is O(N).

Landmark-based elastic registration using approximating thin-plate splines.

PubMed

Rohr, K; Stiehl, H S; Sprengel, R; Buzug, T M; Weese, J; Kuhn, M H

2001-06-01

We consider elastic image registration based on a set of corresponding anatomical point landmarks and approximating thin-plate splines. This approach is an extension of the original interpolating thin-plate spline approach and allows to take into account landmark localization errors. The extension is important for clinical applications since landmark extraction is always prone to error. Our approach is based on a minimizing functional and can cope with isotropic as well as anisotropic landmark errors. In particular, in the latter case it is possible to include different types of landmarks, e.g., unique point landmarks as well as arbitrary edge points. Also, the scheme is general with respect to the image dimension and the order of smoothness of the underlying functional. Optimal affine transformations as well as interpolating thin-plate splines are special cases of this scheme. To localize landmarks we use a semi-automatic approach which is based on three-dimensional (3-D) differential operators. Experimental results are presented for two-dimensional as well as 3-D tomographic images of the human brain.

A Novel Multi-Receiver Signcryption Scheme with Complete Anonymity.

PubMed

Pang, Liaojun; Yan, Xuxia; Zhao, Huiyang; Hu, Yufei; Li, Huixian

2016-01-01

Anonymity, which is more and more important to multi-receiver schemes, has been taken into consideration by many researchers recently. To protect the receiver anonymity, in 2010, the first multi-receiver scheme based on the Lagrange interpolating polynomial was proposed. To ensure the sender's anonymity, the concept of the ring signature was proposed in 2005, but afterwards, this scheme was proven to has some weakness and at the same time, a completely anonymous multi-receiver signcryption scheme is proposed. In this completely anonymous scheme, the sender anonymity is achieved by improving the ring signature, and the receiver anonymity is achieved by also using the Lagrange interpolating polynomial. Unfortunately, the Lagrange interpolation method was proven a failure to protect the anonymity of receivers, because each authorized receiver could judge whether anyone else is authorized or not. Therefore, the completely anonymous multi-receiver signcryption mentioned above can only protect the sender anonymity. In this paper, we propose a new completely anonymous multi-receiver signcryption scheme with a new polynomial technology used to replace the Lagrange interpolating polynomial, which can mix the identity information of receivers to save it as a ciphertext element and prevent the authorized receivers from verifying others. With the receiver anonymity, the proposed scheme also owns the anonymity of the sender at the same time. Meanwhile, the decryption fairness and public verification are also provided.

Numerical simulation of supersonic and hypersonic inlet flow fields

NASA Technical Reports Server (NTRS)

Mcrae, D. Scott; Kontinos, Dean A.

1995-01-01

This report summarizes the research performed by North Carolina State University and NASA Ames Research Center under Cooperative Agreement NCA2-719, 'Numerical Simulation of Supersonic and Hypersonic Inlet Flow Fields". Four distinct rotated upwind schemes were developed and investigated to determine accuracy and practicality. The scheme found to have the best combination of attributes, including reduction to grid alignment with no rotation, was the cell centered non-orthogonal (CCNO) scheme. In 2D, the CCNO scheme improved rotation when flux interpolation was extended to second order. In 3D, improvements were less dramatic in all cases, with second order flux interpolation showing the least improvement over grid aligned upwinding. The reduction in improvement is attributed to uncertainty in determining optimum rotation angle and difficulty in performing accurate and efficient interpolation of the angle in 3D. The CCNO rotational technique will prove very useful for increasing accuracy when second order interpolation is not appropriate and will materially improve inlet flow solutions.

Medical image enhancement using resolution synthesis

NASA Astrophysics Data System (ADS)

Wong, Tak-Shing; Bouman, Charles A.; Thibault, Jean-Baptiste; Sauer, Ken D.

2011-03-01

We introduce a post-processing approach to improve the quality of CT reconstructed images. The scheme is adapted from the resolution-synthesis (RS)1 interpolation algorithm. In this approach, we consider the input image, scanned at a particular dose level, as a degraded version of a high quality image scanned at a high dose level. Image enhancement is achieved by predicting the high quality image by classification based linear regression. To improve the robustness of our scheme, we also apply the minimum description length principle to determine the optimal number of predictors to use in the scheme, and the ridge regression to regularize the design of the predictors. Experimental results show that our scheme is effective in reducing the noise in images reconstructed from filtered back projection without significant loss of image details. Alternatively, our scheme can also be applied to reduce dose while maintaining image quality at an acceptable level.

Advanced texture filtering: a versatile framework for reconstructing multi-dimensional image data on heterogeneous architectures

NASA Astrophysics Data System (ADS)

Zellmann, Stefan; Percan, Yvonne; Lang, Ulrich

2015-01-01

Reconstruction of 2-d image primitives or of 3-d volumetric primitives is one of the most common operations performed by the rendering components of modern visualization systems. Because this operation is often aided by GPUs, reconstruction is typically restricted to first-order interpolation. With the advent of in situ visualization, the assumption that rendering algorithms are in general executed on GPUs is however no longer adequate. We thus propose a framework that provides versatile texture filtering capabilities: up to third-order reconstruction using various types of cubic filtering and interpolation primitives; cache-optimized algorithms that integrate seamlessly with GPGPU rendering or with software rendering that was optimized for cache-friendly "Structure of Array" (SoA) access patterns; a memory management layer (MML) that gracefully hides the complexities of extra data copies necessary for memory access optimizations such as swizzling, for rendering on GPGPUs, or for reconstruction schemes that rely on pre-filtered data arrays. We prove the effectiveness of our software architecture by integrating it into and validating it using the open source direct volume rendering (DVR) software DeskVOX.

Concurrent topological design of composite structures and materials containing multiple phases of distinct Poisson's ratios

NASA Astrophysics Data System (ADS)

Long, Kai; Yuan, Philip F.; Xu, Shanqing; Xie, Yi Min

2018-04-01

Most studies on composites assume that the constituent phases have different values of stiffness. Little attention has been paid to the effect of constituent phases having distinct Poisson's ratios. This research focuses on a concurrent optimization method for simultaneously designing composite structures and materials with distinct Poisson's ratios. The proposed method aims to minimize the mean compliance of the macrostructure with a given mass of base materials. In contrast to the traditional interpolation of the stiffness matrix through numerical results, an interpolation scheme of the Young's modulus and Poisson's ratio using different parameters is adopted. The numerical results demonstrate that the Poisson effect plays a key role in reducing the mean compliance of the final design. An important contribution of the present study is that the proposed concurrent optimization method can automatically distribute base materials with distinct Poisson's ratios between the macrostructural and microstructural levels under a single constraint of the total mass.

Edge directed image interpolation with Bamberger pyramids

NASA Astrophysics Data System (ADS)

Rosiles, Jose Gerardo

2005-08-01

Image interpolation is a standard feature in digital image editing software, digital camera systems and printers. Classical methods for resizing produce blurred images with unacceptable quality. Bamberger Pyramids and filter banks have been successfully used for texture and image analysis. They provide excellent multiresolution and directional selectivity. In this paper we present an edge-directed image interpolation algorithm which takes advantage of the simultaneous spatial-directional edge localization at the subband level. The proposed algorithm outperform classical schemes like bilinear and bicubic schemes from the visual and numerical point of views.

High Order Semi-Lagrangian Advection Scheme

NASA Astrophysics Data System (ADS)

Malaga, Carlos; Mandujano, Francisco; Becerra, Julian

2014-11-01

In most fluid phenomena, advection plays an important roll. A numerical scheme capable of making quantitative predictions and simulations must compute correctly the advection terms appearing in the equations governing fluid flow. Here we present a high order forward semi-Lagrangian numerical scheme specifically tailored to compute material derivatives. The scheme relies on the geometrical interpretation of material derivatives to compute the time evolution of fields on grids that deform with the material fluid domain, an interpolating procedure of arbitrary order that preserves the moments of the interpolated distributions, and a nonlinear mapping strategy to perform interpolations between undeformed and deformed grids. Additionally, a discontinuity criterion was implemented to deal with discontinuous fields and shocks. Tests of pure advection, shock formation and nonlinear phenomena are presented to show performance and convergence of the scheme. The high computational cost is considerably reduced when implemented on massively parallel architectures found in graphic cards. The authors acknowledge funding from Fondo Sectorial CONACYT-SENER Grant Number 42536 (DGAJ-SPI-34-170412-217).

Assimilation of remote sensing observations into a sediment transport model of China's largest freshwater lake: spatial and temporal effects.

PubMed

Zhang, Peng; Chen, Xiaoling; Lu, Jianzhong; Zhang, Wei

2015-12-01

Numerical models are important tools that are used in studies of sediment dynamics in inland and coastal waters, and these models can now benefit from the use of integrated remote sensing observations. This study explores a scheme for assimilating remotely sensed suspended sediment (from charge-coupled device (CCD) images obtained from the Huanjing (HJ) satellite) into a two-dimensional sediment transport model of Poyang Lake, the largest freshwater lake in China. Optimal interpolation is used as the assimilation method, and model predictions are obtained by combining four remote sensing images. The parameters for optimal interpolation are determined through a series of assimilation experiments evaluating the sediment predictions based on field measurements. The model with assimilation of remotely sensed sediment reduces the root-mean-square error of the predicted sediment concentrations by 39.4% relative to the model without assimilation, demonstrating the effectiveness of the assimilation scheme. The spatial effect of assimilation is explored by comparing model predictions with remotely sensed sediment, revealing that the model with assimilation generates reasonable spatial distribution patterns of suspended sediment. The temporal effect of assimilation on the model's predictive capabilities varies spatially, with an average temporal effect of approximately 10.8 days. The current velocities which dominate the rate and direction of sediment transport most likely result in spatial differences in the temporal effect of assimilation on model predictions.

Constructing polyatomic potential energy surfaces by interpolating diabatic Hamiltonian matrices with demonstration on green fluorescent protein chromophore

DOE Office of Scientific and Technical Information (OSTI.GOV)

Park, Jae Woo; Rhee, Young Min, E-mail: ymrhee@postech.ac.kr; Department of Chemistry, Pohang University of Science and Technology

2014-04-28

Simulating molecular dynamics directly on quantum chemically obtained potential energy surfaces is generally time consuming. The cost becomes overwhelming especially when excited state dynamics is aimed with multiple electronic states. The interpolated potential has been suggested as a remedy for the cost issue in various simulation settings ranging from fast gas phase reactions of small molecules to relatively slow condensed phase dynamics with complex surrounding. Here, we present a scheme for interpolating multiple electronic surfaces of a relatively large molecule, with an intention of applying it to studying nonadiabatic behaviors. The scheme starts with adiabatic potential information and its diabaticmore » transformation, both of which can be readily obtained, in principle, with quantum chemical calculations. The adiabatic energies and their derivatives on each interpolation center are combined with the derivative coupling vectors to generate the corresponding diabatic Hamiltonian and its derivatives, and they are subsequently adopted in producing a globally defined diabatic Hamiltonian function. As a demonstration, we employ the scheme to build an interpolated Hamiltonian of a relatively large chromophore, para-hydroxybenzylidene imidazolinone, in reference to its all-atom analytical surface model. We show that the interpolation is indeed reliable enough to reproduce important features of the reference surface model, such as its adiabatic energies and derivative couplings. In addition, nonadiabatic surface hopping simulations with interpolation yield population transfer dynamics that is well in accord with the result generated with the reference analytic surface. With these, we conclude by suggesting that the interpolation of diabatic Hamiltonians will be applicable for studying nonadiabatic behaviors of sizeable molecules.« less

A rational interpolation method to compute frequency response

NASA Technical Reports Server (NTRS)

Kenney, Charles; Stubberud, Stephen; Laub, Alan J.

1993-01-01

A rational interpolation method for approximating a frequency response is presented. The method is based on a product formulation of finite differences, thereby avoiding the numerical problems incurred by near-equal-valued subtraction. Also, resonant pole and zero cancellation schemes are developed that increase the accuracy and efficiency of the interpolation method. Selection techniques of interpolation points are also discussed.

Wavelet-Smoothed Interpolation of Masked Scientific Data for JPEG 2000 Compression

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brislawn, Christopher M.

2012-08-13

How should we manage scientific data with 'holes'? Some applications, like JPEG 2000, expect logically rectangular data, but some sources, like the Parallel Ocean Program (POP), generate data that isn't defined on certain subsets. We refer to grid points that lack well-defined, scientifically meaningful sample values as 'masked' samples. Wavelet-smoothing is a highly scalable interpolation scheme for regions with complex boundaries on logically rectangular grids. Computation is based on forward/inverse discrete wavelet transforms, so runtime complexity and memory scale linearly with respect to sample count. Efficient state-of-the-art minimal realizations yield small constants (O(10)) for arithmetic complexity scaling, and in-situ implementationmore » techniques make optimal use of memory. Implementation in two dimensions using tensor product filter banks is straighsorward and should generalize routinely to higher dimensions. No hand-tuning required when the interpolation mask changes, making the method aeractive for problems with time-varying masks. Well-suited for interpolating undefined samples prior to JPEG 2000 encoding. The method outperforms global mean interpolation, as judged by both SNR rate-distortion performance and low-rate artifact mitigation, for data distributions whose histograms do not take the form of sharply peaked, symmetric, unimodal probability density functions. These performance advantages can hold even for data whose distribution differs only moderately from the peaked unimodal case, as demonstrated by POP salinity data. The interpolation method is very general and is not tied to any particular class of applications, could be used for more generic smooth interpolation.« less

Efficient Geometry Minimization and Transition Structure Optimization Using Interpolated Potential Energy Surfaces and Iteratively Updated Hessians.

PubMed

Zheng, Jingjing; Frisch, Michael J

2017-12-12

An efficient geometry optimization algorithm based on interpolated potential energy surfaces with iteratively updated Hessians is presented in this work. At each step of geometry optimization (including both minimization and transition structure search), an interpolated potential energy surface is properly constructed by using the previously calculated information (energies, gradients, and Hessians/updated Hessians), and Hessians of the two latest geometries are updated in an iterative manner. The optimized minimum or transition structure on the interpolated surface is used for the starting geometry of the next geometry optimization step. The cost of searching the minimum or transition structure on the interpolated surface and iteratively updating Hessians is usually negligible compared with most electronic structure single gradient calculations. These interpolated potential energy surfaces are often better representations of the true potential energy surface in a broader range than a local quadratic approximation that is usually used in most geometry optimization algorithms. Tests on a series of large and floppy molecules and transition structures both in gas phase and in solutions show that the new algorithm can significantly improve the optimization efficiency by using the iteratively updated Hessians and optimizations on interpolated surfaces.

A Data Assimilation System For Operational Weather Forecast In Galicia Region (nw Spain)

NASA Astrophysics Data System (ADS)

Balseiro, C. F.; Souto, M. J.; Pérez-Muñuzuri, V.; Brewster, K.; Xue, M.

Regional weather forecast models, such as the Advanced Regional Prediction System (ARPS), over complex environments with varying local influences require an accurate meteorological analysis that should include all local meteorological measurements available. In this work, the ARPS Data Analysis System (ADAS) (Xue et al. 2001) is applied as a three-dimensional weather analysis tool to include surface station and rawinsonde data with the NCEP AVN forecasts as the analysis background. Currently in ADAS, a set of five meteorological variables are considered during the analysis: horizontal grid-relative wind components, pressure, potential temperature and spe- cific humidity. The analysis is used for high resolution numerical weather prediction for the Galicia region. The analysis method used in ADAS is based on the successive corrective scheme of Bratseth (1986), which asymptotically approaches the result of a statistical (optimal) interpolation, but at lower computational cost. As in the optimal interpolation scheme, the Bratseth interpolation method can take into account the rel- ative error between background and observational data, therefore they are relatively insensitive to large variations in data density and can integrate data of mixed accuracy. This method can be applied economically in an operational setting, providing signifi- cant improvement over the background model forecast as well as any analysis without high-resolution local observations. A one-way nesting is applied for weather forecast in Galicia region, and the use of this assimilation system in both domains shows better results not only in initial conditions but also in all forecast periods. Bratseth, A.M. (1986): "Statistical interpolation by means of successive corrections." Tellus, 38A, 439-447. Souto, M. J., Balseiro, C. F., Pérez-Muñuzuri, V., Xue, M. Brewster, K., (2001): "Im- pact of cloud analysis on numerical weather prediction in the galician region of Spain". Submitted to Journal of Applied Meteorology. Xue, M., Wang. D., Gao, J., Brewster, K, Droegemeier, K. K., (2001): "The Advanced Regional Prediction System (ARPS), storm-scale numerical weather prediction and data assimilation". Meteor. Atmos Physics. Accepted

Convergence Analysis of Triangular MAC Schemes for Two Dimensional Stokes Equations

PubMed Central

Wang, Ming; Zhong, Lin

2015-01-01

In this paper, we consider the use of H(div) elements in the velocity–pressure formulation to discretize Stokes equations in two dimensions. We address the error estimate of the element pair RT0–P0, which is known to be suboptimal, and render the error estimate optimal by the symmetry of the grids and by the superconvergence result of Lagrange inter-polant. By enlarging RT0 such that it becomes a modified BDM-type element, we develop a new discretization BDM1b–P0. We, therefore, generalize the classical MAC scheme on rectangular grids to triangular grids and retain all the desirable properties of the MAC scheme: exact divergence-free, solver-friendly, and local conservation of physical quantities. Further, we prove that the proposed discretization BDM1b–P0 achieves the optimal convergence rate for both velocity and pressure on general quasi-uniform grids, and one and half order convergence rate for the vorticity and a recovered pressure. We demonstrate the validity of theories developed here by numerical experiments. PMID:26041948

A rapid parallelization of cone-beam projection and back-projection operator based on texture fetching interpolation

NASA Astrophysics Data System (ADS)

Xie, Lizhe; Hu, Yining; Chen, Yang; Shi, Luyao

2015-03-01

Projection and back-projection are the most computational consuming parts in Computed Tomography (CT) reconstruction. Parallelization strategies using GPU computing techniques have been introduced. We in this paper present a new parallelization scheme for both projection and back-projection. The proposed method is based on CUDA technology carried out by NVIDIA Corporation. Instead of build complex model, we aimed on optimizing the existing algorithm and make it suitable for CUDA implementation so as to gain fast computation speed. Besides making use of texture fetching operation which helps gain faster interpolation speed, we fixed sampling numbers in the computation of projection, to ensure the synchronization of blocks and threads, thus prevents the latency caused by inconsistent computation complexity. Experiment results have proven the computational efficiency and imaging quality of the proposed method.

A prototype upper-atmospheric data assimilation scheme based on optimal interpolation: 2. Numerical experiments

NASA Astrophysics Data System (ADS)

Akmaev, R. a.

1999-04-01

In Part 1 of this work ([Akmaev, 1999]), an overview of the theory of optimal interpolation (OI) ([Gandin, 1963]) and related techniques of data assimilation based on linear optimal estimation ([Liebelt, 1967]; [Catlin, 1989]; [Mendel, 1995]) is presented. The approach implies the use in data analysis of additional statistical information in the form of statistical moments, e.g., the mean and covariance (correlation). The a priori statistical characteristics, if available, make it possible to constrain expected errors and obtain optimal in some sense estimates of the true state from a set of observations in a given domain in space and/or time. The primary objective of OI is to provide estimates away from the observations, i.e., to fill in data voids in the domain under consideration. Additionally, OI performs smoothing suppressing the noise, i.e., the spectral components that are presumably not present in the true signal. Usually, the criterion of optimality is minimum variance of the expected errors and the whole approach may be considered constrained least squares or least squares with a priori information. Obviously, data assimilation techniques capable of incorporating any additional information are potentially superior to techniques that have no access to such information as, for example, the conventional least squares (e.g., [Liebelt, 1967]; [Weisberg, 1985]; [Press et al., 1992]; [Mendel, 1995]).

A multi-material topology optimization approach for wrinkle-free design of cable-suspended membrane structures

NASA Astrophysics Data System (ADS)

Luo, Yangjun; Niu, Yanzhuang; Li, Ming; Kang, Zhan

2017-06-01

In order to eliminate stress-related wrinkles in cable-suspended membrane structures and to provide simple and reliable deployment, this study presents a multi-material topology optimization model and an effective solution procedure for generating optimal connected layouts for membranes and cables. On the basis of the principal stress criterion of membrane wrinkling behavior and the density-based interpolation of multi-phase materials, the optimization objective is to maximize the total structural stiffness while satisfying principal stress constraints and specified material volume requirements. By adopting the cosine-type relaxation scheme to avoid the stress singularity phenomenon, the optimization model is successfully solved through a standard gradient-based algorithm. Four-corner tensioned membrane structures with different loading cases were investigated to demonstrate the effectiveness of the proposed method in automatically finding the optimal design composed of curved boundary cables and wrinkle-free membranes.

High order cell-centered scheme totally based on cell average

NASA Astrophysics Data System (ADS)

Liu, Ze-Yu; Cai, Qing-Dong

2018-05-01

This work clarifies the concept of cell average by pointing out the differences between cell average and cell centroid value, which are averaged cell-centered value and pointwise cell-centered value, respectively. Interpolation based on cell averages is constructed and high order QUICK-like numerical scheme is designed for such interpolation. A new approach of error analysis is introduced in this work, which is similar to Taylor’s expansion.

Thermodynamic evaluation of transonic compressor rotors using the finite volume approach

NASA Technical Reports Server (NTRS)

Moore, J.; Nicholson, S.; Moore, J. G.

1985-01-01

Research at NASA Lewis Research Center gave the opportunity to incorporate new control volumes in the Denton 3-D finite-volume time marching code. For duct flows, the new control volumes require no transverse smoothing and this allows calculations with large transverse gradients in properties without significant numerical total pressure losses. Possibilities for improving the Denton code to obtain better distributions of properties through shocks were demonstrated. Much better total pressure distributions through shocks are obtained when the interpolated effective pressure, needed to stabilize the solution procedure, is used to calculate the total pressure. This simple change largely eliminates the undershoot in total pressure down-stream of a shock. Overshoots and undershoots in total pressure can then be further reduced by a factor of 10 by adopting the effective density method, rather than the effective pressure method. Use of a Mach number dependent interpolation scheme for pressure then removes the overshoot in static pressure downstream of a shock. The stability of interpolation schemes used for the calculation of effective density is analyzed and a Mach number dependent scheme is developed, combining the advantages of the correct perfect gas equation for subsonic flow with the stability of 2-point and 3-point interpolation schemes for supersonic flow.

Integration of electromagnetic induction sensor data in soil sampling scheme optimization using simulated annealing.

PubMed

Barca, E; Castrignanò, A; Buttafuoco, G; De Benedetto, D; Passarella, G

2015-07-01

Soil survey is generally time-consuming, labor-intensive, and costly. Optimization of sampling scheme allows one to reduce the number of sampling points without decreasing or even increasing the accuracy of investigated attribute. Maps of bulk soil electrical conductivity (EC a ) recorded with electromagnetic induction (EMI) sensors could be effectively used to direct soil sampling design for assessing spatial variability of soil moisture. A protocol, using a field-scale bulk EC a survey, has been applied in an agricultural field in Apulia region (southeastern Italy). Spatial simulated annealing was used as a method to optimize spatial soil sampling scheme taking into account sampling constraints, field boundaries, and preliminary observations. Three optimization criteria were used. the first criterion (minimization of mean of the shortest distances, MMSD) optimizes the spreading of the point observations over the entire field by minimizing the expectation of the distance between an arbitrarily chosen point and its nearest observation; the second criterion (minimization of weighted mean of the shortest distances, MWMSD) is a weighted version of the MMSD, which uses the digital gradient of the grid EC a data as weighting function; and the third criterion (mean of average ordinary kriging variance, MAOKV) minimizes mean kriging estimation variance of the target variable. The last criterion utilizes the variogram model of soil water content estimated in a previous trial. The procedures, or a combination of them, were tested and compared in a real case. Simulated annealing was implemented by the software MSANOS able to define or redesign any sampling scheme by increasing or decreasing the original sampling locations. The output consists of the computed sampling scheme, the convergence time, and the cooling law, which can be an invaluable support to the process of sampling design. The proposed approach has found the optimal solution in a reasonable computation time. The use of bulk EC a gradient as an exhaustive variable, known at any node of an interpolation grid, has allowed the optimization of the sampling scheme, distinguishing among areas with different priority levels.

Analysis/forecast experiments with a multivariate statistical analysis scheme using FGGE data

NASA Technical Reports Server (NTRS)

Baker, W. E.; Bloom, S. C.; Nestler, M. S.

1985-01-01

A three-dimensional, multivariate, statistical analysis method, optimal interpolation (OI) is described for modeling meteorological data from widely dispersed sites. The model was developed to analyze FGGE data at the NASA-Goddard Laboratory of Atmospherics. The model features a multivariate surface analysis over the oceans, including maintenance of the Ekman balance and a geographically dependent correlation function. Preliminary comparisons are made between the OI model and similar schemes employed at the European Center for Medium Range Weather Forecasts and the National Meteorological Center. The OI scheme is used to provide input to a GCM, and model error correlations are calculated for forecasts of 500 mb vertical water mixing ratios and the wind profiles. Comparisons are made between the predictions and measured data. The model is shown to be as accurate as a successive corrections model out to 4.5 days.

On the Quality of Velocity Interpolation Schemes for Marker-In-Cell Methods on 3-D Staggered Grids

NASA Astrophysics Data System (ADS)

Kaus, B.; Pusok, A. E.; Popov, A.

2015-12-01

The marker-in-cell method is generally considered to be a flexible and robust method to model advection of heterogenous non-diffusive properties (i.e. rock type or composition) in geodynamic problems or incompressible Stokes problems. In this method, Lagrangian points carrying compositional information are advected with the ambient velocity field on an immobile, Eulerian grid. However, velocity interpolation from grid points to marker locations is often performed without preserving the zero divergence of the velocity field at the interpolated locations (i.e. non-conservative). Such interpolation schemes can induce non-physical clustering of markers when strong velocity gradients are present (Jenny et al., 2001) and this may, eventually, result in empty grid cells, a serious numerical violation of the marker-in-cell method. Solutions to this problem include: using larger mesh resolutions and/or marker densities, or repeatedly controlling the marker distribution (i.e. inject/delete), but which does not have an established physical background. To remedy this at low computational costs, Jenny et al. (2001) and Meyer and Jenny (2004) proposed a simple, conservative velocity interpolation (CVI) scheme for 2-D staggered grid, while Wang et al. (2015) extended the formulation to 3-D finite element methods. Here, we follow up with these studies and report on the quality of velocity interpolation methods for 2-D and 3-D staggered grids. We adapt the formulations from both Jenny et al. (2001) and Wang et al. (2015) for use on 3-D staggered grids, where the velocity components have different node locations as compared to finite element, where they share the same node location. We test the different interpolation schemes (CVI and non-CVI) in combination with different advection schemes (Euler, RK2 and RK4) and with/out marker control on Stokes problems with strong velocity gradients, which are discretized using a finite difference method. We show that a conservative formulation reduces the dispersion or clustering of markers and that the density of markers remains steady over time without the need of additional marker control. Jenny et al. (2001, J Comp Phys, 166, 218-252 Meyer and Jenny (2004), Proc Appl Math Mech, 4, 466-467 Wang et al. (2015), G3, Vol.16 Funding was provided by the ERC Starting Grant #258830.

Quantitative Tomography for Continuous Variable Quantum Systems

NASA Astrophysics Data System (ADS)

Landon-Cardinal, Olivier; Govia, Luke C. G.; Clerk, Aashish A.

2018-03-01

We present a continuous variable tomography scheme that reconstructs the Husimi Q function (Wigner function) by Lagrange interpolation, using measurements of the Q function (Wigner function) at the Padua points, conjectured to be optimal sampling points for two dimensional reconstruction. Our approach drastically reduces the number of measurements required compared to using equidistant points on a regular grid, although reanalysis of such experiments is possible. The reconstruction algorithm produces a reconstructed function with exponentially decreasing error and quasilinear runtime in the number of Padua points. Moreover, using the interpolating polynomial of the Q function, we present a technique to directly estimate the density matrix elements of the continuous variable state, with only a linear propagation of input measurement error. Furthermore, we derive a state-independent analytical bound on this error, such that our estimate of the density matrix is accompanied by a measure of its uncertainty.

An improved local radial point interpolation method for transient heat conduction analysis

NASA Astrophysics Data System (ADS)

Wang, Feng; Lin, Gao; Zheng, Bao-Jing; Hu, Zhi-Qiang

2013-06-01

The smoothing thin plate spline (STPS) interpolation using the penalty function method according to the optimization theory is presented to deal with transient heat conduction problems. The smooth conditions of the shape functions and derivatives can be satisfied so that the distortions hardly occur. Local weak forms are developed using the weighted residual method locally from the partial differential equations of the transient heat conduction. Here the Heaviside step function is used as the test function in each sub-domain to avoid the need for a domain integral. Essential boundary conditions can be implemented like the finite element method (FEM) as the shape functions possess the Kronecker delta property. The traditional two-point difference method is selected for the time discretization scheme. Three selected numerical examples are presented in this paper to demonstrate the availability and accuracy of the present approach comparing with the traditional thin plate spline (TPS) radial basis functions.

Optimization of Time-Dependent Particle Tracing Using Tetrahedral Decomposition

NASA Technical Reports Server (NTRS)

Kenwright, David; Lane, David

1995-01-01

An efficient algorithm is presented for computing particle paths, streak lines and time lines in time-dependent flows with moving curvilinear grids. The integration, velocity interpolation and step-size control are all performed in physical space which avoids the need to transform the velocity field into computational space. This leads to higher accuracy because there are no Jacobian matrix approximations or expensive matrix inversions. Integration accuracy is maintained using an adaptive step-size control scheme which is regulated by the path line curvature. The problem of cell-searching, point location and interpolation in physical space is simplified by decomposing hexahedral cells into tetrahedral cells. This enables the point location to be done analytically and substantially faster than with a Newton-Raphson iterative method. Results presented show this algorithm is up to six times faster than particle tracers which operate on hexahedral cells yet produces almost identical particle trajectories.

Interpolation Hermite Polynomials For Finite Element Method

NASA Astrophysics Data System (ADS)

Gusev, Alexander; Vinitsky, Sergue; Chuluunbaatar, Ochbadrakh; Chuluunbaatar, Galmandakh; Gerdt, Vladimir; Derbov, Vladimir; Góźdź, Andrzej; Krassovitskiy, Pavel

2018-02-01

We describe a new algorithm for analytic calculation of high-order Hermite interpolation polynomials of the simplex and give their classification. A typical example of triangle element, to be built in high accuracy finite element schemes, is given.

Spectral collocation method with a flexible angular discretization scheme for radiative transfer in multi-layer graded index medium

NASA Astrophysics Data System (ADS)

Wei, Linyang; Qi, Hong; Sun, Jianping; Ren, Yatao; Ruan, Liming

2017-05-01

The spectral collocation method (SCM) is employed to solve the radiative transfer in multi-layer semitransparent medium with graded index. A new flexible angular discretization scheme is employed to discretize the solid angle domain freely to overcome the limit of the number of discrete radiative direction when adopting traditional SN discrete ordinate scheme. Three radial basis function interpolation approaches, named as multi-quadric (MQ), inverse multi-quadric (IMQ) and inverse quadratic (IQ) interpolation, are employed to couple the radiative intensity at the interface between two adjacent layers and numerical experiments show that MQ interpolation has the highest accuracy and best stability. Variable radiative transfer problems in double-layer semitransparent media with different thermophysical properties are investigated and the influence of these thermophysical properties on the radiative transfer procedure in double-layer semitransparent media is also analyzed. All the simulated results show that the present SCM with the new angular discretization scheme can predict the radiative transfer in multi-layer semitransparent medium with graded index efficiently and accurately.

Use of shape-preserving interpolation methods in surface modeling

NASA Technical Reports Server (NTRS)

Ftitsch, F. N.

1984-01-01

In many large-scale scientific computations, it is necessary to use surface models based on information provided at only a finite number of points (rather than determined everywhere via an analytic formula). As an example, an equation of state (EOS) table may provide values of pressure as a function of temperature and density for a particular material. These values, while known quite accurately, are typically known only on a rectangular (but generally quite nonuniform) mesh in (T,d)-space. Thus interpolation methods are necessary to completely determine the EOS surface. The most primitive EOS interpolation scheme is bilinear interpolation. This has the advantages of depending only on local information, so that changes in data remote from a mesh element have no effect on the surface over the element, and of preserving shape information, such as monotonicity. Most scientific calculations, however, require greater smoothness. Standard higher-order interpolation schemes, such as Coons patches or bicubic splines, while providing the requisite smoothness, tend to produce surfaces that are not physically reasonable. This means that the interpolant may have bumps or wiggles that are not supported by the data. The mathematical quantification of ideas such as physically reasonable and visually pleasing is examined.

Comparison of Optimum Interpolation and Cressman Analyses

NASA Technical Reports Server (NTRS)

Baker, W. E.; Bloom, S. C.; Nestler, M. S.

1984-01-01

The objective of this investigation is to develop a state-of-the-art optimum interpolation (O/I) objective analysis procedure for use in numerical weather prediction studies. A three-dimensional multivariate O/I analysis scheme has been developed. Some characteristics of the GLAS O/I compared with those of the NMC and ECMWF systems are summarized. Some recent enhancements of the GLAS scheme include a univariate analysis of water vapor mixing ratio, a geographically dependent model prediction error correlation function and a multivariate oceanic surface analysis.

Comparison of Optimum Interpolation and Cressman Analyses

NASA Technical Reports Server (NTRS)

Baker, W. E.; Bloom, S. C.; Nestler, M. S.

1985-01-01

The development of a state of the art optimum interpolation (O/I) objective analysis procedure for use in numerical weather prediction studies was investigated. A three dimensional multivariate O/I analysis scheme was developed. Some characteristics of the GLAS O/I compared with those of the NMC and ECMWF systems are summarized. Some recent enhancements of the GLAS scheme include a univariate analysis of water vapor mixing ratio, a geographically dependent model prediction error correlation function and a multivariate oceanic surface analysis.

Cubic scaling algorithms for RPA correlation using interpolative separable density fitting

NASA Astrophysics Data System (ADS)

Lu, Jianfeng; Thicke, Kyle

2017-12-01

We present a new cubic scaling algorithm for the calculation of the RPA correlation energy. Our scheme splits up the dependence between the occupied and virtual orbitals in χ0 by use of Cauchy's integral formula. This introduces an additional integral to be carried out, for which we provide a geometrically convergent quadrature rule. Our scheme also uses the newly developed Interpolative Separable Density Fitting algorithm to further reduce the computational cost in a way analogous to that of the Resolution of Identity method.

High-Order Semi-Discrete Central-Upwind Schemes for Multi-Dimensional Hamilton-Jacobi Equations

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron; Biegel, Bran R. (Technical Monitor)

2002-01-01

We present high-order semi-discrete central-upwind numerical schemes for approximating solutions of multi-dimensional Hamilton-Jacobi (HJ) equations. This scheme is based on the use of fifth-order central interpolants like those developed in [1], in fluxes presented in [3]. These interpolants use the weighted essentially nonoscillatory (WENO) approach to avoid spurious oscillations near singularities, and become "central-upwind" in the semi-discrete limit. This scheme provides numerical approximations whose error is as much as an order of magnitude smaller than those in previous WENO-based fifth-order methods [2, 1]. Thee results are discussed via examples in one, two and three dimensions. We also pregnant explicit N-dimensional formulas for the fluxes, discuss their monotonicity and tl!e connection between this method and that in [2].

Subsurface water parameters: optimization approach to their determination from remotely sensed water color data.

PubMed

Jain, S C; Miller, J R

1976-04-01

A method, using an optimization scheme, has been developed for the interpretation of spectral albedo (or spectral reflectance) curves obtained from remotely sensed water color data. This method used a two-flow model of the radiation flow and solves for the albedo. Optimization fitting of predicted to observed reflectance data is performed by a quadratic interpolation method for the variables chlorophyll concentration and scattering coefficient. The technique is applied to airborne water color data obtained from Kawartha Lakes, Sargasso Sea, and Nova Scotia coast. The modeled spectral albedo curves are compared to those obtained experimentally, and the computed optimum water parameters are compared to ground truth values. It is shown that the backscattered spectral signal contains information that can be interpreted to give quantitative estimates of the chlorophyll concentration and turbidity in the waters studied.

Comparison of different interpolation operators including nonlinear subdivision schemes in the simulation of particle trajectories

NASA Astrophysics Data System (ADS)

Bensiali, Bouchra; Bodi, Kowsik; Ciraolo, Guido; Ghendrih, Philippe; Liandrat, Jacques

2013-03-01

In this work, we compare different interpolation operators in the context of particle tracking with an emphasis on situations involving velocity field with steep gradients. Since, in this case, most classical methods give rise to the Gibbs phenomenon (generation of oscillations near discontinuities), we present new methods for particle tracking based on subdivision schemes and especially on the Piecewise Parabolic Harmonic (PPH) scheme which has shown its advantage in image processing in presence of strong contrasts. First an analytic univariate case with a discontinuous velocity field is considered in order to highlight the effect of the Gibbs phenomenon on trajectory calculation. Theoretical results are provided. Then, we show, regardless of the interpolation method, the need to use a conservative approach when integrating a conservative problem with a velocity field deriving from a potential. Finally, the PPH scheme is applied in a more realistic case of a time-dependent potential encountered in the edge turbulence of magnetically confined plasmas, to compare the propagation of density structures (turbulence bursts) with the dynamics of test particles. This study highlights the difference between particle transport and density transport in turbulent fields.

Incompressibility without tears - How to avoid restrictions of mixed formulation

NASA Technical Reports Server (NTRS)

Zienkiewicz, O. C.; Wu, J.

1991-01-01

Several time-stepping schemes for incompressibility problems are presented which can be solved directly for steady state or iteratively through the time domain. The difficulty of mixed interpolation is avoided by using these schemes. The schemes are applicable to problems of fluid and solid mechanics.

Well-conditioned fractional collocation methods using fractional Birkhoff interpolation basis

NASA Astrophysics Data System (ADS)

Jiao, Yujian; Wang, Li-Lian; Huang, Can

2016-01-01

The purpose of this paper is twofold. Firstly, we provide explicit and compact formulas for computing both Caputo and (modified) Riemann-Liouville (RL) fractional pseudospectral differentiation matrices (F-PSDMs) of any order at general Jacobi-Gauss-Lobatto (JGL) points. We show that in the Caputo case, it suffices to compute F-PSDM of order μ ∈ (0 , 1) to compute that of any order k + μ with integer k ≥ 0, while in the modified RL case, it is only necessary to evaluate a fractional integral matrix of order μ ∈ (0 , 1). Secondly, we introduce suitable fractional JGL Birkhoff interpolation problems leading to new interpolation polynomial basis functions with remarkable properties: (i) the matrix generated from the new basis yields the exact inverse of F-PSDM at "interior" JGL points; (ii) the matrix of the highest fractional derivative in a collocation scheme under the new basis is diagonal; and (iii) the resulted linear system is well-conditioned in the Caputo case, while in the modified RL case, the eigenvalues of the coefficient matrix are highly concentrated. In both cases, the linear systems of the collocation schemes using the new basis can be solved by an iterative solver within a few iterations. Notably, the inverse can be computed in a very stable manner, so this offers optimal preconditioners for usual fractional collocation methods for fractional differential equations (FDEs). It is also noteworthy that the choice of certain special JGL points with parameters related to the order of the equations can ease the implementation. We highlight that the use of the Bateman's fractional integral formulas and fast transforms between Jacobi polynomials with different parameters, is essential for our algorithm development.

Efficient and Adaptive Methods for Computing Accurate Potential Surfaces for Quantum Nuclear Effects: Applications to Hydrogen-Transfer Reactions.

PubMed

DeGregorio, Nicole; Iyengar, Srinivasan S

2018-01-09

We present two sampling measures to gauge critical regions of potential energy surfaces. These sampling measures employ (a) the instantaneous quantum wavepacket density, an approximation to the (b) potential surface, its (c) gradients, and (d) a Shannon information theory based expression that estimates the local entropy associated with the quantum wavepacket. These four criteria together enable a directed sampling of potential surfaces that appears to correctly describe the local oscillation frequencies, or the local Nyquist frequency, of a potential surface. The sampling functions are then utilized to derive a tessellation scheme that discretizes the multidimensional space to enable efficient sampling of potential surfaces. The sampled potential surface is then combined with four different interpolation procedures, namely, (a) local Hermite curve interpolation, (b) low-pass filtered Lagrange interpolation, (c) the monomial symmetrization approximation (MSA) developed by Bowman and co-workers, and (d) a modified Shepard algorithm. The sampling procedure and the fitting schemes are used to compute (a) potential surfaces in highly anharmonic hydrogen-bonded systems and (b) study hydrogen-transfer reactions in biogenic volatile organic compounds (isoprene) where the transferring hydrogen atom is found to demonstrate critical quantum nuclear effects. In the case of isoprene, the algorithm discussed here is used to derive multidimensional potential surfaces along a hydrogen-transfer reaction path to gauge the effect of quantum-nuclear degrees of freedom on the hydrogen-transfer process. Based on the decreased computational effort, facilitated by the optimal sampling of the potential surfaces through the use of sampling functions discussed here, and the accuracy of the associated potential surfaces, we believe the method will find great utility in the study of quantum nuclear dynamics problems, of which application to hydrogen-transfer reactions and hydrogen-bonded systems is demonstrated here.

Interpolation Method Needed for Numerical Uncertainty

NASA Technical Reports Server (NTRS)

Groves, Curtis E.; Ilie, Marcel; Schallhorn, Paul A.

2014-01-01

Using Computational Fluid Dynamics (CFD) to predict a flow field is an approximation to the exact problem and uncertainties exist. There is a method to approximate the errors in CFD via Richardson's Extrapolation. This method is based off of progressive grid refinement. To estimate the errors, the analyst must interpolate between at least three grids. This paper describes a study to find an appropriate interpolation scheme that can be used in Richardson's extrapolation or other uncertainty method to approximate errors.

Multi-level adaptive finite element methods. 1: Variation problems

NASA Technical Reports Server (NTRS)

Brandt, A.

1979-01-01

A general numerical strategy for solving partial differential equations and other functional problems by cycling between coarser and finer levels of discretization is described. Optimal discretization schemes are provided together with very fast general solvers. It is described in terms of finite element discretizations of general nonlinear minimization problems. The basic processes (relaxation sweeps, fine-grid-to-coarse-grid transfers of residuals, coarse-to-fine interpolations of corrections) are directly and naturally determined by the objective functional and the sequence of approximation spaces. The natural processes, however, are not always optimal. Concrete examples are given and some new techniques are reviewed. Including the local truncation extrapolation and a multilevel procedure for inexpensively solving chains of many boundary value problems, such as those arising in the solution of time-dependent problems.

GPU color space conversion

NASA Astrophysics Data System (ADS)

Chase, Patrick; Vondran, Gary

2011-01-01

Tetrahedral interpolation is commonly used to implement continuous color space conversions from sparse 3D and 4D lookup tables. We investigate the implementation and optimization of tetrahedral interpolation algorithms for GPUs, and compare to the best known CPU implementations as well as to a well known GPU-based trilinear implementation. We show that a 500 NVIDIA GTX-580 GPU is 3x faster than a 1000 Intel Core i7 980X CPU for 3D interpolation, and 9x faster for 4D interpolation. Performance-relevant GPU attributes are explored including thread scheduling, local memory characteristics, global memory hierarchy, and cache behaviors. We consider existing tetrahedral interpolation algorithms and tune based on the structure and branching capabilities of current GPUs. Global memory performance is improved by reordering and expanding the lookup table to ensure optimal access behaviors. Per multiprocessor local memory is exploited to implement optimally coalesced global memory accesses, and local memory addressing is optimized to minimize bank conflicts. We explore the impacts of lookup table density upon computation and memory access costs. Also presented are CPU-based 3D and 4D interpolators, using SSE vector operations that are faster than any previously published solution.

Directional view interpolation for compensation of sparse angular sampling in cone-beam CT.

PubMed

Bertram, Matthias; Wiegert, Jens; Schafer, Dirk; Aach, Til; Rose, Georg

2009-07-01

In flat detector cone-beam computed tomography and related applications, sparse angular sampling frequently leads to characteristic streak artifacts. To overcome this problem, it has been suggested to generate additional views by means of interpolation. The practicality of this approach is investigated in combination with a dedicated method for angular interpolation of 3-D sinogram data. For this purpose, a novel dedicated shape-driven directional interpolation algorithm based on a structure tensor approach is developed. Quantitative evaluation shows that this method clearly outperforms conventional scene-based interpolation schemes. Furthermore, the image quality trade-offs associated with the use of interpolated intermediate views are systematically evaluated for simulated and clinical cone-beam computed tomography data sets of the human head. It is found that utilization of directionally interpolated views significantly reduces streak artifacts and noise, at the expense of small introduced image blur.

Application of Super-Resolution Convolutional Neural Network for Enhancing Image Resolution in Chest CT.

PubMed

Umehara, Kensuke; Ota, Junko; Ishida, Takayuki

2017-10-18

In this study, the super-resolution convolutional neural network (SRCNN) scheme, which is the emerging deep-learning-based super-resolution method for enhancing image resolution in chest CT images, was applied and evaluated using the post-processing approach. For evaluation, 89 chest CT cases were sampled from The Cancer Imaging Archive. The 89 CT cases were divided randomly into 45 training cases and 44 external test cases. The SRCNN was trained using the training dataset. With the trained SRCNN, a high-resolution image was reconstructed from a low-resolution image, which was down-sampled from an original test image. For quantitative evaluation, two image quality metrics were measured and compared to those of the conventional linear interpolation methods. The image restoration quality of the SRCNN scheme was significantly higher than that of the linear interpolation methods (p < 0.001 or p < 0.05). The high-resolution image reconstructed by the SRCNN scheme was highly restored and comparable to the original reference image, in particular, for a ×2 magnification. These results indicate that the SRCNN scheme significantly outperforms the linear interpolation methods for enhancing image resolution in chest CT images. The results also suggest that SRCNN may become a potential solution for generating high-resolution CT images from standard CT images.

Accuracy of parameterized proton range models; A comparison

NASA Astrophysics Data System (ADS)

Pettersen, H. E. S.; Chaar, M.; Meric, I.; Odland, O. H.; Sølie, J. R.; Röhrich, D.

2018-03-01

An accurate calculation of proton ranges in phantoms or detector geometries is crucial for decision making in proton therapy and proton imaging. To this end, several parameterizations of the range-energy relationship exist, with different levels of complexity and accuracy. In this study we compare the accuracy of four different parameterizations models for proton range in water: Two analytical models derived from the Bethe equation, and two different interpolation schemes applied to range-energy tables. In conclusion, a spline interpolation scheme yields the highest reproduction accuracy, while the shape of the energy loss-curve is best reproduced with the differentiated Bragg-Kleeman equation.

Pricing and simulation for real estate index options: Radial basis point interpolation

NASA Astrophysics Data System (ADS)

Gong, Pu; Zou, Dong; Wang, Jiayue

2018-06-01

This study employs the meshfree radial basis point interpolation (RBPI) for pricing real estate derivatives contingent on real estate index. This method combines radial and polynomial basis functions, which can guarantee the interpolation scheme with Kronecker property and effectively improve accuracy. An exponential change of variables, a mesh refinement algorithm and the Richardson extrapolation are employed in this study to implement the RBPI. Numerical results are presented to examine the computational efficiency and accuracy of our method.

Optimal reorientation of asymmetric underactuated spacecraft using differential flatness and receding horizon control

NASA Astrophysics Data System (ADS)

Cai, Wei-wei; Yang, Le-ping; Zhu, Yan-wei

2015-01-01

This paper presents a novel method integrating nominal trajectory optimization and tracking for the reorientation control of an underactuated spacecraft with only two available control torque inputs. By employing a pseudo input along the uncontrolled axis, the flatness property of a general underactuated spacecraft is extended explicitly, by which the reorientation trajectory optimization problem is formulated into the flat output space with all the differential constraints eliminated. Ultimately, the flat output optimization problem is transformed into a nonlinear programming problem via the Chebyshev pseudospectral method, which is improved by the conformal map and barycentric rational interpolation techniques to overcome the side effects of the differential matrix's ill-conditions on numerical accuracy. Treating the trajectory tracking control as a state regulation problem, we develop a robust closed-loop tracking control law using the receding-horizon control method, and compute the feedback control at each control cycle rapidly via the differential transformation method. Numerical simulation results show that the proposed control scheme is feasible and effective for the reorientation maneuver.

Comparison of the common spatial interpolation methods used to analyze potentially toxic elements surrounding mining regions.

PubMed

Ding, Qian; Wang, Yong; Zhuang, Dafang

2018-04-15

The appropriate spatial interpolation methods must be selected to analyze the spatial distributions of Potentially Toxic Elements (PTEs), which is a precondition for evaluating PTE pollution. The accuracy and effect of different spatial interpolation methods, which include inverse distance weighting interpolation (IDW) (power = 1, 2, 3), radial basis function interpolation (RBF) (basis function: thin-plate spline (TPS), spline with tension (ST), completely regularized spline (CRS), multiquadric (MQ) and inverse multiquadric (IMQ)) and ordinary kriging interpolation (OK) (semivariogram model: spherical, exponential, gaussian and linear), were compared using 166 unevenly distributed soil PTE samples (As, Pb, Cu and Zn) in the Suxian District, Chenzhou City, Hunan Province as the study subject. The reasons for the accuracy differences of the interpolation methods and the uncertainties of the interpolation results are discussed, then several suggestions for improving the interpolation accuracy are proposed, and the direction of pollution control is determined. The results of this study are as follows: (i) RBF-ST and OK (exponential) are the optimal interpolation methods for As and Cu, and the optimal interpolation method for Pb and Zn is RBF-IMQ. (ii) The interpolation uncertainty is positively correlated with the PTE concentration, and higher uncertainties are primarily distributed around mines, which is related to the strong spatial variability of PTE concentrations caused by human interference. (iii) The interpolation accuracy can be improved by increasing the sample size around the mines, introducing auxiliary variables in the case of incomplete sampling and adopting the partition prediction method. (iv) It is necessary to strengthen the prevention and control of As and Pb pollution, particularly in the central and northern areas. The results of this study can provide an effective reference for the optimization of interpolation methods and parameters for unevenly distributed soil PTE data in mining areas. Copyright © 2018 Elsevier Ltd. All rights reserved.

When Interpolation-Induced Reflection Artifact Meets Time-Frequency Analysis.

PubMed

Lin, Yu-Ting; Flandrin, Patrick; Wu, Hau-Tieng

2016-10-01

While extracting the temporal dynamical features based on the time-frequency analyses, like the reassignment and synchrosqueezing transform, attracts more and more interest in biomedical data analysis, we should be careful about artifacts generated by interpolation schemes, in particular when the sampling rate is not significantly higher than the frequency of the oscillatory component we are interested in. We formulate the problem called the reflection effect and provide a theoretical justification of the statement. We also show examples in the anesthetic depth analysis with clear but undesirable artifacts. The artifact associated with the reflection effect exists not only theoretically but practically as well. Its influence is pronounced when we apply the time-frequency analyses to extract the time-varying dynamics hidden inside the signal. We have to carefully deal with the artifact associated with the reflection effect by choosing a proper interpolation scheme.

Super-resolution convolutional neural network for the improvement of the image quality of magnified images in chest radiographs

NASA Astrophysics Data System (ADS)

Umehara, Kensuke; Ota, Junko; Ishimaru, Naoki; Ohno, Shunsuke; Okamoto, Kentaro; Suzuki, Takanori; Shirai, Naoki; Ishida, Takayuki

2017-02-01

Single image super-resolution (SR) method can generate a high-resolution (HR) image from a low-resolution (LR) image by enhancing image resolution. In medical imaging, HR images are expected to have a potential to provide a more accurate diagnosis with the practical application of HR displays. In recent years, the super-resolution convolutional neural network (SRCNN), which is one of the state-of-the-art deep learning based SR methods, has proposed in computer vision. In this study, we applied and evaluated the SRCNN scheme to improve the image quality of magnified images in chest radiographs. For evaluation, a total of 247 chest X-rays were sampled from the JSRT database. The 247 chest X-rays were divided into 93 training cases with non-nodules and 152 test cases with lung nodules. The SRCNN was trained using the training dataset. With the trained SRCNN, the HR image was reconstructed from the LR one. We compared the image quality of the SRCNN and conventional image interpolation methods, nearest neighbor, bilinear and bicubic interpolations. For quantitative evaluation, we measured two image quality metrics, peak signal-to-noise ratio (PSNR) and structural similarity (SSIM). In the SRCNN scheme, PSNR and SSIM were significantly higher than those of three interpolation methods (p<0.001). Visual assessment confirmed that the SRCNN produced much sharper edge than conventional interpolation methods without any obvious artifacts. These preliminary results indicate that the SRCNN scheme significantly outperforms conventional interpolation algorithms for enhancing image resolution and that the use of the SRCNN can yield substantial improvement of the image quality of magnified images in chest radiographs.

Maximally Informative Statistics for Localization and Mapping

NASA Technical Reports Server (NTRS)

Deans, Matthew C.

2001-01-01

This paper presents an algorithm for localization and mapping for a mobile robot using monocular vision and odometry as its means of sensing. The approach uses the Variable State Dimension filtering (VSDF) framework to combine aspects of Extended Kalman filtering and nonlinear batch optimization. This paper describes two primary improvements to the VSDF. The first is to use an interpolation scheme based on Gaussian quadrature to linearize measurements rather than relying on analytic Jacobians. The second is to replace the inverse covariance matrix in the VSDF with its Cholesky factor to improve the computational complexity. Results of applying the filter to the problem of localization and mapping with omnidirectional vision are presented.

Kernel reconstruction methods for Doppler broadening - Temperature interpolation by linear combination of reference cross sections at optimally chosen temperatures

NASA Astrophysics Data System (ADS)

Ducru, Pablo; Josey, Colin; Dibert, Karia; Sobes, Vladimir; Forget, Benoit; Smith, Kord

2017-04-01

This article establishes a new family of methods to perform temperature interpolation of nuclear interactions cross sections, reaction rates, or cross sections times the energy. One of these quantities at temperature T is approximated as a linear combination of quantities at reference temperatures (Tj). The problem is formalized in a cross section independent fashion by considering the kernels of the different operators that convert cross section related quantities from a temperature T0 to a higher temperature T - namely the Doppler broadening operation. Doppler broadening interpolation of nuclear cross sections is thus here performed by reconstructing the kernel of the operation at a given temperature T by means of linear combination of kernels at reference temperatures (Tj). The choice of the L2 metric yields optimal linear interpolation coefficients in the form of the solutions of a linear algebraic system inversion. The optimization of the choice of reference temperatures (Tj) is then undertaken so as to best reconstruct, in the L∞ sense, the kernels over a given temperature range [Tmin ,Tmax ]. The performance of these kernel reconstruction methods is then assessed in light of previous temperature interpolation methods by testing them upon isotope 238U. Temperature-optimized free Doppler kernel reconstruction significantly outperforms all previous interpolation-based methods, achieving 0.1% relative error on temperature interpolation of 238U total cross section over the temperature range [ 300 K , 3000 K ] with only 9 reference temperatures.

A hierarchical transition state search algorithm

NASA Astrophysics Data System (ADS)

del Campo, Jorge M.; Köster, Andreas M.

2008-07-01

A hierarchical transition state search algorithm is developed and its implementation in the density functional theory program deMon2k is described. This search algorithm combines the double ended saddle interpolation method with local uphill trust region optimization. A new formalism for the incorporation of the distance constrain in the saddle interpolation method is derived. The similarities between the constrained optimizations in the local trust region method and the saddle interpolation are highlighted. The saddle interpolation and local uphill trust region optimizations are validated on a test set of 28 representative reactions. The hierarchical transition state search algorithm is applied to an intramolecular Diels-Alder reaction with several internal rotors, which makes automatic transition state search rather challenging. The obtained reaction mechanism is discussed in the context of the experimentally observed product distribution.

Error Estimation of An Ensemble Statistical Seasonal Precipitation Prediction Model

NASA Technical Reports Server (NTRS)

Shen, Samuel S. P.; Lau, William K. M.; Kim, Kyu-Myong; Li, Gui-Long

2001-01-01

This NASA Technical Memorandum describes an optimal ensemble canonical correlation forecasting model for seasonal precipitation. Each individual forecast is based on the canonical correlation analysis (CCA) in the spectral spaces whose bases are empirical orthogonal functions (EOF). The optimal weights in the ensemble forecasting crucially depend on the mean square error of each individual forecast. An estimate of the mean square error of a CCA prediction is made also using the spectral method. The error is decomposed onto EOFs of the predictand and decreases linearly according to the correlation between the predictor and predictand. Since new CCA scheme is derived for continuous fields of predictor and predictand, an area-factor is automatically included. Thus our model is an improvement of the spectral CCA scheme of Barnett and Preisendorfer. The improvements include (1) the use of area-factor, (2) the estimation of prediction error, and (3) the optimal ensemble of multiple forecasts. The new CCA model is applied to the seasonal forecasting of the United States (US) precipitation field. The predictor is the sea surface temperature (SST). The US Climate Prediction Center's reconstructed SST is used as the predictor's historical data. The US National Center for Environmental Prediction's optimally interpolated precipitation (1951-2000) is used as the predictand's historical data. Our forecast experiments show that the new ensemble canonical correlation scheme renders a reasonable forecasting skill. For example, when using September-October-November SST to predict the next season December-January-February precipitation, the spatial pattern correlation between the observed and predicted are positive in 46 years among the 50 years of experiments. The positive correlations are close to or greater than 0.4 in 29 years, which indicates excellent performance of the forecasting model. The forecasting skill can be further enhanced when several predictors are used.

Interpolation Method Needed for Numerical Uncertainty Analysis of Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Groves, Curtis; Ilie, Marcel; Schallhorn, Paul

2014-01-01

Using Computational Fluid Dynamics (CFD) to predict a flow field is an approximation to the exact problem and uncertainties exist. There is a method to approximate the errors in CFD via Richardson's Extrapolation. This method is based off of progressive grid refinement. To estimate the errors in an unstructured grid, the analyst must interpolate between at least three grids. This paper describes a study to find an appropriate interpolation scheme that can be used in Richardson's extrapolation or other uncertainty method to approximate errors. Nomenclature

Hybrid threshold adaptable quantum secret sharing scheme with reverse Huffman-Fibonacci-tree coding.

PubMed

Lai, Hong; Zhang, Jun; Luo, Ming-Xing; Pan, Lei; Pieprzyk, Josef; Xiao, Fuyuan; Orgun, Mehmet A

2016-08-12

With prevalent attacks in communication, sharing a secret between communicating parties is an ongoing challenge. Moreover, it is important to integrate quantum solutions with classical secret sharing schemes with low computational cost for the real world use. This paper proposes a novel hybrid threshold adaptable quantum secret sharing scheme, using an m-bonacci orbital angular momentum (OAM) pump, Lagrange interpolation polynomials, and reverse Huffman-Fibonacci-tree coding. To be exact, we employ entangled states prepared by m-bonacci sequences to detect eavesdropping. Meanwhile, we encode m-bonacci sequences in Lagrange interpolation polynomials to generate the shares of a secret with reverse Huffman-Fibonacci-tree coding. The advantages of the proposed scheme is that it can detect eavesdropping without joint quantum operations, and permits secret sharing for an arbitrary but no less than threshold-value number of classical participants with much lower bandwidth. Also, in comparison with existing quantum secret sharing schemes, it still works when there are dynamic changes, such as the unavailability of some quantum channel, the arrival of new participants and the departure of participants. Finally, we provide security analysis of the new hybrid quantum secret sharing scheme and discuss its useful features for modern applications.

Hybrid threshold adaptable quantum secret sharing scheme with reverse Huffman-Fibonacci-tree coding

PubMed Central

Lai, Hong; Zhang, Jun; Luo, Ming-Xing; Pan, Lei; Pieprzyk, Josef; Xiao, Fuyuan; Orgun, Mehmet A.

2016-01-01

With prevalent attacks in communication, sharing a secret between communicating parties is an ongoing challenge. Moreover, it is important to integrate quantum solutions with classical secret sharing schemes with low computational cost for the real world use. This paper proposes a novel hybrid threshold adaptable quantum secret sharing scheme, using an m-bonacci orbital angular momentum (OAM) pump, Lagrange interpolation polynomials, and reverse Huffman-Fibonacci-tree coding. To be exact, we employ entangled states prepared by m-bonacci sequences to detect eavesdropping. Meanwhile, we encode m-bonacci sequences in Lagrange interpolation polynomials to generate the shares of a secret with reverse Huffman-Fibonacci-tree coding. The advantages of the proposed scheme is that it can detect eavesdropping without joint quantum operations, and permits secret sharing for an arbitrary but no less than threshold-value number of classical participants with much lower bandwidth. Also, in comparison with existing quantum secret sharing schemes, it still works when there are dynamic changes, such as the unavailability of some quantum channel, the arrival of new participants and the departure of participants. Finally, we provide security analysis of the new hybrid quantum secret sharing scheme and discuss its useful features for modern applications. PMID:27515908

Kernel reconstruction methods for Doppler broadening — Temperature interpolation by linear combination of reference cross sections at optimally chosen temperatures

DOE PAGES

Ducru, Pablo; Josey, Colin; Dibert, Karia; ...

2017-01-25

This paper establishes a new family of methods to perform temperature interpolation of nuclear interactions cross sections, reaction rates, or cross sections times the energy. One of these quantities at temperature T is approximated as a linear combination of quantities at reference temperatures (T j). The problem is formalized in a cross section independent fashion by considering the kernels of the different operators that convert cross section related quantities from a temperature T 0 to a higher temperature T — namely the Doppler broadening operation. Doppler broadening interpolation of nuclear cross sections is thus here performed by reconstructing the kernelmore » of the operation at a given temperature T by means of linear combination of kernels at reference temperatures (T j). The choice of the L 2 metric yields optimal linear interpolation coefficients in the form of the solutions of a linear algebraic system inversion. The optimization of the choice of reference temperatures (T j) is then undertaken so as to best reconstruct, in the L∞ sense, the kernels over a given temperature range [T min,T max]. The performance of these kernel reconstruction methods is then assessed in light of previous temperature interpolation methods by testing them upon isotope 238U. Temperature-optimized free Doppler kernel reconstruction significantly outperforms all previous interpolation-based methods, achieving 0.1% relative error on temperature interpolation of 238U total cross section over the temperature range [300 K,3000 K] with only 9 reference temperatures.« less

Solid-perforated panel layout optimization by topology optimization based on unified transfer matrix.

PubMed

Kim, Yoon Jae; Kim, Yoon Young

2010-10-01

This paper presents a numerical method for the optimization of the sequencing of solid panels, perforated panels and air gaps and their respective thickness for maximizing sound transmission loss and/or absorption. For the optimization, a method based on the topology optimization formulation is proposed. It is difficult to employ only the commonly-used material interpolation technique because the involved layers exhibit fundamentally different acoustic behavior. Thus, an optimization method formulation using a so-called unified transfer matrix is newly proposed. The key idea is to form elements of the transfer matrix such that interpolated elements by the layer design variables can be those of air, perforated and solid panel layers. The problem related to the interpolation is addressed and bench mark-type problems such as sound transmission or absorption maximization problems are solved to check the efficiency of the developed method.

Experimental demonstration of non-iterative interpolation-based partial ICI compensation in100G RGI-DP-CO-OFDM transport systems.

PubMed

Mousa-Pasandi, Mohammad E; Zhuge, Qunbi; Xu, Xian; Osman, Mohamed M; El-Sahn, Ziad A; Chagnon, Mathieu; Plant, David V

2012-07-02

We experimentally investigate the performance of a low-complexity non-iterative phase noise induced inter-carrier interference (ICI) compensation algorithm in reduced-guard-interval dual-polarization coherent-optical orthogonal-frequency-division-multiplexing (RGI-DP-CO-OFDM) transport systems. This interpolation-based ICI compensator estimates the time-domain phase noise samples by a linear interpolation between the CPE estimates of the consecutive OFDM symbols. We experimentally study the performance of this scheme for a 28 Gbaud QPSK RGI-DP-CO-OFDM employing a low cost distributed feedback (DFB) laser. Experimental results using a DFB laser with the linewidth of 2.6 MHz demonstrate 24% and 13% improvement in transmission reach with respect to the conventional equalizer (CE) in presence of weak and strong dispersion-enhanced-phase-noise (DEPN), respectively. A brief analysis of the computational complexity of this scheme in terms of the number of required complex multiplications is provided. This practical approach does not suffer from error propagation while enjoying low computational complexity.

Error analysis of filtering operations in pixel-duplicated images of diabetic retinopathy

NASA Astrophysics Data System (ADS)

Mehrubeoglu, Mehrube; McLauchlan, Lifford

2010-08-01

In this paper, diabetic retinopathy is chosen for a sample target image to demonstrate the effectiveness of image enlargement through pixel duplication in identifying regions of interest. Pixel duplication is presented as a simpler alternative to data interpolation techniques for detecting small structures in the images. A comparative analysis is performed on different image processing schemes applied to both original and pixel-duplicated images. Structures of interest are detected and and classification parameters optimized for minimum false positive detection in the original and enlarged retinal pictures. The error analysis demonstrates the advantages as well as shortcomings of pixel duplication in image enhancement when spatial averaging operations (smoothing filters) are also applied.

A fast and accurate dihedral interpolation loop subdivision scheme

NASA Astrophysics Data System (ADS)

Shi, Zhuo; An, Yalei; Wang, Zhongshuai; Yu, Ke; Zhong, Si; Lan, Rushi; Luo, Xiaonan

2018-04-01

In this paper, we propose a fast and accurate dihedral interpolation Loop subdivision scheme for subdivision surfaces based on triangular meshes. In order to solve the problem of surface shrinkage, we keep the limit condition unchanged, which is important. Extraordinary vertices are handled using modified Butterfly rules. Subdivision schemes are computationally costly as the number of faces grows exponentially at higher levels of subdivision. To address this problem, our approach is to use local surface information to adaptively refine the model. This is achieved simply by changing the threshold value of the dihedral angle parameter, i.e., the angle between the normals of a triangular face and its adjacent faces. We then demonstrate the effectiveness of the proposed method for various 3D graphic triangular meshes, and extensive experimental results show that it can match or exceed the expected results at lower computational cost.

A Lagrangian particle method with remeshing for tracer transport on the sphere

DOE PAGES

Bosler, Peter Andrew; Kent, James; Krasny, Robert; ...

2017-03-30

A Lagrangian particle method (called LPM) based on the flow map is presented for tracer transport on the sphere. The particles carry tracer values and are located at the centers and vertices of triangular Lagrangian panels. Remeshing is applied to control particle disorder and two schemes are compared, one using direct tracer interpolation and another using inverse flow map interpolation with sampling of the initial tracer density. Test cases include a moving-vortices flow and reversing-deformational flow with both zero and nonzero divergence, as well as smooth and discontinuous tracers. We examine the accuracy of the computed tracer density and tracermore » integral, and preservation of nonlinear correlation in a pair of tracers. Here, we compare results obtained using LPM and the Lin–Rood finite-volume scheme. An adaptive particle/panel refinement scheme is demonstrated.« less

A Lagrangian particle method with remeshing for tracer transport on the sphere

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bosler, Peter Andrew; Kent, James; Krasny, Robert

A Lagrangian particle method (called LPM) based on the flow map is presented for tracer transport on the sphere. The particles carry tracer values and are located at the centers and vertices of triangular Lagrangian panels. Remeshing is applied to control particle disorder and two schemes are compared, one using direct tracer interpolation and another using inverse flow map interpolation with sampling of the initial tracer density. Test cases include a moving-vortices flow and reversing-deformational flow with both zero and nonzero divergence, as well as smooth and discontinuous tracers. We examine the accuracy of the computed tracer density and tracermore » integral, and preservation of nonlinear correlation in a pair of tracers. Here, we compare results obtained using LPM and the Lin–Rood finite-volume scheme. An adaptive particle/panel refinement scheme is demonstrated.« less

Gaussian Process Interpolation for Uncertainty Estimation in Image Registration

PubMed Central

Wachinger, Christian; Golland, Polina; Reuter, Martin; Wells, William

2014-01-01

Intensity-based image registration requires resampling images on a common grid to evaluate the similarity function. The uncertainty of interpolation varies across the image, depending on the location of resampled points relative to the base grid. We propose to perform Bayesian inference with Gaussian processes, where the covariance matrix of the Gaussian process posterior distribution estimates the uncertainty in interpolation. The Gaussian process replaces a single image with a distribution over images that we integrate into a generative model for registration. Marginalization over resampled images leads to a new similarity measure that includes the uncertainty of the interpolation. We demonstrate that our approach increases the registration accuracy and propose an efficient approximation scheme that enables seamless integration with existing registration methods. PMID:25333127

LPV Controller Interpolation for Improved Gain-Scheduling Control Performance

NASA Technical Reports Server (NTRS)

Wu, Fen; Kim, SungWan

2002-01-01

In this paper, a new gain-scheduling control design approach is proposed by combining LPV (linear parameter-varying) control theory with interpolation techniques. The improvement of gain-scheduled controllers can be achieved from local synthesis of Lyapunov functions and continuous construction of a global Lyapunov function by interpolation. It has been shown that this combined LPV control design scheme is capable of improving closed-loop performance derived from local performance improvement. The gain of the LPV controller will also change continuously across parameter space. The advantages of the newly proposed LPV control is demonstrated through a detailed AMB controller design example.

Numerical solution of transport equation for applications in environmental hydraulics and hydrology

NASA Astrophysics Data System (ADS)

Rashidul Islam, M.; Hanif Chaudhry, M.

1997-04-01

The advective term in the one-dimensional transport equation, when numerically discretized, produces artificial diffusion. To minimize such artificial diffusion, which vanishes only for Courant number equal to unity, transport owing to advection has been modeled separately. The numerical solution of the advection equation for a Gaussian initial distribution is well established; however, large oscillations are observed when applied to an initial distribution with sleep gradients, such as trapezoidal distribution of a constituent or propagation of mass from a continuous input. In this study, the application of seven finite-difference schemes and one polynomial interpolation scheme is investigated to solve the transport equation for both Gaussian and non-Gaussian (trapezoidal) initial distributions. The results obtained from the numerical schemes are compared with the exact solutions. A constant advective velocity is assumed throughout the transport process. For a Gaussian distribution initial condition, all eight schemes give excellent results, except the Lax scheme which is diffusive. In application to the trapezoidal initial distribution, explicit finite-difference schemes prove to be superior to implicit finite-difference schemes because the latter produce large numerical oscillations near the steep gradients. The Warming-Kutler-Lomax (WKL) explicit scheme is found to be better among this group. The Hermite polynomial interpolation scheme yields the best result for a trapezoidal distribution among all eight schemes investigated. The second-order accurate schemes are sufficiently accurate for most practical problems, but the solution of unusual problems (concentration with steep gradient) requires the application of higher-order (e.g. third- and fourth-order) accurate schemes.

Learning the dynamics of objects by optimal functional interpolation.

PubMed

Ahn, Jong-Hoon; Kim, In Young

2012-09-01

Many areas of science and engineering rely on functional data and their numerical analysis. The need to analyze time-varying functional data raises the general problem of interpolation, that is, how to learn a smooth time evolution from a finite number of observations. Here, we introduce optimal functional interpolation (OFI), a numerical algorithm that interpolates functional data over time. Unlike the usual interpolation or learning algorithms, the OFI algorithm obeys the continuity equation, which describes the transport of some types of conserved quantities, and its implementation shows smooth, continuous flows of quantities. Without the need to take into account equations of motion such as the Navier-Stokes equation or the diffusion equation, OFI is capable of learning the dynamics of objects such as those represented by mass, image intensity, particle concentration, heat, spectral density, and probability density.

Single image super-resolution using self-optimizing mask via fractional-order gradient interpolation and reconstruction.

PubMed

Yang, Qi; Zhang, Yanzhu; Zhao, Tiebiao; Chen, YangQuan

2017-04-04

Image super-resolution using self-optimizing mask via fractional-order gradient interpolation and reconstruction aims to recover detailed information from low-resolution images and reconstruct them into high-resolution images. Due to the limited amount of data and information retrieved from low-resolution images, it is difficult to restore clear, artifact-free images, while still preserving enough structure of the image such as the texture. This paper presents a new single image super-resolution method which is based on adaptive fractional-order gradient interpolation and reconstruction. The interpolated image gradient via optimal fractional-order gradient is first constructed according to the image similarity and afterwards the minimum energy function is employed to reconstruct the final high-resolution image. Fractional-order gradient based interpolation methods provide an additional degree of freedom which helps optimize the implementation quality due to the fact that an extra free parameter α-order is being used. The proposed method is able to produce a rich texture detail while still being able to maintain structural similarity even under large zoom conditions. Experimental results show that the proposed method performs better than current single image super-resolution techniques. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Ameliorating slice gaps in multislice magnetic resonance images: an interpolation scheme.

PubMed

Kashou, Nasser H; Smith, Mark A; Roberts, Cynthia J

2015-01-01

Standard two-dimension (2D) magnetic resonance imaging (MRI) clinical acquisition protocols utilize orthogonal plane images which contain slice gaps (SG). The purpose of this work is to introduce a novel interpolation method for these orthogonal plane MRI 2D datasets. Three goals can be achieved: (1) increasing the resolution based on a priori knowledge of scanning protocol, (2) ameliorating the loss of data as a result of SG and (3) reconstructing a three-dimension (3D) dataset from 2D images. MRI data was collected using a 3T GE scanner and simulated using Matlab. The procedure for validating the MRI data combination algorithm was performed using a Shepp-Logan and a Gaussian phantom in both 2D and 3D of varying matrix sizes (64-512), as well as on one MRI dataset of a human brain and on an American College of Radiology magnetic resonance accreditation phantom. The squared error and mean squared error were computed in comparing this scheme to common interpolating functions employed in MR consoles and workstations. The mean structure similarity matrix was computed in 2D as a means of qualitative image assessment. Additionally, MRI scans were used for qualitative assessment of the method. This new scheme was consistently more accurate than upsampling each orientation separately and averaging the upsampled data. An efficient new interpolation approach to resolve SG was developed. This scheme effectively fills in the missing data points by using orthogonal plane images. To date, there have been few attempts to combine the information of three MRI plane orientations using brain images. This has specific applications for clinical MRI, functional MRI, diffusion-weighted imaging/diffusion tensor imaging and MR angiography where 2D slice acquisition are used. In these cases, the 2D data can be combined using our method in order to obtain 3D volume.

Optimal interpolation and the Kalman filter. [for analysis of numerical weather predictions

NASA Technical Reports Server (NTRS)

Cohn, S.; Isaacson, E.; Ghil, M.

1981-01-01

The estimation theory of stochastic-dynamic systems is described and used in a numerical study of optimal interpolation. The general form of data assimilation methods is reviewed. The Kalman-Bucy, KB filter, and optimal interpolation (OI) filters are examined for effectiveness in performance as gain matrices using a one-dimensional form of the shallow-water equations. Control runs in the numerical analyses were performed for a ten-day forecast in concert with the OI method. The effects of optimality, initialization, and assimilation were studied. It was found that correct initialization is necessary in order to localize errors, especially near boundary points. Also, the use of small forecast error growth rates over data-sparse areas was determined to offset inaccurate modeling of correlation functions near boundaries.

Numerically stable formulas for a particle-based explicit exponential integrator

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth

2015-05-01

Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this scheme involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function.

Wavelet-based adaptation methodology combined with finite difference WENO to solve ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Do, Seongju; Li, Haojun; Kang, Myungjoo

2017-06-01

In this paper, we present an accurate and efficient wavelet-based adaptive weighted essentially non-oscillatory (WENO) scheme for hydrodynamics and ideal magnetohydrodynamics (MHD) equations arising from the hyperbolic conservation systems. The proposed method works with the finite difference weighted essentially non-oscillatory (FD-WENO) method in space and the third order total variation diminishing (TVD) Runge-Kutta (RK) method in time. The philosophy of this work is to use the lifted interpolating wavelets as not only detector for singularities but also interpolator. Especially, flexible interpolations can be performed by an inverse wavelet transformation. When the divergence cleaning method introducing auxiliary scalar field ψ is applied to the base numerical schemes for imposing divergence-free condition to the magnetic field in a MHD equation, the approximations to derivatives of ψ require the neighboring points. Moreover, the fifth order WENO interpolation requires large stencil to reconstruct high order polynomial. In such cases, an efficient interpolation method is necessary. The adaptive spatial differentiation method is considered as well as the adaptation of grid resolutions. In order to avoid the heavy computation of FD-WENO, in the smooth regions fixed stencil approximation without computing the non-linear WENO weights is used, and the characteristic decomposition method is replaced by a component-wise approach. Numerical results demonstrate that with the adaptive method we are able to resolve the solutions that agree well with the solution of the corresponding fine grid.

Polyhedral Interpolation for Optimal Reaction Control System Jet Selection

NASA Technical Reports Server (NTRS)

Gefert, Leon P.; Wright, Theodore

2014-01-01

An efficient algorithm is described for interpolating optimal values for spacecraft Reaction Control System jet firing duty cycles. The algorithm uses the symmetrical geometry of the optimal solution to reduce the number of calculations and data storage requirements to a level that enables implementation on the small real time flight control systems used in spacecraft. The process minimizes acceleration direction errors, maximizes control authority, and minimizes fuel consumption.

Local finite element enrichment strategies for 2D contact computations and a corresponding post-processing scheme

NASA Astrophysics Data System (ADS)

Sauer, Roger A.

2013-08-01

Recently an enriched contact finite element formulation has been developed that substantially increases the accuracy of contact computations while keeping the additional numerical effort at a minimum reported by Sauer (Int J Numer Meth Eng, 87: 593-616, 2011). Two enrich-ment strategies were proposed, one based on local p-refinement using Lagrange interpolation and one based on Hermite interpolation that produces C 1-smoothness on the contact surface. Both classes, which were initially considered for the frictionless Signorini problem, are extended here to friction and contact between deformable bodies. For this, a symmetric contact formulation is used that allows the unbiased treatment of both contact partners. This paper also proposes a post-processing scheme for contact quantities like the contact pressure. The scheme, which provides a more accurate representation than the raw data, is based on an averaging procedure that is inspired by mortar formulations. The properties of the enrichment strategies and the corresponding post-processing scheme are illustrated by several numerical examples considering sliding and peeling contact in the presence of large deformations.

Numerical Methods for Nonlinear Fokker-Planck Collision Operator in TEMPEST

NASA Astrophysics Data System (ADS)

Kerbel, G.; Xiong, Z.

2006-10-01

Early implementations of Fokker-Planck collision operator and moment computations in TEMPEST used low order polynomial interpolation schemes to reuse conservative operators developed for speed/pitch-angle (v, θ) coordinates. When this approach proved to be too inaccurate we developed an alternative higher order interpolation scheme for the Rosenbluth potentials and a high order finite volume method in TEMPEST (,) coordinates. The collision operator is thus generated by using the expansion technique in (v, θ) coordinates for the diffusion coefficients only, and then the fluxes for the conservative differencing are computed directly in the TEMPEST (,) coordinates. Combined with a cut-cell treatment at the turning-point boundary, this new approach is shown to have much better accuracy and conservation properties.

Temperature Data Assimilation with Salinity Corrections: Validation for the NSIPP Ocean Data Assimilation System in the Tropical Pacific Ocean, 1993-1998

NASA Technical Reports Server (NTRS)

Troccoli, Alberto; Rienecker, Michele M.; Keppenne, Christian L.; Johnson, Gregory C.

2003-01-01

The NASA Seasonal-to-Interannual Prediction Project (NSIPP) has developed an Ocean data assimilation system to initialize the quasi-isopycnal ocean model used in our experimental coupled-model forecast system. Initial tests of the system have focused on the assimilation of temperature profiles in an optimal interpolation framework. It is now recognized that correction of temperature only often introduces spurious water masses. The resulting density distribution can be statically unstable and also have a detrimental impact on the velocity distribution. Several simple schemes have been developed to try to correct these deficiencies. Here the salinity field is corrected by using a scheme which assumes that the temperature-salinity relationship of the model background is preserved during the assimilation. The scheme was first introduced for a zlevel model by Troccoli and Haines (1999). A large set of subsurface observations of salinity and temperature is used to cross-validate two data assimilation experiments run for the 6-year period 1993-1998. In these two experiments only subsurface temperature observations are used, but in one case the salinity field is also updated whenever temperature observations are available.

An adaptive interpolation scheme for molecular potential energy surfaces

NASA Astrophysics Data System (ADS)

Kowalewski, Markus; Larsson, Elisabeth; Heryudono, Alfa

2016-08-01

The calculation of potential energy surfaces for quantum dynamics can be a time consuming task—especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm based on polyharmonic splines combined with a partition of unity approach. The adaptive node refinement allows to greatly reduce the number of sample points by employing a local error estimate. The algorithm and its scaling behavior are evaluated for a model function in 2, 3, and 4 dimensions. The developed algorithm allows for a more rapid and reliable interpolation of a potential energy surface within a given accuracy compared to the non-adaptive version.

Novel Integration of Frame Rate Up Conversion and HEVC Coding Based on Rate-Distortion Optimization.

PubMed

Guo Lu; Xiaoyun Zhang; Li Chen; Zhiyong Gao

2018-02-01

Frame rate up conversion (FRUC) can improve the visual quality by interpolating new intermediate frames. However, high frame rate videos by FRUC are confronted with more bitrate consumption or annoying artifacts of interpolated frames. In this paper, a novel integration framework of FRUC and high efficiency video coding (HEVC) is proposed based on rate-distortion optimization, and the interpolated frames can be reconstructed at encoder side with low bitrate cost and high visual quality. First, joint motion estimation (JME) algorithm is proposed to obtain robust motion vectors, which are shared between FRUC and video coding. What's more, JME is embedded into the coding loop and employs the original motion search strategy in HEVC coding. Then, the frame interpolation is formulated as a rate-distortion optimization problem, where both the coding bitrate consumption and visual quality are taken into account. Due to the absence of original frames, the distortion model for interpolated frames is established according to the motion vector reliability and coding quantization error. Experimental results demonstrate that the proposed framework can achieve 21% ~ 42% reduction in BDBR, when compared with the traditional methods of FRUC cascaded with coding.

Optimization and comparison of three spatial interpolation methods for electromagnetic levels in the AM band within an urban area.

PubMed

Rufo, Montaña; Antolín, Alicia; Paniagua, Jesús M; Jiménez, Antonio

2018-04-01

A comparative study was made of three methods of interpolation - inverse distance weighting (IDW), spline and ordinary kriging - after optimization of their characteristic parameters. These interpolation methods were used to represent the electric field levels for three emission frequencies (774kHz, 900kHz, and 1107kHz) and for the electrical stimulation quotient, Q E , characteristic of complex electromagnetic environments. Measurements were made with a spectrum analyser in a village in the vicinity of medium-wave radio broadcasting antennas. The accuracy of the models was quantified by comparing their predictions with levels measured at the control points not used to generate the models. The results showed that optimizing the characteristic parameters of each interpolation method allows any of them to be used. However, the best results in terms of the regression coefficient between each model's predictions and the actual control point field measurements were for the IDW method. Copyright © 2018 Elsevier Inc. All rights reserved.

Investigations of interpolation errors of angle encoders for high precision angle metrology

NASA Astrophysics Data System (ADS)

Yandayan, Tanfer; Geckeler, Ralf D.; Just, Andreas; Krause, Michael; Asli Akgoz, S.; Aksulu, Murat; Grubert, Bernd; Watanabe, Tsukasa

2018-06-01

Interpolation errors at small angular scales are caused by the subdivision of the angular interval between adjacent grating lines into smaller intervals when radial gratings are used in angle encoders. They are often a major error source in precision angle metrology and better approaches for determining them at low levels of uncertainty are needed. Extensive investigations of interpolation errors of different angle encoders with various interpolators and interpolation schemes were carried out by adapting the shearing method to the calibration of autocollimators with angle encoders. The results of the laboratories with advanced angle metrology capabilities are presented which were acquired by the use of four different high precision angle encoders/interpolators/rotary tables. State of the art uncertainties down to 1 milliarcsec (5 nrad) were achieved for the determination of the interpolation errors using the shearing method which provides simultaneous access to the angle deviations of the autocollimator and of the angle encoder. Compared to the calibration and measurement capabilities (CMC) of the participants for autocollimators, the use of the shearing technique represents a substantial improvement in the uncertainty by a factor of up to 5 in addition to the precise determination of interpolation errors or their residuals (when compensated). A discussion of the results is carried out in conjunction with the equipment used.

Quantum realization of the nearest neighbor value interpolation method for INEQR

NASA Astrophysics Data System (ADS)

Zhou, RiGui; Hu, WenWen; Luo, GaoFeng; Liu, XingAo; Fan, Ping

2018-07-01

This paper presents the nearest neighbor value (NNV) interpolation algorithm for the improved novel enhanced quantum representation of digital images (INEQR). It is necessary to use interpolation in image scaling because there is an increase or a decrease in the number of pixels. The difference between the proposed scheme and nearest neighbor interpolation is that the concept applied, to estimate the missing pixel value, is guided by the nearest value rather than the distance. Firstly, a sequence of quantum operations is predefined, such as cyclic shift transformations and the basic arithmetic operations. Then, the feasibility of the nearest neighbor value interpolation method for quantum image of INEQR is proven using the previously designed quantum operations. Furthermore, quantum image scaling algorithm in the form of circuits of the NNV interpolation for INEQR is constructed for the first time. The merit of the proposed INEQR circuit lies in their low complexity, which is achieved by utilizing the unique properties of quantum superposition and entanglement. Finally, simulation-based experimental results involving different classical images and ratios (i.e., conventional or non-quantum) are simulated based on the classical computer's MATLAB 2014b software, which demonstrates that the proposed interpolation method has higher performances in terms of high resolution compared to the nearest neighbor and bilinear interpolation.

Suboptimal schemes for atmospheric data assimilation based on the Kalman filter

NASA Technical Reports Server (NTRS)

Todling, Ricardo; Cohn, Stephen E.

1994-01-01

This work is directed toward approximating the evolution of forecast error covariances for data assimilation. The performance of different algorithms based on simplification of the standard Kalman filter (KF) is studied. These are suboptimal schemes (SOSs) when compared to the KF, which is optimal for linear problems with known statistics. The SOSs considered here are several versions of optimal interpolation (OI), a scheme for height error variance advection, and a simplified KF in which the full height error covariance is advected. To employ a methodology for exact comparison among these schemes, a linear environment is maintained, in which a beta-plane shallow-water model linearized about a constant zonal flow is chosen for the test-bed dynamics. The results show that constructing dynamically balanced forecast error covariances rather than using conventional geostrophically balanced ones is essential for successful performance of any SOS. A posteriori initialization of SOSs to compensate for model - data imbalance sometimes results in poor performance. Instead, properly constructed dynamically balanced forecast error covariances eliminate the need for initialization. When the SOSs studied here make use of dynamically balanced forecast error covariances, the difference among their performances progresses naturally from conventional OI to the KF. In fact, the results suggest that even modest enhancements of OI, such as including an approximate dynamical equation for height error variances while leaving height error correlation structure homogeneous, go a long way toward achieving the performance of the KF, provided that dynamically balanced cross-covariances are constructed and that model errors are accounted for properly. The results indicate that such enhancements are necessary if unconventional data are to have a positive impact.

Reducing Interpolation Artifacts for Mutual Information Based Image Registration

PubMed Central

Soleimani, H.; Khosravifard, M.A.

2011-01-01

Medical image registration methods which use mutual information as similarity measure have been improved in recent decades. Mutual Information is a basic concept of Information theory which indicates the dependency of two random variables (or two images). In order to evaluate the mutual information of two images their joint probability distribution is required. Several interpolation methods, such as Partial Volume (PV) and bilinear, are used to estimate joint probability distribution. Both of these two methods yield some artifacts on mutual information function. Partial Volume-Hanning window (PVH) and Generalized Partial Volume (GPV) methods are introduced to remove such artifacts. In this paper we show that the acceptable performance of these methods is not due to their kernel function. It's because of the number of pixels which incorporate in interpolation. Since using more pixels requires more complex and time consuming interpolation process, we propose a new interpolation method which uses only four pixels (the same as PV and bilinear interpolations) and removes most of the artifacts. Experimental results of the registration of Computed Tomography (CT) images show superiority of the proposed scheme. PMID:22606673

A novel interpolation approach for the generation of 3D-geometric digital bone models from image stacks

PubMed Central

Mittag, U.; Kriechbaumer, A.; Rittweger, J.

2017-01-01

The authors propose a new 3D interpolation algorithm for the generation of digital geometric 3D-models of bones from existing image stacks obtained by peripheral Quantitative Computed Tomography (pQCT) or Magnetic Resonance Imaging (MRI). The technique is based on the interpolation of radial gray value profiles of the pQCT cross sections. The method has been validated by using an ex-vivo human tibia and by comparing interpolated pQCT images with images from scans taken at the same position. A diversity index of <0.4 (1 meaning maximal diversity) even for the structurally complex region of the epiphysis, along with the good agreement of mineral-density-weighted cross-sectional moment of inertia (CSMI), demonstrate the high quality of our interpolation approach. Thus the authors demonstrate that this interpolation scheme can substantially improve the generation of 3D models from sparse scan sets, not only with respect to the outer shape but also with respect to the internal gray-value derived material property distribution. PMID:28574415

Hybrid Quantum Mechanics/Molecular Mechanics Solvation Scheme for Computing Free Energies of Reactions at Metal-Water Interfaces.

PubMed

Faheem, Muhammad; Heyden, Andreas

2014-08-12

We report the development of a quantum mechanics/molecular mechanics free energy perturbation (QM/MM-FEP) method for modeling chemical reactions at metal-water interfaces. This novel solvation scheme combines planewave density function theory (DFT), periodic electrostatic embedded cluster method (PEECM) calculations using Gaussian-type orbitals, and classical molecular dynamics (MD) simulations to obtain a free energy description of a complex metal-water system. We derive a potential of mean force (PMF) of the reaction system within the QM/MM framework. A fixed-size, finite ensemble of MM conformations is used to permit precise evaluation of the PMF of QM coordinates and its gradient defined within this ensemble. Local conformations of adsorbed reaction moieties are optimized using sequential MD-sampling and QM-optimization steps. An approximate reaction coordinate is constructed using a number of interpolated states and the free energy difference between adjacent states is calculated using the QM/MM-FEP method. By avoiding on-the-fly QM calculations and by circumventing the challenges associated with statistical averaging during MD sampling, a computational speedup of multiple orders of magnitude is realized. The method is systematically validated against the results of ab initio QM calculations and demonstrated for C-C cleavage in double-dehydrogenated ethylene glycol on a Pt (111) model surface.

Regionalizing nonparametric models of precipitation amounts on different temporal scales

NASA Astrophysics Data System (ADS)

Mosthaf, Tobias; Bárdossy, András

2017-05-01

Parametric distribution functions are commonly used to model precipitation amounts corresponding to different durations. The precipitation amounts themselves are crucial for stochastic rainfall generators and weather generators. Nonparametric kernel density estimates (KDEs) offer a more flexible way to model precipitation amounts. As already stated in their name, these models do not exhibit parameters that can be easily regionalized to run rainfall generators at ungauged locations as well as at gauged locations. To overcome this deficiency, we present a new interpolation scheme for nonparametric models and evaluate it for different temporal resolutions ranging from hourly to monthly. During the evaluation, the nonparametric methods are compared to commonly used parametric models like the two-parameter gamma and the mixed-exponential distribution. As water volume is considered to be an essential parameter for applications like flood modeling, a Lorenz-curve-based criterion is also introduced. To add value to the estimation of data at sub-daily resolutions, we incorporated the plentiful daily measurements in the interpolation scheme, and this idea was evaluated. The study region is the federal state of Baden-Württemberg in the southwest of Germany with more than 500 rain gauges. The validation results show that the newly proposed nonparametric interpolation scheme provides reasonable results and that the incorporation of daily values in the regionalization of sub-daily models is very beneficial.

A characteristics-based method for solving the transport equation and its application to the process of mantle differentiation and continental root growth

NASA Astrophysics Data System (ADS)

de Smet, Jeroen H.; van den Berg, Arie P.; Vlaar, Nico J.; Yuen, David A.

2000-03-01

Purely advective transport of composition is of major importance in the Geosciences, and efficient and accurate solution methods are needed. A characteristics-based method is used to solve the transport equation. We employ a new hybrid interpolation scheme, which allows for the tuning of stability and accuracy through a threshold parameter ɛth. Stability is established by bilinear interpolations, and bicubic splines are used to maintain accuracy. With this scheme, numerical instabilities can be suppressed by allowing numerical diffusion to work in time and locally in space. The scheme can be applied efficiently for preliminary modelling purposes. This can be followed by detailed high-resolution experiments. First, the principal effects of this hybrid interpolation method are illustrated and some tests are presented for numerical solutions of the transport equation. Second, we illustrate that this approach works successfully for a previously developed continental evolution model for the convecting upper mantle. In this model the transport equation contains a source term, which describes the melt production in pressure-released partial melting. In this model, a characteristic phenomenon of small-scale melting diapirs is observed (De Smet et al.1998; De Smet et al. 1999). High-resolution experiments with grid cells down to 700m horizontally and 515m vertically result in highly detailed observations of the diapiric melting phenomenon.

Meshless Method with Operator Splitting Technique for Transient Nonlinear Bioheat Transfer in Two-Dimensional Skin Tissues

PubMed Central

Zhang, Ze-Wei; Wang, Hui; Qin, Qing-Hua

2015-01-01

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the analysis, the OSM is used first to separate the Laplacian operator and the nonlinear source term, and then the second-order time-stepping schemes are employed for approximating two splitting operators to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. Subsequently, the RBF interpolation and the MFS involving the fundamental solution of the Laplace equation are respectively employed to obtain approximated particular and homogeneous solutions of the nonhomogeneous Helmholtz-type governing equation. Finally, the full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations for determining unknowns at each time step. The proposed method is verified by comparison of other methods. Furthermore, the sensitivity of the coefficients in the cases of a linear and an exponential relationship of TDBPR is investigated to reveal their bioheat effect on the skin tissue. PMID:25603180

Meshless method with operator splitting technique for transient nonlinear bioheat transfer in two-dimensional skin tissues.

PubMed

Zhang, Ze-Wei; Wang, Hui; Qin, Qing-Hua

2015-01-16

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the analysis, the OSM is used first to separate the Laplacian operator and the nonlinear source term, and then the second-order time-stepping schemes are employed for approximating two splitting operators to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. Subsequently, the RBF interpolation and the MFS involving the fundamental solution of the Laplace equation are respectively employed to obtain approximated particular and homogeneous solutions of the nonhomogeneous Helmholtz-type governing equation. Finally, the full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations for determining unknowns at each time step. The proposed method is verified by comparison of other methods. Furthermore, the sensitivity of the coefficients in the cases of a linear and an exponential relationship of TDBPR is investigated to reveal their bioheat effect on the skin tissue.

Surface reconstruction and deformation monitoring of stratospheric airship based on laser scanning technology

NASA Astrophysics Data System (ADS)

Guo, Kai; Xie, Yongjie; Ye, Hu; Zhang, Song; Li, Yunfei

2018-04-01

Due to the uncertainty of stratospheric airship's shape and the security problem caused by the uncertainty, surface reconstruction and surface deformation monitoring of airship was conducted based on laser scanning technology and a √3-subdivision scheme based on Shepard interpolation was developed. Then, comparison was conducted between our subdivision scheme and the original √3-subdivision scheme. The result shows our subdivision scheme could reduce the shrinkage of surface and the number of narrow triangles. In addition, our subdivision scheme could keep the sharp features. So, surface reconstruction and surface deformation monitoring of airship could be conducted precisely by our subdivision scheme.

Renormalization of QCD in the interpolating momentum subtraction scheme at three loops

NASA Astrophysics Data System (ADS)

Gracey, J. A.; Simms, R. M.

2018-04-01

We introduce a more general set of kinematic renormalization schemes than the original momentum subtraction schemes of Celmaster and Gonsalves. These new schemes will depend on a parameter ω , which tags the external momentum of one of the legs of the three-point vertex functions in QCD. In each of the three new schemes, we renormalize QCD in the Landau and maximal Abelian gauges and establish the three-loop renormalization group functions in each gauge. For an application, we evaluate two critical exponents at the Banks-Zaks fixed point and demonstrate that their values appear to be numerically scheme independent in a subrange of the conformal window.

Conical intersection seams in polyenes derived from their chemical composition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nenov, Artur; Vivie-Riedle, Regina de

2012-08-21

The knowledge of conical intersection seams is important to predict and explain the outcome of ultrafast reactions in photochemistry and photobiology. They define the energetic low-lying reachable regions that allow for the ultrafast non-radiative transitions. In complex molecules it is not straightforward to locate them. We present a systematic approach to predict conical intersection seams in multifunctionalized polyenes and their sensitivity to substituent effects. Included are seams that facilitate the photoreaction of interest as well as seams that open competing loss channels. The method is based on the extended two-electron two-orbital method [A. Nenov and R. de Vivie-Riedle, J. Chem.more » Phys. 135, 034304 (2011)]. It allows to extract the low-lying regions for non-radiative transitions, which are then divided into small linear segments. Rules of thumb are introduced to find the support points for these segments, which are then used in a linear interpolation scheme for a first estimation of the intersection seams. Quantum chemical optimization of the linear interpolated structures yields the final energetic position. We demonstrate our method for the example of the electrocyclic isomerization of trifluoromethyl-pyrrolylfulgide.« less

CONORBIT: constrained optimization by radial basis function interpolation in trust regions

DOE PAGES

Regis, Rommel G.; Wild, Stefan M.

2016-09-26

Here, this paper presents CONORBIT (CONstrained Optimization by Radial Basis function Interpolation in Trust regions), a derivative-free algorithm for constrained black-box optimization where the objective and constraint functions are computationally expensive. CONORBIT employs a trust-region framework that uses interpolating radial basis function (RBF) models for the objective and constraint functions, and is an extension of the ORBIT algorithm. It uses a small margin for the RBF constraint models to facilitate the generation of feasible iterates, and extensive numerical tests confirm that such a margin is helpful in improving performance. CONORBIT is compared with other algorithms on 27 test problems, amore » chemical process optimization problem, and an automotive application. Numerical results show that CONORBIT performs better than COBYLA, a sequential penalty derivative-free method, an augmented Lagrangian method, a direct search method, and another RBF-based algorithm on the test problems and on the automotive application.« less

A 3D Optimal Interpolation Assimilation Scheme of HF Radar Current Data into a Numerical Ocean Model

NASA Astrophysics Data System (ADS)

Ragnoli, Emanuele; Zhuk, Sergiy; Donncha, Fearghal O.; Suits, Frank; Hartnett, Michael

2013-04-01

In this work a technique for the 3D assimilation of ocean surface current measurements into a numerical ocean model based on data from High Frequency Radar (HFR) systems is presented. The technique is the combination of supplementary forcing on the surface and of and Ekman layer projection of the correction in the depth. Optimal interpolation through BLUE (Best Linear Unbiased Estimator) of the model predicted velocity and HFR observations is computed in order to derive a supplementary forcing applied at the surface boundary. In the depth the assimilation is propagated using an additional Ekman pumping (vertical velocity) based on the correction achieved by BLUE. In this work a HFR data assimilation system for hydrodynamic modelling of Galway Bay in Ireland is developed; it demonstrates the viability of adopting data assimilation techniques to improve the performance of numerical models in regions characterized by significant wind-driven flows. A network of CODAR Seasonde high frequency radars (HFR) deployed within Galway Bay, on the West Coast of Ireland, provides flow measurements adopted for this study. This system provides real-time synoptic measurements of both ocean surface currents and ocean surface waves in regions of the bay where radials from two or more radars intersect. Radar systems have a number of unique advantages in ocean modelling data assimilation schemes, namely, the ability to provide two-dimensional mapping of surface currents at resolutions that capture the complex structure related to coastal topography and the intrinsic instability scales of coastal circulation at a relatively low-cost. The radar system used in this study operates at a frequency of 25MHz which provides a sampling range of 25km at a spatial resolution of 300m.A detailed dataset of HFR observed velocities is collected at 60 minute intervals for a period chosen for comparison due to frequent occurrences of highly-energetic, storm-force events. In conjunction with this, a comprehensive weather station, tide gauge and river monitoring program is conducted. The data are then used to maintain density fields within the model and to force the wind direction and magnitude on flows. The Data Assimilation scheme is then assessed and validated via HFR surface flow measurements.

Method of Characteristics Calculations and Computer Code for Materials with Arbitrary Equations of State and Using Orthogonal Polynomial Least Square Surface Fits

NASA Technical Reports Server (NTRS)

Chang, T. S.

1974-01-01

A numerical scheme using the method of characteristics to calculate the flow properties and pressures behind decaying shock waves for materials under hypervelocity impact is developed. Time-consuming double interpolation subroutines are replaced by a technique based on orthogonal polynomial least square surface fits. Typical calculated results are given and compared with the double interpolation results. The complete computer program is included.

A case study of aerosol data assimilation with the Community Multi-scale Air Quality Model over the contiguous United States using 3D-Var and optimal interpolation methods

NASA Astrophysics Data System (ADS)

Tang, Youhua; Pagowski, Mariusz; Chai, Tianfeng; Pan, Li; Lee, Pius; Baker, Barry; Kumar, Rajesh; Delle Monache, Luca; Tong, Daniel; Kim, Hyun-Cheol

2017-12-01

This study applies the Gridpoint Statistical Interpolation (GSI) 3D-Var assimilation tool originally developed by the National Centers for Environmental Prediction (NCEP), to improve surface PM2.5 predictions over the contiguous United States (CONUS) by assimilating aerosol optical depth (AOD) and surface PM2.5 in version 5.1 of the Community Multi-scale Air Quality (CMAQ) modeling system. An optimal interpolation (OI) method implemented earlier (Tang et al., 2015) for the CMAQ modeling system is also tested for the same period (July 2011) over the same CONUS. Both GSI and OI methods assimilate surface PM2.5 observations at 00:00, 06:00, 12:00 and 18:00 UTC, and MODIS AOD at 18:00 UTC. The assimilations of observations using both GSI and OI generally help reduce the prediction biases and improve correlation between model predictions and observations. In the GSI experiments, assimilation of surface PM2.5 (particle matter with diameter < 2.5 µm) leads to stronger increments in surface PM2.5 compared to its MODIS AOD assimilation at the 550 nm wavelength. In contrast, we find a stronger OI impact of the MODIS AOD on surface aerosols at 18:00 UTC compared to the surface PM2.5 OI method. GSI produces smoother result and yields overall better correlation coefficient and root mean squared error (RMSE). It should be noted that the 3D-Var and OI methods used here have several big differences besides the data assimilation schemes. For instance, the OI uses relatively big model uncertainties, which helps yield smaller mean biases, but sometimes causes the RMSE to increase. We also examine and discuss the sensitivity of the assimilation experiments' results to the AOD forward operators.

An adaptive moving finite volume scheme for modeling flood inundation over dry and complex topography

NASA Astrophysics Data System (ADS)

Zhou, Feng; Chen, Guoxian; Huang, Yuefei; Yang, Jerry Zhijian; Feng, Hui

2013-04-01

A new geometrical conservative interpolation on unstructured meshes is developed for preserving still water equilibrium and positivity of water depth at each iteration of mesh movement, leading to an adaptive moving finite volume (AMFV) scheme for modeling flood inundation over dry and complex topography. Unlike traditional schemes involving position-fixed meshes, the iteration process of the AFMV scheme moves a fewer number of the meshes adaptively in response to flow variables calculated in prior solutions and then simulates their posterior values on the new meshes. At each time step of the simulation, the AMFV scheme consists of three parts: an adaptive mesh movement to shift the vertices position, a geometrical conservative interpolation to remap the flow variables by summing the total mass over old meshes to avoid the generation of spurious waves, and a partial differential equations(PDEs) discretization to update the flow variables for a new time step. Five different test cases are presented to verify the computational advantages of the proposed scheme over nonadaptive methods. The results reveal three attractive features: (i) the AMFV scheme could preserve still water equilibrium and positivity of water depth within both mesh movement and PDE discretization steps; (ii) it improved the shock-capturing capability for handling topographic source terms and wet-dry interfaces by moving triangular meshes to approximate the spatial distribution of time-variant flood processes; (iii) it was able to solve the shallow water equations with a relatively higher accuracy and spatial-resolution with a lower computational cost.

A New Ensemble Canonical Correlation Prediction Scheme for Seasonal Precipitation

NASA Technical Reports Server (NTRS)

Kim, Kyu-Myong; Lau, William K. M.; Li, Guilong; Shen, Samuel S. P.; Lau, William K. M. (Technical Monitor)

2001-01-01

Department of Mathematical Sciences, University of Alberta, Edmonton, Canada This paper describes the fundamental theory of the ensemble canonical correlation (ECC) algorithm for the seasonal climate forecasting. The algorithm is a statistical regression sch eme based on maximal correlation between the predictor and predictand. The prediction error is estimated by a spectral method using the basis of empirical orthogonal functions. The ECC algorithm treats the predictors and predictands as continuous fields and is an improvement from the traditional canonical correlation prediction. The improvements include the use of area-factor, estimation of prediction error, and the optimal ensemble of multiple forecasts. The ECC is applied to the seasonal forecasting over various parts of the world. The example presented here is for the North America precipitation. The predictor is the sea surface temperature (SST) from different ocean basins. The Climate Prediction Center's reconstructed SST (1951-1999) is used as the predictor's historical data. The optimally interpolated global monthly precipitation is used as the predictand?s historical data. Our forecast experiments show that the ECC algorithm renders very high skill and the optimal ensemble is very important to the high value.

Research progress and hotspot analysis of spatial interpolation

NASA Astrophysics Data System (ADS)

Jia, Li-juan; Zheng, Xin-qi; Miao, Jin-li

2018-02-01

In this paper, the literatures related to spatial interpolation between 1982 and 2017, which are included in the Web of Science core database, are used as data sources, and the visualization analysis is carried out according to the co-country network, co-category network, co-citation network, keywords co-occurrence network. It is found that spatial interpolation has experienced three stages: slow development, steady development and rapid development; The cross effect between 11 clustering groups, the main convergence of spatial interpolation theory research, the practical application and case study of spatial interpolation and research on the accuracy and efficiency of spatial interpolation. Finding the optimal spatial interpolation is the frontier and hot spot of the research. Spatial interpolation research has formed a theoretical basis and research system framework, interdisciplinary strong, is widely used in various fields.

Quasi interpolation with Voronoi splines.

PubMed

Mirzargar, Mahsa; Entezari, Alireza

2011-12-01

We present a quasi interpolation framework that attains the optimal approximation-order of Voronoi splines for reconstruction of volumetric data sampled on general lattices. The quasi interpolation framework of Voronoi splines provides an unbiased reconstruction method across various lattices. Therefore this framework allows us to analyze and contrast the sampling-theoretic performance of general lattices, using signal reconstruction, in an unbiased manner. Our quasi interpolation methodology is implemented as an efficient FIR filter that can be applied online or as a preprocessing step. We present visual and numerical experiments that demonstrate the improved accuracy of reconstruction across lattices, using the quasi interpolation framework. © 2011 IEEE

An adaptive interpolation scheme for molecular potential energy surfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kowalewski, Markus, E-mail: mkowalew@uci.edu; Larsson, Elisabeth; Heryudono, Alfa

The calculation of potential energy surfaces for quantum dynamics can be a time consuming task—especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm based on polyharmonic splines combined with a partition of unity approach. The adaptive node refinement allows to greatly reduce the number of sample points by employing a local error estimate. The algorithm and its scaling behavior are evaluated for a model function in 2, 3, and 4 dimensions. The developed algorithm allows for a more rapid and reliable interpolation of a potential energy surface within amore » given accuracy compared to the non-adaptive version.« less

Information geometry and its application to theoretical statistics and diffusion tensor magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Wisniewski, Nicholas Andrew

This dissertation is divided into two parts. First we present an exact solution to a generalization of the Behrens-Fisher problem by embedding the problem in the Riemannian manifold of Normal distributions. From this we construct a geometric hypothesis testing scheme. Secondly we investigate the most commonly used geometric methods employed in tensor field interpolation for DT-MRI analysis and cardiac computer modeling. We computationally investigate a class of physiologically motivated orthogonal tensor invariants, both at the full tensor field scale and at the scale of a single interpolation by doing a decimation/interpolation experiment. We show that Riemannian-based methods give the best results in preserving desirable physiological features.

A new multigrid formulation for high order finite difference methods on summation-by-parts form

NASA Astrophysics Data System (ADS)

Ruggiu, Andrea A.; Weinerfelt, Per; Nordström, Jan

2018-04-01

Multigrid schemes for high order finite difference methods on summation-by-parts form are studied by comparing the effect of different interpolation operators. By using the standard linear prolongation and restriction operators, the Galerkin condition leads to inaccurate coarse grid discretizations. In this paper, an alternative class of interpolation operators that bypass this issue and preserve the summation-by-parts property on each grid level is considered. Clear improvements of the convergence rate for relevant model problems are achieved.

Py-SPHViewer: Cosmological simulations using Smoothed Particle Hydrodynamics

NASA Astrophysics Data System (ADS)

Benítez-Llambay, Alejandro

2017-12-01

Py-SPHViewer visualizes and explores N-body + Hydrodynamics simulations. The code interpolates the underlying density field (or any other property) traced by a set of particles, using the Smoothed Particle Hydrodynamics (SPH) interpolation scheme, thus producing not only beautiful but also useful scientific images. Py-SPHViewer enables the user to explore simulated volumes using different projections. Py-SPHViewer also provides a natural way to visualize (in a self-consistent fashion) gas dynamical simulations, which use the same technique to compute the interactions between particles.

River bathymetry estimation based on the floodplains topography.

NASA Astrophysics Data System (ADS)

Bureš, Luděk; Máca, Petr; Roub, Radek; Pech, Pavel; Hejduk, Tomáš; Novák, Pavel

2017-04-01

Topographic model including River bathymetry (bed topography) is required for hydrodynamic simulation, water quality modelling, flood inundation mapping, sediment transport, ecological and geomorphologic assessments. The most common way to create the river bathymetry is to use of the spatial interpolation of discrete points or cross sections data. The quality of the generated bathymetry is dependent on the quality of the measurements, on the used technology and on the size of input dataset. Extensive measurements are often time consuming and expensive. Other option for creating of the river bathymetry is to use the methods of mathematical modelling. In the presented contribution we created the river bathymetry model. Model is based on the analytical curves. The curves are bent into shape of the cross sections. For the best description of the river bathymetry we need to know the values of the model parameters. For finding these parameters we use of the global optimization methods. The global optimization schemes is based on heuristics inspired by the natural processes. We use new type of DE (differential evolution) for finding the solutions of inverse problems, related to the parameters of mathematical model of river bed surfaces. The presented analysis discuss the dependence of model parameters on the selected characteristics. Selected characteristics are: (1) Topographic characteristics (slope and curvature in the left and right floodplains) determined on the base of DTM 5G (digital terrain model). (2) Optimization scheme. (3) Type of used analytical curves. The novel approach is applied on the three parts of Vltava river in Czech Republic. Each part of the river is described on the base of the point field. The point fields was measured with ADCP probe River surveyor M9. This work was supported by the Technology Agency of the Czech Republic, programme Alpha (project TA04020042 - New technologies bathymetry of rivers and reservoirs to determine their storage capacity and monitor the amount and dynamics of sediments) and Internal Grant Agency of Faculty of Environmental Sciences (CULS) (IGA/20164233). Keywords: bathymetry, global optimization, bed topography References: Merwade, Venkatesh. "Effect of spatial trends on interpolation of river bathymetry." Journal of Hydrology, 371.1, 169-181, 2009. Legleiter, Carl J., and Phaedon C. Kyriakidis. Spatial prediction of river channel topography by kriging. Earth Surface Processes and Landforms, 33.6 , 841-867, 2008. P. Maca and P. Pech and and J. Pavlasek. Comparing the Selected Transfer Functions and Local Optimization Methods for Neural Network Flood Runoff Forecast. Mathematical Problems in Engineering, vol. 2014, Article ID 782351, 10 pages, 2014. M. Jakubcova and P. Maca and and P. Pech. A Comparison of Selected Modifications of the Particle Swarm Optimization Algorithm. Journal of Applied Mathematics, vol. 2014, Article ID 293087, 10 pages, 2014.

A kriging metamodel-assisted robust optimization method based on a reverse model

NASA Astrophysics Data System (ADS)

Zhou, Hui; Zhou, Qi; Liu, Congwei; Zhou, Taotao

2018-02-01

The goal of robust optimization methods is to obtain a solution that is both optimum and relatively insensitive to uncertainty factors. Most existing robust optimization approaches use outer-inner nested optimization structures where a large amount of computational effort is required because the robustness of each candidate solution delivered from the outer level should be evaluated in the inner level. In this article, a kriging metamodel-assisted robust optimization method based on a reverse model (K-RMRO) is first proposed, in which the nested optimization structure is reduced into a single-loop optimization structure to ease the computational burden. Ignoring the interpolation uncertainties from kriging, K-RMRO may yield non-robust optima. Hence, an improved kriging-assisted robust optimization method based on a reverse model (IK-RMRO) is presented to take the interpolation uncertainty of kriging metamodel into consideration. In IK-RMRO, an objective switching criterion is introduced to determine whether the inner level robust optimization or the kriging metamodel replacement should be used to evaluate the robustness of design alternatives. The proposed criterion is developed according to whether or not the robust status of the individual can be changed because of the interpolation uncertainties from the kriging metamodel. Numerical and engineering cases are used to demonstrate the applicability and efficiency of the proposed approach.

Single-Image Super-Resolution Based on Rational Fractal Interpolation.

PubMed

Zhang, Yunfeng; Fan, Qinglan; Bao, Fangxun; Liu, Yifang; Zhang, Caiming

2018-08-01

This paper presents a novel single-image super-resolution (SR) procedure, which upscales a given low-resolution (LR) input image to a high-resolution image while preserving the textural and structural information. First, we construct a new type of bivariate rational fractal interpolation model and investigate its analytical properties. This model has different forms of expression with various values of the scaling factors and shape parameters; thus, it can be employed to better describe image features than current interpolation schemes. Furthermore, this model combines the advantages of rational interpolation and fractal interpolation, and its effectiveness is validated through theoretical analysis. Second, we develop a single-image SR algorithm based on the proposed model. The LR input image is divided into texture and non-texture regions, and then, the image is interpolated according to the characteristics of the local structure. Specifically, in the texture region, the scaling factor calculation is the critical step. We present a method to accurately calculate scaling factors based on local fractal analysis. Extensive experiments and comparisons with the other state-of-the-art methods show that our algorithm achieves competitive performance, with finer details and sharper edges.

Triangle based TVD schemes for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Durlofsky, Louis J.; Osher, Stanley; Engquist, Bjorn

1990-01-01

A triangle based total variation diminishing (TVD) scheme for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed. The novelty of the scheme lies in the nature of the preprocessing of the cell averaged data, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedures. Two such limiting procedures are suggested. The resulting method is considerably more simple than other triangle based non-oscillatory approximations which, like this scheme, approximate the flux up to second order accuracy. Numerical results for linear advection and Burgers' equation are presented.

Adaptive image coding based on cubic-spline interpolation

NASA Astrophysics Data System (ADS)

Jiang, Jian-Xing; Hong, Shao-Hua; Lin, Tsung-Ching; Wang, Lin; Truong, Trieu-Kien

2014-09-01

It has been investigated that at low bit rates, downsampling prior to coding and upsampling after decoding can achieve better compression performance than standard coding algorithms, e.g., JPEG and H. 264/AVC. However, at high bit rates, the sampling-based schemes generate more distortion. Additionally, the maximum bit rate for the sampling-based scheme to outperform the standard algorithm is image-dependent. In this paper, a practical adaptive image coding algorithm based on the cubic-spline interpolation (CSI) is proposed. This proposed algorithm adaptively selects the image coding method from CSI-based modified JPEG and standard JPEG under a given target bit rate utilizing the so called ρ-domain analysis. The experimental results indicate that compared with the standard JPEG, the proposed algorithm can show better performance at low bit rates and maintain the same performance at high bit rates.

A practical implementation of wave front construction for 3-D isotropic media

NASA Astrophysics Data System (ADS)

Chambers, K.; Kendall, J.-M.

2008-06-01

Wave front construction (WFC) methods are a useful tool for tracking wave fronts and are a natural extension to standard ray shooting methods. Here we describe and implement a simple WFC method that is used to interpolate wavefield properties throughout a 3-D heterogeneous medium. Our approach differs from previous 3-D WFC procedures primarily in the use of a ray interpolation scheme, based on approximating the wave front as a `locally spherical' surface and a `first arrival mode', which reduces computation times, where only first arrivals are required. Both of these features have previously been included in 2-D WFC algorithms; however, until now they have not been extended to 3-D systems. The wave front interpolation scheme allows for rays to be traced from a nearly arbitrary distribution of take-off angles, and the calculation of derivatives with respect to take-off angles is not required for wave front interpolation. However, in regions of steep velocity gradient, the locally spherical approximation is not valid, and it is necessary to backpropagate rays to a sufficiently homogenous region before interpolation of the new ray. Our WFC technique is illustrated using a realistic velocity model, based on a North Sea oil reservoir. We examine wavefield quantities such as traveltimes, ray angles, source take-off angles and geometrical spreading factors, all of which are interpolated on to a regular grid. We compare geometrical spreading factors calculated using two methods: using the ray Jacobian and by taking the ratio of a triangular area of wave front to the corresponding solid angle at the source. The results show that care must be taken when using ray Jacobians to calculate geometrical spreading factors, as the poles of the source coordinate system produce unreliable values, which can be spread over a large area, as only a few initial rays are traced in WFC. We also show that the use of the first arrival mode can reduce computation time by ~65 per cent, with the accuracy of the interpolated traveltimes, ray angles and source take-off angles largely unchanged. However, the first arrival mode does lead to inaccuracies in interpolated angles near caustic surfaces, as well as small variations in geometrical spreading factors for ray tubes that have passed through caustic surfaces.

Optimized theory for simple and molecular fluids.

PubMed

Marucho, M; Montgomery Pettitt, B

2007-03-28

An optimized closure approximation for both simple and molecular fluids is presented. A smooth interpolation between Perkus-Yevick and hypernetted chain closures is optimized by minimizing the free energy self-consistently with respect to the interpolation parameter(s). The molecular version is derived from a refinement of the method for simple fluids. In doing so, a method is proposed which appropriately couples an optimized closure with the variant of the diagrammatically proper integral equation recently introduced by this laboratory [K. M. Dyer et al., J. Chem. Phys. 123, 204512 (2005)]. The simplicity of the expressions involved in this proposed theory has allowed the authors to obtain an analytic expression for the approximate excess chemical potential. This is shown to be an efficient tool to estimate, from first principles, the numerical value of the interpolation parameters defining the aforementioned closure. As a preliminary test, representative models for simple fluids and homonuclear diatomic Lennard-Jones fluids were analyzed, obtaining site-site correlation functions in excellent agreement with simulation data.

Space-time interpolation of satellite winds in the tropics

NASA Astrophysics Data System (ADS)

Patoux, Jérôme; Levy, Gad

2013-09-01

A space-time interpolator for creating average geophysical fields from satellite measurements is presented and tested. It is designed for optimal spatiotemporal averaging of heterogeneous data. While it is illustrated with satellite surface wind measurements in the tropics, the methodology can be useful for interpolating, analyzing, and merging a wide variety of heterogeneous and satellite data in the atmosphere and ocean over the entire globe. The spatial and temporal ranges of the interpolator are determined by averaging satellite and in situ measurements over increasingly larger space and time windows and matching the corresponding variability at each scale. This matching provides a relationship between temporal and spatial ranges, but does not provide a unique pair of ranges as a solution to all averaging problems. The pair of ranges most appropriate for a given application can be determined by performing a spectral analysis of the interpolated fields and choosing the smallest values that remove any or most of the aliasing due to the uneven sampling by the satellite. The methodology is illustrated with the computation of average divergence fields over the equatorial Pacific Ocean from SeaWinds-on-QuikSCAT surface wind measurements, for which 72 h and 510 km are suggested as optimal interpolation windows. It is found that the wind variability is reduced over the cold tongue and enhanced over the Pacific warm pool, consistent with the notion that the unstably stratified boundary layer has generally more variable winds and more gustiness than the stably stratified boundary layer. It is suggested that the spectral analysis optimization can be used for any process where time-space correspondence can be assumed.

A numerical study of different projection-based model reduction techniques applied to computational homogenisation

NASA Astrophysics Data System (ADS)

Soldner, Dominic; Brands, Benjamin; Zabihyan, Reza; Steinmann, Paul; Mergheim, Julia

2017-10-01

Computing the macroscopic material response of a continuum body commonly involves the formulation of a phenomenological constitutive model. However, the response is mainly influenced by the heterogeneous microstructure. Computational homogenisation can be used to determine the constitutive behaviour on the macro-scale by solving a boundary value problem at the micro-scale for every so-called macroscopic material point within a nested solution scheme. Hence, this procedure requires the repeated solution of similar microscopic boundary value problems. To reduce the computational cost, model order reduction techniques can be applied. An important aspect thereby is the robustness of the obtained reduced model. Within this study reduced-order modelling (ROM) for the geometrically nonlinear case using hyperelastic materials is applied for the boundary value problem on the micro-scale. This involves the Proper Orthogonal Decomposition (POD) for the primary unknown and hyper-reduction methods for the arising nonlinearity. Therein three methods for hyper-reduction, differing in how the nonlinearity is approximated and the subsequent projection, are compared in terms of accuracy and robustness. Introducing interpolation or Gappy-POD based approximations may not preserve the symmetry of the system tangent, rendering the widely used Galerkin projection sub-optimal. Hence, a different projection related to a Gauss-Newton scheme (Gauss-Newton with Approximated Tensors- GNAT) is favoured to obtain an optimal projection and a robust reduced model.

Multivariate optimum interpolation of surface pressure and winds over oceans

NASA Technical Reports Server (NTRS)

Bloom, S. C.

1984-01-01

The observations of surface pressure are quite sparse over oceanic areas. An effort to improve the analysis of surface pressure over oceans through the development of a multivariate surface analysis scheme which makes use of surface pressure and wind data is discussed. Although the present research used ship winds, future versions of this analysis scheme could utilize winds from additional sources, such as satellite scatterometer data.

Development of Three-Dimensional DRAGON Grid Technology

NASA Technical Reports Server (NTRS)

Zheng, Yao; Kiou, Meng-Sing; Civinskas, Kestutis C.

1999-01-01

For a typical three dimensional flow in a practical engineering device, the time spent in grid generation can take 70 percent of the total analysis effort, resulting in a serious bottleneck in the design/analysis cycle. The present research attempts to develop a procedure that can considerably reduce the grid generation effort. The DRAGON grid, as a hybrid grid, is created by means of a Direct Replacement of Arbitrary Grid Overlapping by Nonstructured grid. The DRAGON grid scheme is an adaptation to the Chimera thinking. The Chimera grid is a composite structured grid, composing a set of overlapped structured grids, which are independently generated and body-fitted. The grid is of high quality and amenable for efficient solution schemes. However, the interpolation used in the overlapped region between grids introduces error, especially when a sharp-gradient region is encountered. The DRAGON grid scheme is capable of completely eliminating the interpolation and preserving the conservation property. It maximizes the advantages of the Chimera scheme and adapts the strengths of the unstructured and while at the same time keeping its weaknesses minimal. In the present paper, we describe the progress towards extending the DRAGON grid technology into three dimensions. Essential and programming aspects of the extension, and new challenges for the three-dimensional cases, are addressed.

Cryo-EM image alignment based on nonuniform fast Fourier transform.

PubMed

Yang, Zhengfan; Penczek, Pawel A

2008-08-01

In single particle analysis, two-dimensional (2-D) alignment is a fundamental step intended to put into register various particle projections of biological macromolecules collected at the electron microscope. The efficiency and quality of three-dimensional (3-D) structure reconstruction largely depends on the computational speed and alignment accuracy of this crucial step. In order to improve the performance of alignment, we introduce a new method that takes advantage of the highly accurate interpolation scheme based on the gridding method, a version of the nonuniform fast Fourier transform, and utilizes a multi-dimensional optimization algorithm for the refinement of the orientation parameters. Using simulated data, we demonstrate that by using less than half of the sample points and taking twice the runtime, our new 2-D alignment method achieves dramatically better alignment accuracy than that based on quadratic interpolation. We also apply our method to image to volume registration, the key step in the single particle EM structure refinement protocol. We find that in this case the accuracy of the method not only surpasses the accuracy of the commonly used real-space implementation, but results are achieved in much shorter time, making gridding-based alignment a perfect candidate for efficient structure determination in single particle analysis.

Cryo-EM Image Alignment Based on Nonuniform Fast Fourier Transform

PubMed Central

Yang, Zhengfan; Penczek, Pawel A.

2008-01-01

In single particle analysis, two-dimensional (2-D) alignment is a fundamental step intended to put into register various particle projections of biological macromolecules collected at the electron microscope. The efficiency and quality of three-dimensional (3-D) structure reconstruction largely depends on the computational speed and alignment accuracy of this crucial step. In order to improve the performance of alignment, we introduce a new method that takes advantage of the highly accurate interpolation scheme based on the gridding method, a version of the nonuniform Fast Fourier Transform, and utilizes a multi-dimensional optimization algorithm for the refinement of the orientation parameters. Using simulated data, we demonstrate that by using less than half of the sample points and taking twice the runtime, our new 2-D alignment method achieves dramatically better alignment accuracy than that based on quadratic interpolation. We also apply our method to image to volume registration, the key step in the single particle EM structure refinement protocol. We find that in this case the accuracy of the method not only surpasses the accuracy of the commonly used real-space implementation, but results are achieved in much shorter time, making gridding-based alignment a perfect candidate for efficient structure determination in single particle analysis. PMID:18499351

Development of the general interpolants method for the CYBER 200 series of supercomputers

NASA Technical Reports Server (NTRS)

Stalnaker, J. F.; Robinson, M. A.; Spradley, L. W.; Kurzius, S. C.; Thoenes, J.

1988-01-01

The General Interpolants Method (GIM) is a 3-D, time-dependent, hybrid procedure for generating numerical analogs of the conservation laws. This study is directed toward the development and application of the GIM computer code for fluid dynamic research applications as implemented for the Cyber 200 series of supercomputers. An elliptic and quasi-parabolic version of the GIM code are discussed. Turbulence models, algebraic and differential equations, were added to the basic viscous code. An equilibrium reacting chemistry model and an implicit finite difference scheme are also included.

An Energy Decaying Scheme for Nonlinear Dynamics of Shells

NASA Technical Reports Server (NTRS)

Bottasso, Carlo L.; Bauchau, Olivier A.; Choi, Jou-Young; Bushnell, Dennis M. (Technical Monitor)

2000-01-01

A novel integration scheme for nonlinear dynamics of geometrically exact shells is developed based on the inextensible director assumption. The new algorithm is designed so as to imply the strict decay of the system total mechanical energy at each time step, and consequently unconditional stability is achieved in the nonlinear regime. Furthermore, the scheme features tunable high frequency numerical damping and it is therefore stiffly accurate. The method is tested for a finite element spatial formulation of shells based on mixed interpolations of strain tensorial components and on a two-parameter representation of director rotations. The robustness of the, scheme is illustrated with the help of numerical examples.

A MAP-based image interpolation method via Viterbi decoding of Markov chains of interpolation functions.

PubMed

Vedadi, Farhang; Shirani, Shahram

2014-01-01

A new method of image resolution up-conversion (image interpolation) based on maximum a posteriori sequence estimation is proposed. Instead of making a hard decision about the value of each missing pixel, we estimate the missing pixels in groups. At each missing pixel of the high resolution (HR) image, we consider an ensemble of candidate interpolation methods (interpolation functions). The interpolation functions are interpreted as states of a Markov model. In other words, the proposed method undergoes state transitions from one missing pixel position to the next. Accordingly, the interpolation problem is translated to the problem of estimating the optimal sequence of interpolation functions corresponding to the sequence of missing HR pixel positions. We derive a parameter-free probabilistic model for this to-be-estimated sequence of interpolation functions. Then, we solve the estimation problem using a trellis representation and the Viterbi algorithm. Using directional interpolation functions and sequence estimation techniques, we classify the new algorithm as an adaptive directional interpolation using soft-decision estimation techniques. Experimental results show that the proposed algorithm yields images with higher or comparable peak signal-to-noise ratios compared with some benchmark interpolation methods in the literature while being efficient in terms of implementation and complexity considerations.

a Study of Multiplexing Schemes for Voice and Data.

NASA Astrophysics Data System (ADS)

Sriram, Kotikalapudi

Voice traffic variations are characterized by on/off transitions of voice calls, and talkspurt/silence transitions of speakers in conversations. A speaker is known to be in silence for more than half the time during a telephone conversation. In this dissertation, we study some schemes which exploit speaker silences for an efficient utilization of the transmission capacity in integrated voice/data multiplexing and in digital speech interpolation. We study two voice/data multiplexing schemes. In each scheme, any time slots momentarily unutilized by the voice traffic are made available to data. In the first scheme, the multiplexer does not use speech activity detectors (SAD), and hence the voice traffic variations are due to call on/off only. In the second scheme, the multiplexer detects speaker silences using SAD and transmits voice only during talkspurts. The multiplexer with SAD performs digital speech interpolation (DSI) as well as dynamic channel allocation to voice and data. The performance of the two schemes is evaluated using discrete-time modeling and analysis. The data delay performance for the case of English speech is compared with that for the case of Japanese speech. A closed form expression for the mean data message delay is derived for the single-channel single-talker case. In a DSI system, occasional speech losses occur whenever the number of speakers in simultaneous talkspurt exceeds the number of TDM voice channels. In a buffered DSI system, speech loss is further reduced at the cost of delay. We propose a novel fixed-delay buffered DSI scheme. In this scheme, speech fill-in/hangover is not required because there are no variable delays. Hence, all silences that naturally occur in speech are fully utilized. Consequently, a substantial improvement in the DSI performance is made possible. The scheme is modeled and analyzed in discrete -time. Its performance is evaluated in terms of the probability of speech clipping, packet rejection ratio, DSI advantage, and the delay.

Effects of empty bins on image upscaling in capsule endoscopy

NASA Astrophysics Data System (ADS)

Rukundo, Olivier

2017-07-01

This paper presents a preliminary study of the effect of empty bins on image upscaling in capsule endoscopy. The presented study was conducted based on results of existing contrast enhancement and interpolation methods. A low contrast enhancement method based on pixels consecutiveness and modified bilinear weighting scheme has been developed to distinguish between necessary empty bins and unnecessary empty bins in the effort to minimize the number of empty bins in the input image, before further processing. Linear interpolation methods have been used for upscaling input images with stretched histograms. Upscaling error differences and similarity indices between pairs of interpolation methods have been quantified using the mean squared error and feature similarity index techniques. Simulation results demonstrated more promising effects using the developed method than other contrast enhancement methods mentioned.

The Role of Geometrically Necessary Dislocations in Cantilever Beam Bending Experiments of Single Crystals

PubMed Central

Husser, Edgar; Bargmann, Swantje

2017-01-01

The mechanical behavior of single crystalline, micro-sized copper is investigated in the context of cantilever beam bending experiments. Particular focus is on the role of geometrically necessary dislocations (GNDs) during bending-dominated load conditions and their impact on the characteristic bending size effect. Three different sample sizes are considered in this work with main variation in thickness. A gradient extended crystal plasticity model is presented and applied in a three-dimensional finite-element (FE) framework considering slip system-based edge and screw components of the dislocation density vector. The underlying mathematical model contains non-standard evolution equations for GNDs, crystal-specific interaction relations, and higher-order boundary conditions. Moreover, two element formulations are examined and compared with respect to size-independent as well as size-dependent bending behavior. The first formulation is based on a linear interpolation of the displacement and the GND density field together with a full integration scheme whereas the second is based on a mixed interpolation scheme. While the GND density fields are treated equivalently, the displacement field is interpolated quadratically in combination with a reduced integration scheme. Computational results indicate that GND storage in small cantilever beams strongly influences the evolution of statistically stored dislocations (SSDs) and, hence, the distribution of the total dislocation density. As a particular example, the mechanical bending behavior in the case of a physically motivated limitation of GND storage is studied. The resulting impact on the mechanical bending response as well as on the predicted size effect is analyzed. Obtained results are discussed and related to experimental findings from the literature. PMID:28772657

Area under precision-recall curves for weighted and unweighted data.

PubMed

Keilwagen, Jens; Grosse, Ivo; Grau, Jan

2014-01-01

Precision-recall curves are highly informative about the performance of binary classifiers, and the area under these curves is a popular scalar performance measure for comparing different classifiers. However, for many applications class labels are not provided with absolute certainty, but with some degree of confidence, often reflected by weights or soft labels assigned to data points. Computing the area under the precision-recall curve requires interpolating between adjacent supporting points, but previous interpolation schemes are not directly applicable to weighted data. Hence, even in cases where weights were available, they had to be neglected for assessing classifiers using precision-recall curves. Here, we propose an interpolation for precision-recall curves that can also be used for weighted data, and we derive conditions for classification scores yielding the maximum and minimum area under the precision-recall curve. We investigate accordances and differences of the proposed interpolation and previous ones, and we demonstrate that taking into account existing weights of test data is important for the comparison of classifiers.

Three dimensional unstructured multigrid for the Euler equations

NASA Technical Reports Server (NTRS)

Mavriplis, D. J.

1991-01-01

The three dimensional Euler equations are solved on unstructured tetrahedral meshes using a multigrid strategy. The driving algorithm consists of an explicit vertex-based finite element scheme, which employs an edge-based data structure to assemble the residuals. The multigrid approach employs a sequence of independently generated coarse and fine meshes to accelerate the convergence to steady-state of the fine grid solution. Variables, residuals and corrections are passed back and forth between the various grids of the sequence using linear interpolation. The addresses and weights for interpolation are determined in a preprocessing stage using linear interpolation. The addresses and weights for interpolation are determined in a preprocessing stage using an efficient graph traversal algorithm. The preprocessing operation is shown to require a negligible fraction of the CPU time required by the overall solution procedure, while gains in overall solution efficiencies greater than an order of magnitude are demonstrated on meshes containing up to 350,000 vertices. Solutions using globally regenerated fine meshes as well as adaptively refined meshes are given.

Area under Precision-Recall Curves for Weighted and Unweighted Data

PubMed Central

Grosse, Ivo

2014-01-01

Precision-recall curves are highly informative about the performance of binary classifiers, and the area under these curves is a popular scalar performance measure for comparing different classifiers. However, for many applications class labels are not provided with absolute certainty, but with some degree of confidence, often reflected by weights or soft labels assigned to data points. Computing the area under the precision-recall curve requires interpolating between adjacent supporting points, but previous interpolation schemes are not directly applicable to weighted data. Hence, even in cases where weights were available, they had to be neglected for assessing classifiers using precision-recall curves. Here, we propose an interpolation for precision-recall curves that can also be used for weighted data, and we derive conditions for classification scores yielding the maximum and minimum area under the precision-recall curve. We investigate accordances and differences of the proposed interpolation and previous ones, and we demonstrate that taking into account existing weights of test data is important for the comparison of classifiers. PMID:24651729

[Research on fast implementation method of image Gaussian RBF interpolation based on CUDA].

PubMed

Chen, Hao; Yu, Haizhong

2014-04-01

Image interpolation is often required during medical image processing and analysis. Although interpolation method based on Gaussian radial basis function (GRBF) has high precision, the long calculation time still limits its application in field of image interpolation. To overcome this problem, a method of two-dimensional and three-dimensional medical image GRBF interpolation based on computing unified device architecture (CUDA) is proposed in this paper. According to single instruction multiple threads (SIMT) executive model of CUDA, various optimizing measures such as coalesced access and shared memory are adopted in this study. To eliminate the edge distortion of image interpolation, natural suture algorithm is utilized in overlapping regions while adopting data space strategy of separating 2D images into blocks or dividing 3D images into sub-volumes. Keeping a high interpolation precision, the 2D and 3D medical image GRBF interpolation achieved great acceleration in each basic computing step. The experiments showed that the operative efficiency of image GRBF interpolation based on CUDA platform was obviously improved compared with CPU calculation. The present method is of a considerable reference value in the application field of image interpolation.

Minimization of Poisson’s ratio in anti-tetra-chiral two-phase structure

NASA Astrophysics Data System (ADS)

Idczak, E.; Strek, T.

2017-10-01

One of the most important goal of modern material science is designing structures which exhibit appropriate properties. These properties can be obtained by optimization methods which often use numerical calculations e.g. finite element method (FEM). This paper shows the results of topological optimization which is used to obtain the greatest possible negative Poisson’s ratio of the two-phase composite. The shape is anti-tetra-chiral two-dimensional unit cell of the whole lattice structure which has negative Poisson’s ratio when it is built of one solid material. Two phase used in optimization are two solid materials with positive Poisson’s ratio and Young’s modulus. Distribution of reinforcement hard material inside soft matrix material in anti-tetra-chiral domain influenced mechanical properties of structure. The calculations shows that the resultant structure has negative Poisson’s ratio even eight times smaller than homogenous anti-tetra chiral structure made of classic one material. In the analysis FEM is connected with algorithm Method of Moving Asymptote (MMA). The results of materials’ properties parameters are described and calculated by means of shape interpolation scheme - Solid Isotropic Material with Penalization (SIMP) method.

Large time-step stability of explicit one-dimensional advection schemes

NASA Technical Reports Server (NTRS)

Leonard, B. P.

1993-01-01

There is a wide-spread belief that most explicit one-dimensional advection schemes need to satisfy the so-called 'CFL condition' - that the Courant number, c = udelta(t)/delta(x), must be less than or equal to one, for stability in the von Neumann sense. This puts severe limitations on the time-step in high-speed, fine-grid calculations and is an impetus for the development of implicit schemes, which often require less restrictive time-step conditions for stability, but are more expensive per time-step. However, it turns out that, at least in one dimension, if explicit schemes are formulated in a consistent flux-based conservative finite-volume form, von Neumann stability analysis does not place any restriction on the allowable Courant number. Any explicit scheme that is stable for c is less than 1, with a complex amplitude ratio, G(c), can be easily extended to arbitrarily large c. The complex amplitude ratio is then given by exp(- (Iota)(Nu)(Theta)) G(delta(c)), where N is the integer part of c, and delta(c) = c - N (less than 1); this is clearly stable. The CFL condition is, in fact, not a stability condition at all, but, rather, a 'range restriction' on the 'pieces' in a piece-wise polynomial interpolation. When a global view is taken of the interpolation, the need for a CFL condition evaporates. A number of well-known explicit advection schemes are considered and thus extended to large delta(t). The analysis also includes a simple interpretation of (large delta(t)) total-variation-diminishing (TVD) constraints.

Assimilation of the AVISO Altimetry Data into the Ocean Dynamics Model with a High Spatial Resolution Using Ensemble Optimal Interpolation (EnOI)

NASA Astrophysics Data System (ADS)

Kaurkin, M. N.; Ibrayev, R. A.; Belyaev, K. P.

2018-01-01

A parallel realization of the Ensemble Optimal Interpolation (EnOI) data assimilation (DA) method in conjunction with the eddy-resolving global circulation model is implemented. The results of DA experiments in the North Atlantic with the assimilation of the Archiving, Validation and Interpretation of Satellite Oceanographic (AVISO) data from the Jason-1 satellite are analyzed. The results of simulation are compared with the independent temperature and salinity data from the ARGO drifters.

Transmissivity interpolation using Fluid Flow Log data at different depth level in Liwa Aquifer, UAE.

NASA Astrophysics Data System (ADS)

Gülşen, Esra; Kurtulus, Bedri; Necati Yaylim, Tolga; Avsar, Ozgur

2017-04-01

In groundwater studies, quantification and detection of fluid flows in borehole is an important part of assessment aquifer characteristic at different depths. Monitoring wells disturbs the natural flow field and this disturbance creates different flow paths to an aquifer. Vertical flow fluid analyses are one of the important techniques to deal with the detection and quantification of these vertical flows in borehole/monitoring wells. Liwa region is located about 146 km to the south west of Abu Dhabi city and about 36 km southwest of Madinat Zayed. SWSR (Strategic Water Storage & Recovery Project) comprises three Schemes (A, B and C) and each scheme contains an infiltration basin in the center, 105 recovery wells, 10 clusters and each cluster comprises 3 monitoring wells with different depths; shallow ( 50 m), intermediate ( 75 m) and deep ( 100 m). The scope of this study is to calculate the transmissivity values at different depth and evaluate the Fluid Flow Log (FFL) data for Scheme A (105 recovery wells) in order to understand the aquifer characteristic at different depths. The transmissivity values at different depth levels are calculated using Razack and Huntley (1991) equation for vertical flow rates of 30 m3 /h, 60 m3 /h, 90 m3 /h, 120 m3 /h and then Empirical Bayesian Kriging is used for interpolation in Scheme A using ArcGIS 10.2 software. FFL are drawn by GeODin software. Derivative analysis of fluid flow data are done by Microsoft Office: Excel software. All statistical analyses are calculated by IBMSPSS software. The interpolation results show that the transmissivity values are higher at the top of the aquifer. In other word, the aquifer is found more productive at the upper part of the Liwa aquifer. We are very grateful for financial support and providing us the data to ZETAS Dubai Inc.

Decomposed multidimensional control grid interpolation for common consumer electronic image processing applications

NASA Astrophysics Data System (ADS)

Zwart, Christine M.; Venkatesan, Ragav; Frakes, David H.

2012-10-01

Interpolation is an essential and broadly employed function of signal processing. Accordingly, considerable development has focused on advancing interpolation algorithms toward optimal accuracy. Such development has motivated a clear shift in the state-of-the art from classical interpolation to more intelligent and resourceful approaches, registration-based interpolation for example. As a natural result, many of the most accurate current algorithms are highly complex, specific, and computationally demanding. However, the diverse hardware destinations for interpolation algorithms present unique constraints that often preclude use of the most accurate available options. For example, while computationally demanding interpolators may be suitable for highly equipped image processing platforms (e.g., computer workstations and clusters), only more efficient interpolators may be practical for less well equipped platforms (e.g., smartphones and tablet computers). The latter examples of consumer electronics present a design tradeoff in this regard: high accuracy interpolation benefits the consumer experience but computing capabilities are limited. It follows that interpolators with favorable combinations of accuracy and efficiency are of great practical value to the consumer electronics industry. We address multidimensional interpolation-based image processing problems that are common to consumer electronic devices through a decomposition approach. The multidimensional problems are first broken down into multiple, independent, one-dimensional (1-D) interpolation steps that are then executed with a newly modified registration-based one-dimensional control grid interpolator. The proposed approach, decomposed multidimensional control grid interpolation (DMCGI), combines the accuracy of registration-based interpolation with the simplicity, flexibility, and computational efficiency of a 1-D interpolation framework. Results demonstrate that DMCGI provides improved interpolation accuracy (and other benefits) in image resizing, color sample demosaicing, and video deinterlacing applications, at a computational cost that is manageable or reduced in comparison to popular alternatives.

Positivity-preserving High Order Finite Difference WENO Schemes for Compressible Euler Equations

DTIC Science & Technology

2011-07-15

the WENO reconstruction. We assume that there is a polynomial vector qi(x) = (ρi(x), mi(x), Ei(x)) T with degree k which are (k + 1)-th order accurate...i+ 1 2 = qi(xi+ 1 2 ). The existence of such polynomials can be established by interpolation for WENO schemes. For example, for the fifth or- der...WENO scheme, there is a unique vector of polynomials of degree four qi(x) satisfying qi(xi− 1 2 ) = w+ i− 1 2 , qi(xi+ 1 2 ) = w− i+ 1 2 and 1 ∆x ∫ Ij qi

Implementation of a flow-dependent background error correlation length scale formulation in the NEMOVAR OSTIA system

NASA Astrophysics Data System (ADS)

Fiedler, Emma; Mao, Chongyuan; Good, Simon; Waters, Jennifer; Martin, Matthew

2017-04-01

OSTIA is the Met Office's Operational Sea Surface Temperature (SST) and Ice Analysis system, which produces L4 (globally complete, gridded) analyses on a daily basis. Work is currently being undertaken to replace the original OI (Optimal Interpolation) data assimilation scheme with NEMOVAR, a 3D-Var data assimilation method developed for use with the NEMO ocean model. A dual background error correlation length scale formulation is used for SST in OSTIA, as implemented in NEMOVAR. Short and long length scales are combined according to the ratio of the decomposition of the background error variances into short and long spatial correlations. The pre-defined background error variances vary spatially and seasonally, but not on shorter time-scales. If the derived length scales applied to the daily analysis are too long, SST features may be smoothed out. Therefore a flow-dependent component to determining the effective length scale has also been developed. The total horizontal gradient of the background SST field is used to identify regions where the length scale should be shortened. These methods together have led to an improvement in the resolution of SST features compared to the previous OI analysis system, without the introduction of spurious noise. This presentation will show validation results for feature resolution in OSTIA using the OI scheme, the dual length scale NEMOVAR scheme, and the flow-dependent implementation.

Parallel Anisotropic Tetrahedral Adaptation

NASA Technical Reports Server (NTRS)

Park, Michael A.; Darmofal, David L.

2008-01-01

An adaptive method that robustly produces high aspect ratio tetrahedra to a general 3D metric specification without introducing hybrid semi-structured regions is presented. The elemental operators and higher-level logic is described with their respective domain-decomposed parallelizations. An anisotropic tetrahedral grid adaptation scheme is demonstrated for 1000-1 stretching for a simple cube geometry. This form of adaptation is applicable to more complex domain boundaries via a cut-cell approach as demonstrated by a parallel 3D supersonic simulation of a complex fighter aircraft. To avoid the assumptions and approximations required to form a metric to specify adaptation, an approach is introduced that directly evaluates interpolation error. The grid is adapted to reduce and equidistribute this interpolation error calculation without the use of an intervening anisotropic metric. Direct interpolation error adaptation is illustrated for 1D and 3D domains.

An operator calculus for surface and volume modeling

NASA Technical Reports Server (NTRS)

Gordon, W. J.

1984-01-01

The mathematical techniques which form the foundation for most of the surface and volume modeling techniques used in practice are briefly described. An outline of what may be termed an operator calculus for the approximation and interpolation of functions of more than one independent variable is presented. By considering the linear operators associated with bivariate and multivariate interpolation/approximation schemes, it is shown how they can be compounded by operator multiplication and Boolean addition to obtain a distributive lattice of approximation operators. It is then demonstrated via specific examples how this operator calculus leads to practical techniques for sculptured surface and volume modeling.

Methods of Reverberation Mapping. I. Time-lag Determination by Measures of Randomness

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chelouche, Doron; Pozo-Nuñez, Francisco; Zucker, Shay, E-mail: doron@sci.haifa.ac.il, E-mail: francisco.pozon@gmail.com, E-mail: shayz@post.tau.ac.il

A class of methods for measuring time delays between astronomical time series is introduced in the context of quasar reverberation mapping, which is based on measures of randomness or complexity of the data. Several distinct statistical estimators are considered that do not rely on polynomial interpolations of the light curves nor on their stochastic modeling, and do not require binning in correlation space. Methods based on von Neumann’s mean-square successive-difference estimator are found to be superior to those using other estimators. An optimized von Neumann scheme is formulated, which better handles sparsely sampled data and outperforms current implementations of discretemore » correlation function methods. This scheme is applied to existing reverberation data of varying quality, and consistency with previously reported time delays is found. In particular, the size–luminosity relation of the broad-line region in quasars is recovered with a scatter comparable to that obtained by other works, yet with fewer assumptions made concerning the process underlying the variability. The proposed method for time-lag determination is particularly relevant for irregularly sampled time series, and in cases where the process underlying the variability cannot be adequately modeled.« less

Joint Optimization of Fluence Field Modulation and Regularization in Task-Driven Computed Tomography.

PubMed

Gang, G J; Siewerdsen, J H; Stayman, J W

2017-02-11

This work presents a task-driven joint optimization of fluence field modulation (FFM) and regularization in quadratic penalized-likelihood (PL) reconstruction. Conventional FFM strategies proposed for filtered-backprojection (FBP) are evaluated in the context of PL reconstruction for comparison. We present a task-driven framework that leverages prior knowledge of the patient anatomy and imaging task to identify FFM and regularization. We adopted a maxi-min objective that ensures a minimum level of detectability index ( d' ) across sample locations in the image volume. The FFM designs were parameterized by 2D Gaussian basis functions to reduce dimensionality of the optimization and basis function coefficients were estimated using the covariance matrix adaptation evolutionary strategy (CMA-ES) algorithm. The FFM was jointly optimized with both space-invariant and spatially-varying regularization strength ( β ) - the former via an exhaustive search through discrete values and the latter using an alternating optimization where β was exhaustively optimized locally and interpolated to form a spatially-varying map. The optimal FFM inverts as β increases, demonstrating the importance of a joint optimization. For the task and object investigated, the optimal FFM assigns more fluence through less attenuating views, counter to conventional FFM schemes proposed for FBP. The maxi-min objective homogenizes detectability throughout the image and achieves a higher minimum detectability than conventional FFM strategies. The task-driven FFM designs found in this work are counter to conventional patterns for FBP and yield better performance in terms of the maxi-min objective, suggesting opportunities for improved image quality and/or dose reduction when model-based reconstructions are applied in conjunction with FFM.

Evaluation of Interpolation Effects on Upsampling and Accuracy of Cost Functions-Based Optimized Automatic Image Registration

PubMed Central

Mahmoudzadeh, Amir Pasha; Kashou, Nasser H.

2013-01-01

Interpolation has become a default operation in image processing and medical imaging and is one of the important factors in the success of an intensity-based registration method. Interpolation is needed if the fractional unit of motion is not matched and located on the high resolution (HR) grid. The purpose of this work is to present a systematic evaluation of eight standard interpolation techniques (trilinear, nearest neighbor, cubic Lagrangian, quintic Lagrangian, hepatic Lagrangian, windowed Sinc, B-spline 3rd order, and B-spline 4th order) and to compare the effect of cost functions (least squares (LS), normalized mutual information (NMI), normalized cross correlation (NCC), and correlation ratio (CR)) for optimized automatic image registration (OAIR) on 3D spoiled gradient recalled (SPGR) magnetic resonance images (MRI) of the brain acquired using a 3T GE MR scanner. Subsampling was performed in the axial, sagittal, and coronal directions to emulate three low resolution datasets. Afterwards, the low resolution datasets were upsampled using different interpolation methods, and they were then compared to the high resolution data. The mean squared error, peak signal to noise, joint entropy, and cost functions were computed for quantitative assessment of the method. Magnetic resonance image scans and joint histogram were used for qualitative assessment of the method. PMID:24000283

Evaluation of interpolation effects on upsampling and accuracy of cost functions-based optimized automatic image registration.

PubMed

Mahmoudzadeh, Amir Pasha; Kashou, Nasser H

2013-01-01

Interpolation has become a default operation in image processing and medical imaging and is one of the important factors in the success of an intensity-based registration method. Interpolation is needed if the fractional unit of motion is not matched and located on the high resolution (HR) grid. The purpose of this work is to present a systematic evaluation of eight standard interpolation techniques (trilinear, nearest neighbor, cubic Lagrangian, quintic Lagrangian, hepatic Lagrangian, windowed Sinc, B-spline 3rd order, and B-spline 4th order) and to compare the effect of cost functions (least squares (LS), normalized mutual information (NMI), normalized cross correlation (NCC), and correlation ratio (CR)) for optimized automatic image registration (OAIR) on 3D spoiled gradient recalled (SPGR) magnetic resonance images (MRI) of the brain acquired using a 3T GE MR scanner. Subsampling was performed in the axial, sagittal, and coronal directions to emulate three low resolution datasets. Afterwards, the low resolution datasets were upsampled using different interpolation methods, and they were then compared to the high resolution data. The mean squared error, peak signal to noise, joint entropy, and cost functions were computed for quantitative assessment of the method. Magnetic resonance image scans and joint histogram were used for qualitative assessment of the method.

seNorge2 daily precipitation, an observational gridded dataset over Norway from 1957 to the present day

NASA Astrophysics Data System (ADS)

Lussana, Cristian; Saloranta, Tuomo; Skaugen, Thomas; Magnusson, Jan; Tveito, Ole Einar; Andersen, Jess

2018-02-01

The conventional climate gridded datasets based on observations only are widely used in atmospheric sciences; our focus in this paper is on climate and hydrology. On the Norwegian mainland, seNorge2 provides high-resolution fields of daily total precipitation for applications requiring long-term datasets at regional or national level, where the challenge is to simulate small-scale processes often taking place in complex terrain. The dataset constitutes a valuable meteorological input for snow and hydrological simulations; it is updated daily and presented on a high-resolution grid (1 km of grid spacing). The climate archive goes back to 1957. The spatial interpolation scheme builds upon classical methods, such as optimal interpolation and successive-correction schemes. An original approach based on (spatial) scale-separation concepts has been implemented which uses geographical coordinates and elevation as complementary information in the interpolation. seNorge2 daily precipitation fields represent local precipitation features at spatial scales of a few kilometers, depending on the station network density. In the surroundings of a station or in dense station areas, the predictions are quite accurate even for intense precipitation. For most of the grid points, the performances are comparable to or better than a state-of-the-art pan-European dataset (E-OBS), because of the higher effective resolution of seNorge2. However, in very data-sparse areas, such as in the mountainous region of southern Norway, seNorge2 underestimates precipitation because it does not make use of enough geographical information to compensate for the lack of observations. The evaluation of seNorge2 as the meteorological forcing for the seNorge snow model and the DDD (Distance Distribution Dynamics) rainfall-runoff model shows that both models have been able to make profitable use of seNorge2, partly because of the automatic calibration procedure they incorporate for precipitation. The seNorge2 dataset 1957-2015 is available at https://doi.org/10.5281/zenodo.845733. Daily updates from 2015 onwards are available at http://thredds.met.no/thredds/catalog/metusers/senorge2/seNorge2/provisional_archive/PREC1d/gridded_dataset/catalog.html.

Embedded WENO: A design strategy to improve existing WENO schemes

NASA Astrophysics Data System (ADS)

van Lith, Bart S.; ten Thije Boonkkamp, Jan H. M.; IJzerman, Wilbert L.

2017-02-01

Embedded WENO methods utilise all adjacent smooth substencils to construct a desirable interpolation. Conventional WENO schemes under-use this possibility close to large gradients or discontinuities. We develop a general approach for constructing embedded versions of existing WENO schemes. Embedded methods based on the WENO schemes of Jiang and Shu [1] and on the WENO-Z scheme of Borges et al. [2] are explicitly constructed. Several possible choices are presented that result in either better spectral properties or a higher order of convergence for sufficiently smooth solutions. However, these improvements carry over to discontinuous solutions. The embedded methods are demonstrated to be indeed improvements over their standard counterparts by several numerical examples. All the embedded methods presented have no added computational effort compared to their standard counterparts.

Volume 2: Explicit, multistage upwind schemes for Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Elmiligui, Alaa; Ash, Robert L.

1992-01-01

The objective of this study was to develop a high-resolution-explicit-multi-block numerical algorithm, suitable for efficient computation of the three-dimensional, time-dependent Euler and Navier-Stokes equations. The resulting algorithm has employed a finite volume approach, using monotonic upstream schemes for conservation laws (MUSCL)-type differencing to obtain state variables at cell interface. Variable interpolations were written in the k-scheme formulation. Inviscid fluxes were calculated via Roe's flux-difference splitting, and van Leer's flux-vector splitting techniques, which are considered state of the art. The viscous terms were discretized using a second-order, central-difference operator. Two classes of explicit time integration has been investigated for solving the compressible inviscid/viscous flow problems--two-state predictor-corrector schemes, and multistage time-stepping schemes. The coefficients of the multistage time-stepping schemes have been modified successfully to achieve better performance with upwind differencing. A technique was developed to optimize the coefficients for good high-frequency damping at relatively high CFL numbers. Local time-stepping, implicit residual smoothing, and multigrid procedure were added to the explicit time stepping scheme to accelerate convergence to steady-state. The developed algorithm was implemented successfully in a multi-block code, which provides complete topological and geometric flexibility. The only requirement is C degree continuity of the grid across the block interface. The algorithm has been validated on a diverse set of three-dimensional test cases of increasing complexity. The cases studied were: (1) supersonic corner flow; (2) supersonic plume flow; (3) laminar and turbulent flow over a flat plate; (4) transonic flow over an ONERA M6 wing; and (5) unsteady flow of a compressible jet impinging on a ground plane (with and without cross flow). The emphasis of the test cases was validation of code, and assessment of performance, as well as demonstration of flexibility.

Design and optimization of color lookup tables on a simplex topology.

PubMed

Monga, Vishal; Bala, Raja; Mo, Xuan

2012-04-01

An important computational problem in color imaging is the design of color transforms that map color between devices or from a device-dependent space (e.g., RGB/CMYK) to a device-independent space (e.g., CIELAB) and vice versa. Real-time processing constraints entail that such nonlinear color transforms be implemented using multidimensional lookup tables (LUTs). Furthermore, relatively sparse LUTs (with efficient interpolation) are employed in practice because of storage and memory constraints. This paper presents a principled design methodology rooted in constrained convex optimization to design color LUTs on a simplex topology. The use of n simplexes, i.e., simplexes in n dimensions, as opposed to traditional lattices, recently has been of great interest in color LUT design for simplex topologies that allow both more analytically tractable formulations and greater efficiency in the LUT. In this framework of n-simplex interpolation, our central contribution is to develop an elegant iterative algorithm that jointly optimizes the placement of nodes of the color LUT and the output values at those nodes to minimize interpolation error in an expected sense. This is in contrast to existing work, which exclusively designs either node locations or the output values. We also develop new analytical results for the problem of node location optimization, which reduces to constrained optimization of a large but sparse interpolation matrix in our framework. We evaluate our n -simplex color LUTs against the state-of-the-art lattice (e.g., International Color Consortium profiles) and simplex-based techniques for approximating two representative multidimensional color transforms that characterize a CMYK xerographic printer and an RGB scanner, respectively. The results show that color LUTs designed on simplexes offer very significant benefits over traditional lattice-based alternatives in improving color transform accuracy even with a much smaller number of nodes.

Fourier-interpolation superresolution optical fluctuation imaging (fSOFi) (Conference Presentation)

NASA Astrophysics Data System (ADS)

Enderlein, Joerg; Stein, Simon C.; Huss, Anja; Hähnel, Dirk; Gregor, Ingo

2016-02-01

Stochastic Optical Fluctuation Imaging (SOFI) is a superresolution fluorescence microscopy technique which allows to enhance the spatial resolution of an image by evaluating the temporal fluctuations of blinking fluorescent emitters. SOFI is not based on the identification and localization of single molecules such as in the widely used Photoactivation Localization Microsopy (PALM) or Stochastic Optical Reconstruction Microscopy (STORM), but computes a superresolved image via temporal cumulants from a recorded movie. A technical challenge hereby is that, when directly applying the SOFI algorithm to a movie of raw images, the pixel size of the final SOFI image is the same as that of the original images, which becomes problematic when the final SOFI resolution is much smaller than this value. In the past, sophisticated cross-correlation schemes have been used for tackling this problem. Here, we present an alternative, exact, straightforward, and simple solution using an interpolation scheme based on Fourier transforms. We exemplify the method on simulated and experimental data.

A Comparative Study of Interferometric Regridding Algorithms

NASA Technical Reports Server (NTRS)

Hensley, Scott; Safaeinili, Ali

1999-01-01

THe paper discusses regridding options: (1) The problem of interpolating data that is not sampled on a uniform grid, that is noisy, and contains gaps is a difficult problem. (2) Several interpolation algorithms have been implemented: (a) Nearest neighbor - Fast and easy but shows some artifacts in shaded relief images. (b) Simplical interpolator - uses plane going through three points containing point where interpolation is required. Reasonably fast and accurate. (c) Convolutional - uses a windowed Gaussian approximating the optimal prolate spheroidal weighting function for a specified bandwidth. (d) First or second order surface fitting - Uses the height data centered in a box about a given point and does a weighted least squares surface fit.

Evaluation of the sparse coding super-resolution method for improving image quality of up-sampled images in computed tomography

NASA Astrophysics Data System (ADS)

Ota, Junko; Umehara, Kensuke; Ishimaru, Naoki; Ohno, Shunsuke; Okamoto, Kentaro; Suzuki, Takanori; Shirai, Naoki; Ishida, Takayuki

2017-02-01

As the capability of high-resolution displays grows, high-resolution images are often required in Computed Tomography (CT). However, acquiring high-resolution images takes a higher radiation dose and a longer scanning time. In this study, we applied the Sparse-coding-based Super-Resolution (ScSR) method to generate high-resolution images without increasing the radiation dose. We prepared the over-complete dictionary learned the mapping between low- and highresolution patches and seek a sparse representation of each patch of the low-resolution input. These coefficients were used to generate the high-resolution output. For evaluation, 44 CT cases were used as the test dataset. We up-sampled images up to 2 or 4 times and compared the image quality of the ScSR scheme and bilinear and bicubic interpolations, which are the traditional interpolation schemes. We also compared the image quality of three learning datasets. A total of 45 CT images, 91 non-medical images, and 93 chest radiographs were used for dictionary preparation respectively. The image quality was evaluated by measuring peak signal-to-noise ratio (PSNR) and structure similarity (SSIM). The differences of PSNRs and SSIMs between the ScSR method and interpolation methods were statistically significant. Visual assessment confirmed that the ScSR method generated a high-resolution image with sharpness, whereas conventional interpolation methods generated over-smoothed images. To compare three different training datasets, there were no significance between the CT, the CXR and non-medical datasets. These results suggest that the ScSR provides a robust approach for application of up-sampling CT images and yields substantial high image quality of extended images in CT.

An objective isobaric/isentropic technique for upper air analysis

NASA Technical Reports Server (NTRS)

Mancuso, R. L.; Endlich, R. M.; Ehernberger, L. J.

1981-01-01

An objective meteorological analysis technique is presented whereby both horizontal and vertical upper air analyses are performed. The process used to interpolate grid-point values from the upper-air station data is the same as for grid points on both an isobaric surface and a vertical cross-sectional plane. The nearby data surrounding each grid point are used in the interpolation by means of an anisotropic weighting scheme, which is described. The interpolation for a grid-point potential temperature is performed isobarically; whereas wind, mixing-ratio, and pressure height values are interpolated from data that lie on the isentropic surface that passes through the grid point. Two versions (A and B) of the technique are evaluated by qualitatively comparing computer analyses with subjective handdrawn analyses. The objective products of version A generally have fair correspondence with the subjective analyses and with the station data, and depicted the structure of the upper fronts, tropopauses, and jet streams fairly well. The version B objective products correspond more closely to the subjective analyses, and show the same strong gradients across the upper front with only minor smoothing.

Stereo matching and view interpolation based on image domain triangulation.

PubMed

Fickel, Guilherme Pinto; Jung, Claudio R; Malzbender, Tom; Samadani, Ramin; Culbertson, Bruce

2013-09-01

This paper presents a new approach for stereo matching and view interpolation problems based on triangular tessellations suitable for a linear array of rectified cameras. The domain of the reference image is initially partitioned into triangular regions using edge and scale information, aiming to place vertices along image edges and increase the number of triangles in textured regions. A region-based matching algorithm is then used to find an initial disparity for each triangle, and a refinement stage is applied to change the disparity at the vertices of the triangles, generating a piecewise linear disparity map. A simple post-processing procedure is applied to connect triangles with similar disparities generating a full 3D mesh related to each camera (view), which are used to generate new synthesized views along the linear camera array. With the proposed framework, view interpolation reduces to the trivial task of rendering polygonal meshes, which can be done very fast, particularly when GPUs are employed. Furthermore, the generated views are hole-free, unlike most point-based view interpolation schemes that require some kind of post-processing procedures to fill holes.

A Comparative Study of Three Spatial Interpolation Methodologies for the Analysis of Air Pollution Concentrations in Athens, Greece

NASA Astrophysics Data System (ADS)

Deligiorgi, Despina; Philippopoulos, Kostas; Thanou, Lelouda; Karvounis, Georgios

2010-01-01

Spatial interpolation in air pollution modeling is the procedure for estimating ambient air pollution concentrations at unmonitored locations based on available observations. The selection of the appropriate methodology is based on the nature and the quality of the interpolated data. In this paper, an assessment of three widely used interpolation methodologies is undertaken in order to estimate the errors involved. For this purpose, air quality data from January 2001 to December 2005, from a network of seventeen monitoring stations, operating at the greater area of Athens in Greece, are used. The Nearest Neighbor and the Liner schemes were applied to the mean hourly observations, while the Inverse Distance Weighted (IDW) method to the mean monthly concentrations. The discrepancies of the estimated and measured values are assessed for every station and pollutant, using the correlation coefficient, the scatter diagrams and the statistical residuals. The capability of the methods to estimate air quality data in an area with multiple land-use types and pollution sources, such as Athens, is discussed.

Using Chebyshev polynomial interpolation to improve the computational efficiency of gravity models near an irregularly-shaped asteroid

NASA Astrophysics Data System (ADS)

Hu, Shou-Cun; Ji, Jiang-Hui

2017-12-01

In asteroid rendezvous missions, the dynamical environment near an asteroid’s surface should be made clear prior to launch of the mission. However, most asteroids have irregular shapes, which lower the efficiency of calculating their gravitational field by adopting the traditional polyhedral method. In this work, we propose a method to partition the space near an asteroid adaptively along three spherical coordinates and use Chebyshev polynomial interpolation to represent the gravitational acceleration in each cell. Moreover, we compare four different interpolation schemes to obtain the best precision with identical initial parameters. An error-adaptive octree division is combined to improve the interpolation precision near the surface. As an example, we take the typical irregularly-shaped near-Earth asteroid 4179 Toutatis to demonstrate the advantage of this method; as a result, we show that the efficiency can be increased by hundreds to thousands of times with our method. Our results indicate that this method can be applicable to other irregularly-shaped asteroids and can greatly improve the evaluation efficiency.

EnOI-IAU Initialization Scheme Designed for Decadal Climate Prediction System IAP-DecPreS

NASA Astrophysics Data System (ADS)

Wu, Bo; Zhou, Tianjun; Zheng, Fei

2018-02-01

A decadal climate prediction system named as IAP-DecPreS was constructed in the Institute of Atmospheric Physics (IAP), Chinese Academy of Sciences, based on a fully coupled model FGOALS-s2 and a newly developed initialization scheme, referred to as EnOI-IAU. In this paper, we introduce the design of the EnOI-IAU scheme, assess the accuracies of initialization integrations using the EnOI-IAU and preliminarily evaluate hindcast skill of the IAP-DecPreS. The EnOI-IAU scheme integrates two conventional assimilation approaches, ensemble optimal interpolation (EnOI) and incremental analysis update (IAU). The EnOI and IAU were applied to calculate analysis increments and incorporate them into the model, respectively. Three continuous initialization (INIT) runs were conducted for the period of 1950-2015, in which observational sea surface temperature (SST) from the HadISST1.1 and subsurface ocean temperature profiles from the EN4.1.1 data set were assimilated. Then nine-member 10 year long hindcast runs initiated from the INIT runs were conducted for each year in the period of 1960-2005. The accuracies of the INIT runs are evaluated from the following three aspects: upper 700 m ocean temperature, temporal evolution of SST anomalies, and dominant interdecadal variability modes, Pacific Decadal Oscillation (PDO) and Atlantic Multidecadal Oscillation (AMO). Finally, preliminary evaluation of the ensemble mean of the hindcast runs suggests that the IAP-DecPreS has skill in the prediction of the PDO-related SST anomalies in the midlatitude North Pacific and AMO-related SST anomalies in the tropical North Atlantic.

Performance of Regional Climate Model in Simulating Monsoon Onset Over Indian Subcontinent

NASA Astrophysics Data System (ADS)

Bhatla, R.; Mandal, B.; Verma, Shruti; Ghosh, Soumik; Mall, R. K.

2018-06-01

The performance of various Convective Parameterization Schemes (CPSs) of Regional Climate Model version 4.3 (RegCM-4.3) for simulation of onset phase of Indian summer monsoon (ISM) over Kerala was studied for the period of 2001-2010. The onset date and its associated spatial variation were simulated using RegCM-4.3 four core CPS, namely Kuo, Tiedtke, Emanuel and Grell; and with two mixed convection schemes Mix98 (Emanuel over land and Grell over ocean) and Mix99 (Grell over land and Emanuel over ocean) on the basis of criteria given by the India Meteorological Department (IMD) (Pai and Rajeevan in Indian summer monsoon onset: variability and prediction. National Climate Centre, India Meteorological Department, 2007). It has been found that out of six CPS, two schemes, namely Tiedtke and Mix99 simulated the onset date properly. The onset phase is characterized with several transition phases of atmosphere. Therefore, to study the thermal response or the effect of different sea surface temperature (SST), namely ERA interim (ERSST) and weekly optimal interpolation (OI_WK SST) on Indian summer monsoon, the role of two different types of SST has been used to investigate the simulated onset date. In addition, spatial atmospheric circulation pattern during onset phase were analyzed using reanalyze dataset of ERA Interim (EIN15) and National Oceanic and Atmospheric Administration (NOAA), respectively, for wind and outgoing long-wave radiation (OLR) pattern. Among the six convective schemes of RegCM-4.3 model, Tiedtke is in good agreement with actual onset dates and OI_WK SST forcing is better for simulating onset of ISM over Kerala.

Reducing numerical diffusion for incompressible flow calculations

NASA Technical Reports Server (NTRS)

Claus, R. W.; Neely, G. M.; Syed, S. A.

1984-01-01

A number of approaches for improving the accuracy of incompressible, steady-state flow calculations are examined. Two improved differencing schemes, Quadratic Upstream Interpolation for Convective Kinematics (QUICK) and Skew-Upwind Differencing (SUD), are applied to the convective terms in the Navier-Stokes equations and compared with results obtained using hybrid differencing. In a number of test calculations, it is illustrated that no single scheme exhibits superior performance for all flow situations. However, both SUD and QUICK are shown to be generally more accurate than hybrid differencing.

Automatic Tortuosity-Based Retinopathy of Prematurity Screening System

NASA Astrophysics Data System (ADS)

Sukkaew, Lassada; Uyyanonvara, Bunyarit; Makhanov, Stanislav S.; Barman, Sarah; Pangputhipong, Pannet

Retinopathy of Prematurity (ROP) is an infant disease characterized by increased dilation and tortuosity of the retinal blood vessels. Automatic tortuosity evaluation from retinal digital images is very useful to facilitate an ophthalmologist in the ROP screening and to prevent childhood blindness. This paper proposes a method to automatically classify the image into tortuous and non-tortuous. The process imitates expert ophthalmologists' screening by searching for clearly tortuous vessel segments. First, a skeleton of the retinal blood vessels is extracted from the original infant retinal image using a series of morphological operators. Next, we propose to partition the blood vessels recursively using an adaptive linear interpolation scheme. Finally, the tortuosity is calculated based on the curvature of the resulting vessel segments. The retinal images are then classified into two classes using segments characterized by the highest tortuosity. For an optimal set of training parameters the prediction is as high as 100%.

Planning additional drilling campaign using two-space genetic algorithm: A game theoretical approach

NASA Astrophysics Data System (ADS)

Kumral, Mustafa; Ozer, Umit

2013-03-01

Grade and tonnage are the most important technical uncertainties in mining ventures because of the use of estimations/simulations, which are mostly generated from drill data. Open pit mines are planned and designed on the basis of the blocks representing the entire orebody. Each block has different estimation/simulation variance reflecting uncertainty to some extent. The estimation/simulation realizations are submitted to mine production scheduling process. However, the use of a block model with varying estimation/simulation variances will lead to serious risk in the scheduling. In the medium of multiple simulations, the dispersion variances of blocks can be thought to regard technical uncertainties. However, the dispersion variance cannot handle uncertainty associated with varying estimation/simulation variances of blocks. This paper proposes an approach that generates the configuration of the best additional drilling campaign to generate more homogenous estimation/simulation variances of blocks. In other words, the objective is to find the best drilling configuration in such a way as to minimize grade uncertainty under budget constraint. Uncertainty measure of the optimization process in this paper is interpolation variance, which considers data locations and grades. The problem is expressed as a minmax problem, which focuses on finding the best worst-case performance i.e., minimizing interpolation variance of the block generating maximum interpolation variance. Since the optimization model requires computing the interpolation variances of blocks being simulated/estimated in each iteration, the problem cannot be solved by standard optimization tools. This motivates to use two-space genetic algorithm (GA) approach to solve the problem. The technique has two spaces: feasible drill hole configuration with minimization of interpolation variance and drill hole simulations with maximization of interpolation variance. Two-space interacts to find a minmax solution iteratively. A case study was conducted to demonstrate the performance of approach. The findings showed that the approach could be used to plan a new drilling campaign.

Markov random field model-based edge-directed image interpolation.

PubMed

Li, Min; Nguyen, Truong Q

2008-07-01

This paper presents an edge-directed image interpolation algorithm. In the proposed algorithm, the edge directions are implicitly estimated with a statistical-based approach. In opposite to explicit edge directions, the local edge directions are indicated by length-16 weighting vectors. Implicitly, the weighting vectors are used to formulate geometric regularity (GR) constraint (smoothness along edges and sharpness across edges) and the GR constraint is imposed on the interpolated image through the Markov random field (MRF) model. Furthermore, under the maximum a posteriori-MRF framework, the desired interpolated image corresponds to the minimal energy state of a 2-D random field given the low-resolution image. Simulated annealing methods are used to search for the minimal energy state from the state space. To lower the computational complexity of MRF, a single-pass implementation is designed, which performs nearly as well as the iterative optimization. Simulation results show that the proposed MRF model-based edge-directed interpolation method produces edges with strong geometric regularity. Compared to traditional methods and other edge-directed interpolation methods, the proposed method improves the subjective quality of the interpolated edges while maintaining a high PSNR level.

Directional sinogram interpolation for sparse angular acquisition in cone-beam computed tomography.

PubMed

Zhang, Hua; Sonke, Jan-Jakob

2013-01-01

Cone-beam (CB) computed tomography (CT) is widely used in the field of medical imaging for guidance. Inspired by Betram's directional interpolation (BDI) methods, directional sinogram interpolation (DSI) was implemented to generate more CB projections by optimized (iterative) double-orientation estimation in sinogram space and directional interpolation. A new CBCT was subsequently reconstructed with the Feldkamp algorithm using both the original and interpolated CB projections. The proposed method was evaluated on both phantom and clinical data, and image quality was assessed by correlation ratio (CR) between the interpolated image and a gold standard obtained from full measured projections. Additionally, streak artifact reduction and image blur were assessed. In a CBCT reconstructed by 40 acquired projections over an arc of 360 degree, streak artifacts dropped 20.7% and 6.7% in a thorax phantom, when our method was compared to linear interpolation (LI) and BDI methods. Meanwhile, image blur was assessed by a head-and-neck phantom, where image blur of DSI was 20.1% and 24.3% less than LI and BDI. When our method was compared to LI and DI methods, CR increased by 4.4% and 3.1%. Streak artifacts of sparsely acquired CBCT were decreased by our method and image blur induced by interpolation was constrained to below other interpolation methods.

On the optimal selection of interpolation methods for groundwater contouring: An example of propagation of uncertainty regarding inter-aquifer exchange

NASA Astrophysics Data System (ADS)

Ohmer, Marc; Liesch, Tanja; Goeppert, Nadine; Goldscheider, Nico

2017-11-01

The selection of the best possible method to interpolate a continuous groundwater surface from point data of groundwater levels is a controversial issue. In the present study four deterministic and five geostatistical interpolation methods (global polynomial interpolation, local polynomial interpolation, inverse distance weighting, radial basis function, simple-, ordinary-, universal-, empirical Bayesian and co-Kriging) and six error statistics (ME, MAE, MAPE, RMSE, RMSSE, Pearson R) were examined for a Jurassic karst aquifer and a Quaternary alluvial aquifer. We investigated the possible propagation of uncertainty of the chosen interpolation method on the calculation of the estimated vertical groundwater exchange between the aquifers. Furthermore, we validated the results with eco-hydrogeological data including the comparison between calculated groundwater depths and geographic locations of karst springs, wetlands and surface waters. These results show, that calculated inter-aquifer exchange rates based on different interpolations of groundwater potentials may vary greatly depending on the chosen interpolation method (by factor >10). Therefore, the choice of an interpolation method should be made with care, taking different error measures as well as additional data for plausibility control into account. The most accurate results have been obtained with co-Kriging incorporating secondary data (e.g. topography, river levels).

Deep learning methods for CT image-domain metal artifact reduction

NASA Astrophysics Data System (ADS)

Gjesteby, Lars; Yang, Qingsong; Xi, Yan; Shan, Hongming; Claus, Bernhard; Jin, Yannan; De Man, Bruno; Wang, Ge

2017-09-01

Artifacts resulting from metal objects have been a persistent problem in CT images over the last four decades. A common approach to overcome their effects is to replace corrupt projection data with values synthesized from an interpolation scheme or by reprojection of a prior image. State-of-the-art correction methods, such as the interpolation- and normalization-based algorithm NMAR, often do not produce clinically satisfactory results. Residual image artifacts remain in challenging cases and even new artifacts can be introduced by the interpolation scheme. Metal artifacts continue to be a major impediment, particularly in radiation and proton therapy planning as well as orthopedic imaging. A new solution to the long-standing metal artifact reduction (MAR) problem is deep learning, which has been successfully applied to medical image processing and analysis tasks. In this study, we combine a convolutional neural network (CNN) with the state-of-the-art NMAR algorithm to reduce metal streaks in critical image regions. Training data was synthesized from CT simulation scans of a phantom derived from real patient images. The CNN is able to map metal-corrupted images to artifact-free monoenergetic images to achieve additional correction on top of NMAR for improved image quality. Our results indicate that deep learning is a novel tool to address CT reconstruction challenges, and may enable more accurate tumor volume estimation for radiation therapy planning.

A multistage motion vector processing method for motion-compensated frame interpolation.

PubMed

Huang, Ai- Mei; Nguyen, Truong Q

2008-05-01

In this paper, a novel, low-complexity motion vector processing algorithm at the decoder is proposed for motion-compensated frame interpolation or frame rate up-conversion. We address the problems of having broken edges and deformed structures in an interpolated frame by hierarchically refining motion vectors on different block sizes. Our method explicitly considers the reliability of each received motion vector and has the capability of preserving the structure information. This is achieved by analyzing the distribution of residual energies and effectively merging blocks that have unreliable motion vectors. The motion vector reliability information is also used as a prior knowledge in motion vector refinement using a constrained vector median filter to avoid choosing identical unreliable one. We also propose using chrominance information in our method. Experimental results show that the proposed scheme has better visual quality and is also robust, even in video sequences with complex scenes and fast motion.

Investigations into the shape-preserving interpolants using symbolic computation

NASA Technical Reports Server (NTRS)

Lam, Maria

1988-01-01

Shape representation is a central issue in computer graphics and computer-aided geometric design. Many physical phenomena involve curves and surfaces that are monotone (in some directions) or are convex. The corresponding representation problem is given some monotone or convex data, and a monotone or convex interpolant is found. Standard interpolants need not be monotone or convex even though they may match monotone or convex data. Most of the methods of investigation of this problem involve the utilization of quadratic splines or Hermite polynomials. In this investigation, a similar approach is adopted. These methods require derivative information at the given data points. The key to the problem is the selection of the derivative values to be assigned to the given data points. Schemes for choosing derivatives were examined. Along the way, fitting given data points by a conic section has also been investigated as part of the effort to study shape-preserving quadratic splines.

A simple algorithm to improve the performance of the WENO scheme on non-uniform grids

NASA Astrophysics Data System (ADS)

Huang, Wen-Feng; Ren, Yu-Xin; Jiang, Xiong

2018-02-01

This paper presents a simple approach for improving the performance of the weighted essentially non-oscillatory (WENO) finite volume scheme on non-uniform grids. This technique relies on the reformulation of the fifth-order WENO-JS (WENO scheme presented by Jiang and Shu in J. Comput. Phys. 126:202-228, 1995) scheme designed on uniform grids in terms of one cell-averaged value and its left and/or right interfacial values of the dependent variable. The effect of grid non-uniformity is taken into consideration by a proper interpolation of the interfacial values. On non-uniform grids, the proposed scheme is much more accurate than the original WENO-JS scheme, which was designed for uniform grids. When the grid is uniform, the resulting scheme reduces to the original WENO-JS scheme. In the meantime, the proposed scheme is computationally much more efficient than the fifth-order WENO scheme designed specifically for the non-uniform grids. A number of numerical test cases are simulated to verify the performance of the present scheme.

Fusing Satellite-Derived Irradiance and Point Measurements through Optimal Interpolation

NASA Astrophysics Data System (ADS)

Lorenzo, A.; Morzfeld, M.; Holmgren, W.; Cronin, A.

2016-12-01

Satellite-derived irradiance is widely used throughout the design and operation of a solar power plant. While satellite-derived estimates cover a large area, they also have large errors compared to point measurements from sensors on the ground. We describe an optimal interpolation routine that fuses the broad spatial coverage of satellite-derived irradiance with the high accuracy of point measurements. The routine can be applied to any satellite-derived irradiance and point measurement datasets. Unique aspects of this work include the fact that information is spread using cloud location and thickness and that a number of point measurements are collected from rooftop PV systems. The routine is sensitive to errors in the satellite image geolocation, so care must be taken to adjust the cloud locations based on the solar and satellite geometries. Analysis of the optimal interpolation routine over Tucson, AZ, with 20 point measurements shows a significant improvement in the irradiance estimate for two distinct satellite image to irradiance algorithms. Improved irradiance estimates can be used for resource assessment, distributed generation production estimates, and irradiance forecasts.

A study on characteristics of retrospective optimal interpolation with WRF testbed

NASA Astrophysics Data System (ADS)

Kim, S.; Noh, N.; Lim, G.

2012-12-01

This study presents the application of retrospective optimal interpolation (ROI) with Weather Research and Forecasting model (WRF). Song et al. (2009) suggest ROI method which is an optimal interpolation (OI) that gradually assimilates observations over the analysis window for variance-minimum estimate of an atmospheric state at the initial time of the analysis window. Song and Lim (2011) improve the method by incorporating eigen-decomposition and covariance inflation. ROI method assimilates the data at post analysis time using perturbation method (Errico and Raeder, 1999) without adjoint model. In this study, ROI method is applied to WRF model to validate the algorithm and to investigate the capability. The computational costs for ROI can be reduced due to the eigen-decomposition of background error covariance. Using the background error covariance in eigen-space, 1-profile assimilation experiment is performed. The difference between forecast errors with assimilation and without assimilation is obviously increased as time passed, which means the improvement of forecast error by assimilation. The characteristics and strength/weakness of ROI method are investigated by conducting the experiments with other data assimilation method.

Ortho Image and DTM Generation with Intelligent Methods

NASA Astrophysics Data System (ADS)

Bagheri, H.; Sadeghian, S.

2013-10-01

Nowadays the artificial intelligent algorithms has considered in GIS and remote sensing. Genetic algorithm and artificial neural network are two intelligent methods that are used for optimizing of image processing programs such as edge extraction and etc. these algorithms are very useful for solving of complex program. In this paper, the ability and application of genetic algorithm and artificial neural network in geospatial production process like geometric modelling of satellite images for ortho photo generation and height interpolation in raster Digital Terrain Model production process is discussed. In first, the geometric potential of Ikonos-2 and Worldview-2 with rational functions, 2D & 3D polynomials were tested. Also comprehensive experiments have been carried out to evaluate the viability of the genetic algorithm for optimization of rational function, 2D & 3D polynomials. Considering the quality of Ground Control Points, the accuracy (RMSE) with genetic algorithm and 3D polynomials method for Ikonos-2 Geo image was 0.508 pixel sizes and the accuracy (RMSE) with GA algorithm and rational function method for Worldview-2 image was 0.930 pixel sizes. For more another optimization artificial intelligent methods, neural networks were used. With the use of perceptron network in Worldview-2 image, a result of 0.84 pixel sizes with 4 neurons in middle layer was gained. The final conclusion was that with artificial intelligent algorithms it is possible to optimize the existing models and have better results than usual ones. Finally the artificial intelligence methods, like genetic algorithms as well as neural networks, were examined on sample data for optimizing interpolation and for generating Digital Terrain Models. The results then were compared with existing conventional methods and it appeared that these methods have a high capacity in heights interpolation and that using these networks for interpolating and optimizing the weighting methods based on inverse distance leads to a high accurate estimation of heights.

Selection of Optimal Auxiliary Soil Nutrient Variables for Cokriging Interpolation

PubMed Central

Song, Genxin; Zhang, Jing; Wang, Ke

2014-01-01

In order to explore the selection of the best auxiliary variables (BAVs) when using the Cokriging method for soil attribute interpolation, this paper investigated the selection of BAVs from terrain parameters, soil trace elements, and soil nutrient attributes when applying Cokriging interpolation to soil nutrients (organic matter, total N, available P, and available K). In total, 670 soil samples were collected in Fuyang, and the nutrient and trace element attributes of the soil samples were determined. Based on the spatial autocorrelation of soil attributes, the Digital Elevation Model (DEM) data for Fuyang was combined to explore the coordinate relationship among terrain parameters, trace elements, and soil nutrient attributes. Variables with a high correlation to soil nutrient attributes were selected as BAVs for Cokriging interpolation of soil nutrients, and variables with poor correlation were selected as poor auxiliary variables (PAVs). The results of Cokriging interpolations using BAVs and PAVs were then compared. The results indicated that Cokriging interpolation with BAVs yielded more accurate results than Cokriging interpolation with PAVs (the mean absolute error of BAV interpolation results for organic matter, total N, available P, and available K were 0.020, 0.002, 7.616, and 12.4702, respectively, and the mean absolute error of PAV interpolation results were 0.052, 0.037, 15.619, and 0.037, respectively). The results indicated that Cokriging interpolation with BAVs can significantly improve the accuracy of Cokriging interpolation for soil nutrient attributes. This study provides meaningful guidance and reference for the selection of auxiliary parameters for the application of Cokriging interpolation to soil nutrient attributes. PMID:24927129

Extrapolation of Functions of Many Variables by Means of Metric Analysis

NASA Astrophysics Data System (ADS)

Kryanev, Alexandr; Ivanov, Victor; Romanova, Anastasiya; Sevastianov, Leonid; Udumyan, David

2018-02-01

The paper considers a problem of extrapolating functions of several variables. It is assumed that the values of the function of m variables at a finite number of points in some domain D of the m-dimensional space are given. It is required to restore the value of the function at points outside the domain D. The paper proposes a fundamentally new method for functions of several variables extrapolation. In the presented paper, the method of extrapolating a function of many variables developed by us uses the interpolation scheme of metric analysis. To solve the extrapolation problem, a scheme based on metric analysis methods is proposed. This scheme consists of two stages. In the first stage, using the metric analysis, the function is interpolated to the points of the domain D belonging to the segment of the straight line connecting the center of the domain D with the point M, in which it is necessary to restore the value of the function. In the second stage, based on the auto regression model and metric analysis, the function values are predicted along the above straight-line segment beyond the domain D up to the point M. The presented numerical example demonstrates the efficiency of the method under consideration.

Spatiotemporal Interpolation for Environmental Modelling

PubMed Central

Susanto, Ferry; de Souza, Paulo; He, Jing

2016-01-01

A variation of the reduction-based approach to spatiotemporal interpolation (STI), in which time is treated independently from the spatial dimensions, is proposed in this paper. We reviewed and compared three widely-used spatial interpolation techniques: ordinary kriging, inverse distance weighting and the triangular irregular network. We also proposed a new distribution-based distance weighting (DDW) spatial interpolation method. In this study, we utilised one year of Tasmania’s South Esk Hydrology model developed by CSIRO. Root mean squared error statistical methods were performed for performance evaluations. Our results show that the proposed reduction approach is superior to the extension approach to STI. However, the proposed DDW provides little benefit compared to the conventional inverse distance weighting (IDW) method. We suggest that the improved IDW technique, with the reduction approach used for the temporal dimension, is the optimal combination for large-scale spatiotemporal interpolation within environmental modelling applications. PMID:27509497

Joint Optimization of Fluence Field Modulation and Regularization in Task-Driven Computed Tomography

PubMed Central

Gang, G. J.; Siewerdsen, J. H.; Stayman, J. W.

2017-01-01

Purpose This work presents a task-driven joint optimization of fluence field modulation (FFM) and regularization in quadratic penalized-likelihood (PL) reconstruction. Conventional FFM strategies proposed for filtered-backprojection (FBP) are evaluated in the context of PL reconstruction for comparison. Methods We present a task-driven framework that leverages prior knowledge of the patient anatomy and imaging task to identify FFM and regularization. We adopted a maxi-min objective that ensures a minimum level of detectability index (d′) across sample locations in the image volume. The FFM designs were parameterized by 2D Gaussian basis functions to reduce dimensionality of the optimization and basis function coefficients were estimated using the covariance matrix adaptation evolutionary strategy (CMA-ES) algorithm. The FFM was jointly optimized with both space-invariant and spatially-varying regularization strength (β) - the former via an exhaustive search through discrete values and the latter using an alternating optimization where β was exhaustively optimized locally and interpolated to form a spatially-varying map. Results The optimal FFM inverts as β increases, demonstrating the importance of a joint optimization. For the task and object investigated, the optimal FFM assigns more fluence through less attenuating views, counter to conventional FFM schemes proposed for FBP. The maxi-min objective homogenizes detectability throughout the image and achieves a higher minimum detectability than conventional FFM strategies. Conclusions The task-driven FFM designs found in this work are counter to conventional patterns for FBP and yield better performance in terms of the maxi-min objective, suggesting opportunities for improved image quality and/or dose reduction when model-based reconstructions are applied in conjunction with FFM. PMID:28626290

Joint optimization of fluence field modulation and regularization in task-driven computed tomography

NASA Astrophysics Data System (ADS)

Gang, G. J.; Siewerdsen, J. H.; Stayman, J. W.

2017-03-01

Purpose: This work presents a task-driven joint optimization of fluence field modulation (FFM) and regularization in quadratic penalized-likelihood (PL) reconstruction. Conventional FFM strategies proposed for filtered-backprojection (FBP) are evaluated in the context of PL reconstruction for comparison. Methods: We present a task-driven framework that leverages prior knowledge of the patient anatomy and imaging task to identify FFM and regularization. We adopted a maxi-min objective that ensures a minimum level of detectability index (d') across sample locations in the image volume. The FFM designs were parameterized by 2D Gaussian basis functions to reduce dimensionality of the optimization and basis function coefficients were estimated using the covariance matrix adaptation evolutionary strategy (CMA-ES) algorithm. The FFM was jointly optimized with both space-invariant and spatially-varying regularization strength (β) - the former via an exhaustive search through discrete values and the latter using an alternating optimization where β was exhaustively optimized locally and interpolated to form a spatially-varying map. Results: The optimal FFM inverts as β increases, demonstrating the importance of a joint optimization. For the task and object investigated, the optimal FFM assigns more fluence through less attenuating views, counter to conventional FFM schemes proposed for FBP. The maxi-min objective homogenizes detectability throughout the image and achieves a higher minimum detectability than conventional FFM strategies. Conclusions: The task-driven FFM designs found in this work are counter to conventional patterns for FBP and yield better performance in terms of the maxi-min objective, suggesting opportunities for improved image quality and/or dose reduction when model-based reconstructions are applied in conjunction with FFM.

Novel Threshold Changeable Secret Sharing Schemes Based on Polynomial Interpolation

PubMed Central

Li, Mingchu; Guo, Cheng; Choo, Kim-Kwang Raymond; Ren, Yizhi

2016-01-01

After any distribution of secret sharing shadows in a threshold changeable secret sharing scheme, the threshold may need to be adjusted to deal with changes in the security policy and adversary structure. For example, when employees leave the organization, it is not realistic to expect departing employees to ensure the security of their secret shadows. Therefore, in 2012, Zhang et al. proposed (t → t′, n) and ({t1, t2,⋯, tN}, n) threshold changeable secret sharing schemes. However, their schemes suffer from a number of limitations such as strict limit on the threshold values, large storage space requirement for secret shadows, and significant computation for constructing and recovering polynomials. To address these limitations, we propose two improved dealer-free threshold changeable secret sharing schemes. In our schemes, we construct polynomials to update secret shadows, and use two-variable one-way function to resist collusion attacks and secure the information stored by the combiner. We then demonstrate our schemes can adjust the threshold safely. PMID:27792784

Choice of no-slip curved boundary condition for lattice Boltzmann simulations of high-Reynolds-number flows.

PubMed

Sanjeevi, Sathish K P; Zarghami, Ahad; Padding, Johan T

2018-04-01

Various curved no-slip boundary conditions available in literature improve the accuracy of lattice Boltzmann simulations compared to the traditional staircase approximation of curved geometries. Usually, the required unknown distribution functions emerging from the solid nodes are computed based on the known distribution functions using interpolation or extrapolation schemes. On using such curved boundary schemes, there will be mass loss or gain at each time step during the simulations, especially apparent at high Reynolds numbers, which is called mass leakage. Such an issue becomes severe in periodic flows, where the mass leakage accumulation would affect the computed flow fields over time. In this paper, we examine mass leakage of the most well-known curved boundary treatments for high-Reynolds-number flows. Apart from the existing schemes, we also test different forced mass conservation schemes and a constant density scheme. The capability of each scheme is investigated and, finally, recommendations for choosing a proper boundary condition scheme are given for stable and accurate simulations.

Novel Threshold Changeable Secret Sharing Schemes Based on Polynomial Interpolation.

PubMed

Yuan, Lifeng; Li, Mingchu; Guo, Cheng; Choo, Kim-Kwang Raymond; Ren, Yizhi

2016-01-01

After any distribution of secret sharing shadows in a threshold changeable secret sharing scheme, the threshold may need to be adjusted to deal with changes in the security policy and adversary structure. For example, when employees leave the organization, it is not realistic to expect departing employees to ensure the security of their secret shadows. Therefore, in 2012, Zhang et al. proposed (t → t', n) and ({t1, t2,⋯, tN}, n) threshold changeable secret sharing schemes. However, their schemes suffer from a number of limitations such as strict limit on the threshold values, large storage space requirement for secret shadows, and significant computation for constructing and recovering polynomials. To address these limitations, we propose two improved dealer-free threshold changeable secret sharing schemes. In our schemes, we construct polynomials to update secret shadows, and use two-variable one-way function to resist collusion attacks and secure the information stored by the combiner. We then demonstrate our schemes can adjust the threshold safely.

Choice of no-slip curved boundary condition for lattice Boltzmann simulations of high-Reynolds-number flows

NASA Astrophysics Data System (ADS)

Sanjeevi, Sathish K. P.; Zarghami, Ahad; Padding, Johan T.

2018-04-01

Various curved no-slip boundary conditions available in literature improve the accuracy of lattice Boltzmann simulations compared to the traditional staircase approximation of curved geometries. Usually, the required unknown distribution functions emerging from the solid nodes are computed based on the known distribution functions using interpolation or extrapolation schemes. On using such curved boundary schemes, there will be mass loss or gain at each time step during the simulations, especially apparent at high Reynolds numbers, which is called mass leakage. Such an issue becomes severe in periodic flows, where the mass leakage accumulation would affect the computed flow fields over time. In this paper, we examine mass leakage of the most well-known curved boundary treatments for high-Reynolds-number flows. Apart from the existing schemes, we also test different forced mass conservation schemes and a constant density scheme. The capability of each scheme is investigated and, finally, recommendations for choosing a proper boundary condition scheme are given for stable and accurate simulations.

An approach to unbiased subsample interpolation for motion tracking.

PubMed

McCormick, Matthew M; Varghese, Tomy

2013-04-01

Accurate subsample displacement estimation is necessary for ultrasound elastography because of the small deformations that occur and the subsequent application of a derivative operation on local displacements. Many of the commonly used subsample estimation techniques introduce significant bias errors. This article addresses a reduced bias approach to subsample displacement estimations that consists of a two-dimensional windowed-sinc interpolation with numerical optimization. It is shown that a Welch or Lanczos window with a Nelder-Mead simplex or regular-step gradient-descent optimization is well suited for this purpose. Little improvement results from a sinc window radius greater than four data samples. The strain signal-to-noise ratio (SNR) obtained in a uniformly elastic phantom is compared with other parabolic and cosine interpolation methods; it is found that the strain SNR ratio is improved over parabolic interpolation from 11.0 to 13.6 in the axial direction and 0.7 to 1.1 in the lateral direction for an applied 1% axial deformation. The improvement was most significant for small strains and displacement tracking in the lateral direction. This approach does not rely on special properties of the image or similarity function, which is demonstrated by its effectiveness with the application of a previously described regularization technique.

Signal-to-noise ratio estimation on SEM images using cubic spline interpolation with Savitzky-Golay smoothing.

PubMed

Sim, K S; Kiani, M A; Nia, M E; Tso, C P

2014-01-01

A new technique based on cubic spline interpolation with Savitzky-Golay noise reduction filtering is designed to estimate signal-to-noise ratio of scanning electron microscopy (SEM) images. This approach is found to present better result when compared with two existing techniques: nearest neighbourhood and first-order interpolation. When applied to evaluate the quality of SEM images, noise can be eliminated efficiently with optimal choice of scan rate from real-time SEM images, without generating corruption or increasing scanning time. © 2013 The Authors Journal of Microscopy © 2013 Royal Microscopical Society.

A hybrid Lagrangian Voronoi-SPH scheme

NASA Astrophysics Data System (ADS)

Fernandez-Gutierrez, D.; Souto-Iglesias, A.; Zohdi, T. I.

2018-07-01

A hybrid Lagrangian Voronoi-SPH scheme, with an explicit weakly compressible formulation for both the Voronoi and SPH sub-domains, has been developed. The SPH discretization is substituted by Voronoi elements close to solid boundaries, where SPH consistency and boundary conditions implementation become problematic. A buffer zone to couple the dynamics of both sub-domains is used. This zone is formed by a set of particles where fields are interpolated taking into account SPH particles and Voronoi elements. A particle may move in or out of the buffer zone depending on its proximity to a solid boundary. The accuracy of the coupled scheme is discussed by means of a set of well-known verification benchmarks.

A hybrid Lagrangian Voronoi-SPH scheme

NASA Astrophysics Data System (ADS)

Fernandez-Gutierrez, D.; Souto-Iglesias, A.; Zohdi, T. I.

2017-11-01

A hybrid Lagrangian Voronoi-SPH scheme, with an explicit weakly compressible formulation for both the Voronoi and SPH sub-domains, has been developed. The SPH discretization is substituted by Voronoi elements close to solid boundaries, where SPH consistency and boundary conditions implementation become problematic. A buffer zone to couple the dynamics of both sub-domains is used. This zone is formed by a set of particles where fields are interpolated taking into account SPH particles and Voronoi elements. A particle may move in or out of the buffer zone depending on its proximity to a solid boundary. The accuracy of the coupled scheme is discussed by means of a set of well-known verification benchmarks.

Simulation of Pellet Ablation

NASA Astrophysics Data System (ADS)

Parks, P. B.; Ishizaki, Ryuichi

2000-10-01

In order to clarify the structure of the ablation flow, 2D simulation is carried out with a fluid code solving temporal evolution of MHD equations. The code includes electrostatic sheath effect at the cloud interface.(P.B. Parks et al.), Plasma Phys. Contr. Fusion 38, 571 (1996). An Eulerian cylindrical coordinate system (r,z) is used with z in a spherical pellet. The code uses the Cubic-Interpolated Psudoparticle (CIP) method(H. Takewaki and T. Yabe, J. Comput. Phys. 70), 355 (1987). that divides the fluid equations into non-advection and advection phases. The most essential element of the CIP method is in calculation of the advection phase. In this phase, a cubic interpolated spatial profile is shifted in space according to the total derivative equations, similarly to a particle scheme. Since the profile is interpolated by using the value and the spatial derivative value at each grid point, there is no numerical oscillation in space, that often appears in conventional spline interpolation. A free boundary condition is used in the code. The possibility of a stationary shock will also be shown in the presentation because the supersonic ablation flow across the magnetic field is impeded.

A comparative study of upwind and MacCormack schemes for CAA benchmark problems

NASA Technical Reports Server (NTRS)

Viswanathan, K.; Sankar, L. N.

1995-01-01

In this study, upwind schemes and MacCormack schemes are evaluated as to their suitability for aeroacoustic applications. The governing equations are cast in a curvilinear coordinate system and discretized using finite volume concepts. A flux splitting procedure is used for the upwind schemes, where the signals crossing the cell faces are grouped into two categories: signals that bring information from outside into the cell, and signals that leave the cell. These signals may be computed in several ways, with the desired spatial and temporal accuracy achieved by choosing appropriate interpolating polynomials. The classical MacCormack schemes employed here are fourth order accurate in time and space. Results for categories 1, 4, and 6 of the workshop's benchmark problems are presented. Comparisons are also made with the exact solutions, where available. The main conclusions of this study are finally presented.

Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

1997-01-01

In these lecture notes we describe the construction, analysis, and application of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for hyperbolic conservation laws and related Hamilton- Jacobi equations. ENO and WENO schemes are high order accurate finite difference schemes designed for problems with piecewise smooth solutions containing discontinuities. The key idea lies at the approximation level, where a nonlinear adaptive procedure is used to automatically choose the locally smoothest stencil, hence avoiding crossing discontinuities in the interpolation procedure as much as possible. ENO and WENO schemes have been quite successful in applications, especially for problems containing both shocks and complicated smooth solution structures, such as compressible turbulence simulations and aeroacoustics. These lecture notes are basically self-contained. It is our hope that with these notes and with the help of the quoted references, the reader can understand the algorithms and code them up for applications.

On the error propagation of semi-Lagrange and Fourier methods for advection problems☆

PubMed Central

Einkemmer, Lukas; Ostermann, Alexander

2015-01-01

In this paper we study the error propagation of numerical schemes for the advection equation in the case where high precision is desired. The numerical methods considered are based on the fast Fourier transform, polynomial interpolation (semi-Lagrangian methods using a Lagrange or spline interpolation), and a discontinuous Galerkin semi-Lagrangian approach (which is conservative and has to store more than a single value per cell). We demonstrate, by carrying out numerical experiments, that the worst case error estimates given in the literature provide a good explanation for the error propagation of the interpolation-based semi-Lagrangian methods. For the discontinuous Galerkin semi-Lagrangian method, however, we find that the characteristic property of semi-Lagrangian error estimates (namely the fact that the error increases proportionally to the number of time steps) is not observed. We provide an explanation for this behavior and conduct numerical simulations that corroborate the different qualitative features of the error in the two respective types of semi-Lagrangian methods. The method based on the fast Fourier transform is exact but, due to round-off errors, susceptible to a linear increase of the error in the number of time steps. We show how to modify the Cooley–Tukey algorithm in order to obtain an error growth that is proportional to the square root of the number of time steps. Finally, we show, for a simple model, that our conclusions hold true if the advection solver is used as part of a splitting scheme. PMID:25844018

Curvature Continuous and Bounded Path Planning for Fixed-Wing UAVs

PubMed Central

Jiang, Peng; Li, Deshi; Sun, Tao

2017-01-01

Unmanned Aerial Vehicles (UAVs) play an important role in applications such as data collection and target reconnaissance. An accurate and optimal path can effectively increase the mission success rate in the case of small UAVs. Although path planning for UAVs is similar to that for traditional mobile robots, the special kinematic characteristics of UAVs (such as their minimum turning radius) have not been taken into account in previous studies. In this paper, we propose a locally-adjustable, continuous-curvature, bounded path-planning algorithm for fixed-wing UAVs. To deal with the curvature discontinuity problem, an optimal interpolation algorithm and a key-point shift algorithm are proposed based on the derivation of a curvature continuity condition. To meet the upper bound for curvature and to render the curvature extrema controllable, a local replanning scheme is designed by combining arcs and Bezier curves with monotonic curvature. In particular, a path transition mechanism is built for the replanning phase using minimum curvature circles for a planning philosophy. Numerical results demonstrate that the analytical planning algorithm can effectively generate continuous-curvature paths, while satisfying the curvature upper bound constraint and allowing UAVs to pass through all predefined waypoints in the desired mission region. PMID:28925960

Curvature Continuous and Bounded Path Planning for Fixed-Wing UAVs.

PubMed

Wang, Xiaoliang; Jiang, Peng; Li, Deshi; Sun, Tao

2017-09-19

Unmanned Aerial Vehicles (UAVs) play an important role in applications such as data collection and target reconnaissance. An accurate and optimal path can effectively increase the mission success rate in the case of small UAVs. Although path planning for UAVs is similar to that for traditional mobile robots, the special kinematic characteristics of UAVs (such as their minimum turning radius) have not been taken into account in previous studies. In this paper, we propose a locally-adjustable, continuous-curvature, bounded path-planning algorithm for fixed-wing UAVs. To deal with the curvature discontinuity problem, an optimal interpolation algorithm and a key-point shift algorithm are proposed based on the derivation of a curvature continuity condition. To meet the upper bound for curvature and to render the curvature extrema controllable, a local replanning scheme is designed by combining arcs and Bezier curves with monotonic curvature. In particular, a path transition mechanism is built for the replanning phase using minimum curvature circles for a planning philosophy. Numerical results demonstrate that the analytical planning algorithm can effectively generate continuous-curvature paths, while satisfying the curvature upper bound constraint and allowing UAVs to pass through all predefined waypoints in the desired mission region.

A thermodynamic description for water, hydrogen fluoride and hydrogen dissolutions in cryolite-base molten salts.

PubMed

Wang, Kun; Chartrand, Patrice

2018-06-15

This paper presents a quantitative thermodynamic description for water, hydrogen fluoride and hydrogen dissolutions in cryolite-base molten salts, which is of technological importance to the Hall-Héroult electrolytic aluminum extraction cell. The Modified Quasichemical Model in the Quadruplet Approximation (MQMQA), as used to treat a large variety of molten salt systems, was adopted to thermodynamically describe the present liquid phase; all solid solutions were modeled using the Compound Energy Formalism (CEF); the gas phase was thermodynamically treated as an ideal mixture of all possible species. The model parameters were mainly obtained by critical evaluations and optimizations of thermodynamic and phase equilibrium data available from relative experimental measurements and theoretical predictions (first-principles calculations and empirical estimations) for the lower-order subsystems. These optimized model parameters were thereafter merged within the Kohler/Toop interpolation scheme, facilitating the prediction of gas solubility (H2O, HF and H2) in multicomponent cryolite-base molten salts using the FactSage thermochemical software. Several interesting diagrams were finally obtained in order to provide useful information for the industrial partners dedicated to the Hall-Héroult electrolytic aluminum production or other molten-salt technologies (the purification process and electroslag refining).

Characterization and Modeling of Indium Gallium Antimonide Avalanche Photodiode and of Indium Gallium Arsenide Two-band Detector

NASA Technical Reports Server (NTRS)

2006-01-01

A model of the optical properties of Al(x)Ga(1-x)As(y)Sb(1-y) and In(x)Ga(1-x)As(y)Sb(1-y) is presented, including the refractive, extinction, absorption and reflection coefficients in terms of the optical dielectric function of the materials. Energy levels and model parameters for each binary compound are interpolated to obtain the needed ternaries and quaternaries for various compositions. Bowing parameters are considered in the interpolation scheme to take into account the deviation of the calculated ternary and quaternary values from experimental data due to lattice disorders. The inclusion of temperature effects is currently being considered.

Bayesian calibration of coarse-grained forces: Efficiently addressing transferability

NASA Astrophysics Data System (ADS)

Patrone, Paul N.; Rosch, Thomas W.; Phelan, Frederick R.

2016-04-01

Generating and calibrating forces that are transferable across a range of state-points remains a challenging task in coarse-grained (CG) molecular dynamics. In this work, we present a coarse-graining workflow, inspired by ideas from uncertainty quantification and numerical analysis, to address this problem. The key idea behind our approach is to introduce a Bayesian correction algorithm that uses functional derivatives of CG simulations to rapidly and inexpensively recalibrate initial estimates f0 of forces anchored by standard methods such as force-matching. Taking density-temperature relationships as a running example, we demonstrate that this algorithm, in concert with various interpolation schemes, can be used to efficiently compute physically reasonable force curves on a fine grid of state-points. Importantly, we show that our workflow is robust to several choices available to the modeler, including the interpolation schemes and tools used to construct f0. In a related vein, we also demonstrate that our approach can speed up coarse-graining by reducing the number of atomistic simulations needed as inputs to standard methods for generating CG forces.

A Gridded Daily Min/Max Temperature Dataset With 0.1° Resolution for the Yangtze River Valley and its Error Estimation

NASA Astrophysics Data System (ADS)

Xiong, Qiufen; Hu, Jianglin

2013-05-01

The minimum/maximum (Min/Max) temperature in the Yangtze River valley is decomposed into the climatic mean and anomaly component. A spatial interpolation is developed which combines the 3D thin-plate spline scheme for climatological mean and the 2D Barnes scheme for the anomaly component to create a daily Min/Max temperature dataset. The climatic mean field is obtained by the 3D thin-plate spline scheme because the relationship between the decreases in Min/Max temperature with elevation is robust and reliable on a long time-scale. The characteristics of the anomaly field tend to be related to elevation variation weakly, and the anomaly component is adequately analyzed by the 2D Barnes procedure, which is computationally efficient and readily tunable. With this hybridized interpolation method, a daily Min/Max temperature dataset that covers the domain from 99°E to 123°E and from 24°N to 36°N with 0.1° longitudinal and latitudinal resolution is obtained by utilizing daily Min/Max temperature data from three kinds of station observations, which are national reference climatological stations, the basic meteorological observing stations and the ordinary meteorological observing stations in 15 provinces and municipalities in the Yangtze River valley from 1971 to 2005. The error estimation of the gridded dataset is assessed by examining cross-validation statistics. The results show that the statistics of daily Min/Max temperature interpolation not only have high correlation coefficient (0.99) and interpolation efficiency (0.98), but also the mean bias error is 0.00 °C. For the maximum temperature, the root mean square error is 1.1 °C and the mean absolute error is 0.85 °C. For the minimum temperature, the root mean square error is 0.89 °C and the mean absolute error is 0.67 °C. Thus, the new dataset provides the distribution of Min/Max temperature over the Yangtze River valley with realistic, successive gridded data with 0.1° × 0.1° spatial resolution and daily temporal scale. The primary factors influencing the dataset precision are elevation and terrain complexity. In general, the gridded dataset has a relatively high precision in plains and flatlands and a relatively low precision in mountainous areas.

Comparison of spatiotemporal interpolators for 4D image reconstruction from 2D transesophageal ultrasound

NASA Astrophysics Data System (ADS)

Haak, Alexander; van Stralen, Marijn; van Burken, Gerard; Klein, Stefan; Pluim, Josien P. W.; de Jong, Nico; van der Steen, Antonius F. W.; Bosch, Johan G.

2012-03-01

°For electrophysiology intervention monitoring, we intend to reconstruct 4D ultrasound (US) of structures in the beating heart from 2D transesophageal US by scanplane rotation. The image acquisition is continuous but unsynchronized to the heart rate, which results in a sparsely and irregularly sampled dataset and a spatiotemporal interpolation method is desired. Previously, we showed the potential of normalized convolution (NC) for interpolating such datasets. We explored 4D interpolation by 3 different methods: NC, nearest neighbor (NN), and temporal binning followed by linear interpolation (LTB). The test datasets were derived by slicing three 4D echocardiography datasets at random rotation angles (θ, range: 0-180) and random normalized cardiac phase (τ, range: 0-1). Four different distributions of rotated 2D images with 600, 900, 1350, and 1800 2D input images were created from all TEE sets. A 2D Gaussian kernel was used for NC and optimal kernel sizes (σθ and στ) were found by performing an exhaustive search. The RMS gray value error (RMSE) of the reconstructed images was computed for all interpolation methods. The estimated optimal kernels were in the range of σθ = 3.24 - 3.69°/ στ = 0.045 - 0.048, σθ = 2.79°/ στ = 0.031 - 0.038, σθ = 2.34°/ στ = 0.023 - 0.026, and σθ = 1.89°/ στ = 0.021 - 0.023 for 600, 900, 1350, and 1800 input images respectively. We showed that NC outperforms NN and LTB. For a small number of input images the advantage of NC is more pronounced.

Efficient Implementation of an Optimal Interpolator for Large Spatial Data Sets

NASA Technical Reports Server (NTRS)

Memarsadeghi, Nargess; Mount, David M.

2007-01-01

Interpolating scattered data points is a problem of wide ranging interest. A number of approaches for interpolation have been proposed both from theoretical domains such as computational geometry and in applications' fields such as geostatistics. Our motivation arises from geological and mining applications. In many instances data can be costly to compute and are available only at nonuniformly scattered positions. Because of the high cost of collecting measurements, high accuracy is required in the interpolants. One of the most popular interpolation methods in this field is called ordinary kriging. It is popular because it is a best linear unbiased estimator. The price for its statistical optimality is that the estimator is computationally very expensive. This is because the value of each interpolant is given by the solution of a large dense linear system. In practice, kriging problems have been solved approximately by restricting the domain to a small local neighborhood of points that lie near the query point. Determining the proper size for this neighborhood is a solved by ad hoc methods, and it has been shown that this approach leads to undesirable discontinuities in the interpolant. Recently a more principled approach to approximating kriging has been proposed based on a technique called covariance tapering. This process achieves its efficiency by replacing the large dense kriging system with a much sparser linear system. This technique has been applied to a restriction of our problem, called simple kriging, which is not unbiased for general data sets. In this paper we generalize these results by showing how to apply covariance tapering to the more general problem of ordinary kriging. Through experimentation we demonstrate the space and time efficiency and accuracy of approximating ordinary kriging through the use of covariance tapering combined with iterative methods for solving large sparse systems. We demonstrate our approach on large data sizes arising both from synthetic sources and from real applications.

Scatter correction in cone-beam CT via a half beam blocker technique allowing simultaneous acquisition of scatter and image information

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Ho; Xing Lei; Lee, Rena

2012-05-15

Purpose: X-ray scatter incurred to detectors degrades the quality of cone-beam computed tomography (CBCT) and represents a problem in volumetric image guided and adaptive radiation therapy. Several methods using a beam blocker for the estimation and subtraction of scatter have been proposed. However, due to missing information resulting from the obstruction of the blocker, such methods require dual scanning or dynamically moving blocker to obtain a complete volumetric image. Here, we propose a half beam blocker-based approach, in conjunction with a total variation (TV) regularized Feldkamp-Davis-Kress (FDK) algorithm, to correct scatter-induced artifacts by simultaneously acquiring image and scatter information frommore » a single-rotation CBCT scan. Methods: A half beam blocker, comprising lead strips, is used to simultaneously acquire image data on one side of the projection data and scatter data on the other half side. One-dimensional cubic B-Spline interpolation/extrapolation is applied to derive patient specific scatter information by using the scatter distributions on strips. The estimated scatter is subtracted from the projection image acquired at the opposite view. With scatter-corrected projections where this subtraction is completed, the FDK algorithm based on a cosine weighting function is performed to reconstruct CBCT volume. To suppress the noise in the reconstructed CBCT images produced by geometric errors between two opposed projections and interpolated scatter information, total variation regularization is applied by a minimization using a steepest gradient descent optimization method. The experimental studies using Catphan504 and anthropomorphic phantoms were carried out to evaluate the performance of the proposed scheme. Results: The scatter-induced shading artifacts were markedly suppressed in CBCT using the proposed scheme. Compared with CBCT without a blocker, the nonuniformity value was reduced from 39.3% to 3.1%. The root mean square error relative to values inside the regions of interest selected from a benchmark scatter free image was reduced from 50 to 11.3. The TV regularization also led to a better contrast-to-noise ratio. Conclusions: An asymmetric half beam blocker-based FDK acquisition and reconstruction technique has been established. The proposed scheme enables simultaneous detection of patient specific scatter and complete volumetric CBCT reconstruction without additional requirements such as prior images, dual scans, or moving strips.« less

Optimal sixteenth order convergent method based on quasi-Hermite interpolation for computing roots.

PubMed

Zafar, Fiza; Hussain, Nawab; Fatimah, Zirwah; Kharal, Athar

2014-01-01

We have given a four-step, multipoint iterative method without memory for solving nonlinear equations. The method is constructed by using quasi-Hermite interpolation and has order of convergence sixteen. As this method requires four function evaluations and one derivative evaluation at each step, it is optimal in the sense of the Kung and Traub conjecture. The comparisons are given with some other newly developed sixteenth-order methods. Interval Newton's method is also used for finding the enough accurate initial approximations. Some figures show the enclosure of finitely many zeroes of nonlinear equations in an interval. Basins of attractions show the effectiveness of the method.

[Medical image elastic registration smoothed by unconstrained optimized thin-plate spline].

PubMed

Zhang, Yu; Li, Shuxiang; Chen, Wufan; Liu, Zhexing

2003-12-01

Elastic registration of medical image is an important subject in medical image processing. Previous work has concentrated on selecting the corresponding landmarks manually and then using thin-plate spline interpolating to gain the elastic transformation. However, the landmarks extraction is always prone to error, which will influence the registration results. Localizing the landmarks manually is also difficult and time-consuming. We the optimization theory to improve the thin-plate spline interpolation, and based on it, used an automatic method to extract the landmarks. Combining these two steps, we have proposed an automatic, exact and robust registration method and have gained satisfactory registration results.

Spatial Interpolation of Rain-field Dynamic Time-Space Evolution in Hong Kong

NASA Astrophysics Data System (ADS)

Liu, P.; Tung, Y. K.

2017-12-01

Accurate and reliable measurement and prediction of spatial and temporal distribution of rain-field over a wide range of scales are important topics in hydrologic investigations. In this study, geostatistical treatment of precipitation field is adopted. To estimate the rainfall intensity over a study domain with the sample values and the spatial structure from the radar data, the cumulative distribution functions (CDFs) at all unsampled locations were estimated. Indicator Kriging (IK) was used to estimate the exceedance probabilities for different pre-selected cutoff levels and a procedure was implemented for interpolating CDF values between the thresholds that were derived from the IK. Different interpolation schemes of the CDF were proposed and their influences on the performance were also investigated. The performance measures and visual comparison between the observed rain-field and the IK-based estimation suggested that the proposed method can provide fine results of estimation of indicator variables and is capable of producing realistic image.

Variational data assimilation with a semi-Lagrangian semi-implicit global shallow-water equation model and its adjoint

NASA Technical Reports Server (NTRS)

Li, Y.; Navon, I. M.; Courtier, P.; Gauthier, P.

1993-01-01

An adjoint model is developed for variational data assimilation using the 2D semi-Lagrangian semi-implicit (SLSI) shallow-water equation global model of Bates et al. with special attention being paid to the linearization of the interpolation routines. It is demonstrated that with larger time steps the limit of the validity of the tangent linear model will be curtailed due to the interpolations, especially in regions where sharp gradients in the interpolated variables coupled with strong advective wind occur, a synoptic situation common in the high latitudes. This effect is particularly evident near the pole in the Northern Hemisphere during the winter season. Variational data assimilation experiments of 'identical twin' type with observations available only at the end of the assimilation period perform well with this adjoint model. It is confirmed that the computational efficiency of the semi-Lagrangian scheme is preserved during the minimization process, related to the variational data assimilation procedure.

Application of a medium-range global hydrologic probabilistic forecast scheme to the Ohio River Basin

DOE Office of Scientific and Technical Information (OSTI.GOV)

Voisin, Nathalie; Pappenberger, Florian; Lettenmaier, D. P.

2011-08-15

A 10-day globally applicable flood prediction scheme was evaluated using the Ohio River basin as a test site for the period 2003-2007. The Variable Infiltration Capacity (VIC) hydrology model was initialized with the European Centre for Medium Range Weather Forecasts (ECMWF) analysis temperatures and wind, and Tropical Rainfall Monitoring Mission Multi Satellite Precipitation Analysis (TMPA) precipitation up to the day of forecast. In forecast mode, the VIC model was then forced with a calibrated and statistically downscaled ECMWF ensemble prediction system (EPS) 10-day ensemble forecast. A parallel set up was used where ECMWF EPS forecasts were interpolated to the spatialmore » scale of the hydrology model. Each set of forecasts was extended by 5 days using monthly mean climatological variables and zero precipitation in order to account for the effect of initial conditions. The 15-day spatially distributed ensemble runoff forecasts were then routed to four locations in the basin, each with different drainage areas. Surrogates for observed daily runoff and flow were provided by the reference run, specifically VIC simulation forced with ECMWF analysis fields and TMPA precipitation fields. The flood prediction scheme using the calibrated and downscaled ECMWF EPS forecasts was shown to be more accurate and reliable than interpolated forecasts for both daily distributed runoff forecasts and daily flow forecasts. Initial and antecedent conditions dominated the flow forecasts for lead times shorter than the time of concentration depending on the flow forecast amounts and the drainage area sizes. The flood prediction scheme had useful skill for the 10 following days at all sites.« less

Interpolation of longitudinal shape and image data via optimal mass transport

NASA Astrophysics Data System (ADS)

Gao, Yi; Zhu, Liang-Jia; Bouix, Sylvain; Tannenbaum, Allen

2014-03-01

Longitudinal analysis of medical imaging data has become central to the study of many disorders. Unfortunately, various constraints (study design, patient availability, technological limitations) restrict the acquisition of data to only a few time points, limiting the study of continuous disease/treatment progression. Having the ability to produce a sensible time interpolation of the data can lead to improved analysis, such as intuitive visualizations of anatomical changes, or the creation of more samples to improve statistical analysis. In this work, we model interpolation of medical image data, in particular shape data, using the theory of optimal mass transport (OMT), which can construct a continuous transition from two time points while preserving "mass" (e.g., image intensity, shape volume) during the transition. The theory even allows a short extrapolation in time and may help predict short-term treatment impact or disease progression on anatomical structure. We apply the proposed method to the hippocampus-amygdala complex in schizophrenia, the heart in atrial fibrillation, and full head MR images in traumatic brain injury.

A panoramic imaging system based on fish-eye lens

NASA Astrophysics Data System (ADS)

Wang, Ye; Hao, Chenyang

2017-10-01

Panoramic imaging has been closely watched as one of the major technologies of AR and VR. Mainstream panoramic imaging techniques lenses include fish-eye lenses, image splicing, and catadioptric imaging system. Meanwhile, fish-eyes are widely used in the big picture video surveillance. The advantage of fish-eye lenses is that they are easy to operate and cost less, but how to solve the image distortion of fish-eye lenses has always been a very important topic. In this paper, the image calibration algorithm of fish-eye lens is studied by comparing the method of interpolation, bilinear interpolation and double three interpolation, which are used to optimize the images.

Depth-time interpolation of feature trends extracted from mobile microelectrode data with kernel functions.

PubMed

Wong, Stephen; Hargreaves, Eric L; Baltuch, Gordon H; Jaggi, Jurg L; Danish, Shabbar F

2012-01-01

Microelectrode recording (MER) is necessary for precision localization of target structures such as the subthalamic nucleus during deep brain stimulation (DBS) surgery. Attempts to automate this process have produced quantitative temporal trends (feature activity vs. time) extracted from mobile MER data. Our goal was to evaluate computational methods of generating spatial profiles (feature activity vs. depth) from temporal trends that would decouple automated MER localization from the clinical procedure and enhance functional localization in DBS surgery. We evaluated two methods of interpolation (standard vs. kernel) that generated spatial profiles from temporal trends. We compared interpolated spatial profiles to true spatial profiles that were calculated with depth windows, using correlation coefficient analysis. Excellent approximation of true spatial profiles is achieved by interpolation. Kernel-interpolated spatial profiles produced superior correlation coefficient values at optimal kernel widths (r = 0.932-0.940) compared to standard interpolation (r = 0.891). The choice of kernel function and kernel width resulted in trade-offs in smoothing and resolution. Interpolation of feature activity to create spatial profiles from temporal trends is accurate and can standardize and facilitate MER functional localization of subcortical structures. The methods are computationally efficient, enhancing localization without imposing additional constraints on the MER clinical procedure during DBS surgery. Copyright © 2012 S. Karger AG, Basel.

Two-argument total scatter factor for small fields simultaneously collimated by MLC and jaws: application to stereotactic radiosurgery and radiotherapy

NASA Astrophysics Data System (ADS)

Han, Zhaohui; Friesen, Scott; Hacker, Fred; Zygmanski, Piotr

2018-01-01

Direct use of the total scatter factor (S tot) for independent monitor unit (MU) calculations can be a good alternative approach to the traditional separate treatment of head/collimator scatter (S c) and phantom scatter (S p), especially for stereotactic small fields under the simultaneous collimation of secondary jaws and tertiary multileaf collimators (MLC). We have carried out the measurement of S tot in water for field sizes down to 0.5  ×  0.5 cm2 on a Varian TrueBeam STx medical linear accelerator (linac) equipped with high definition MLCs. Both the jaw field size (c) and MLC field size (s) significantly impact the linac output factors, especially when c \\gg s and s is small (e.g. s  <  5 cm). The combined influence of MLC and jaws gives rise to a two-argument dependence of the total scatter factor, S tot(c,s), which is difficult to functionally decouple. The (c,s) dependence can be conceived as a set of s-dependent functions (‘branches’) defined on domain [s min, s max  =  c] for a given jaw size of c. We have also developed a heuristic model of S tot to assist the clinical implementation of the measured S tot data for small field dosimetry. The model has two components: (i) empirical fit formula for the s-dependent branches and (ii) interpolation scheme between the branches. The interpolation scheme preserves the characteristic shape of the measured branches and effectively transforms the measured trapezoidal domain in (c,s) plane to a rectangular domain to facilitate easier two-dimensional interpolation to determine S tot for arbitrary (c,s) combinations. Both the empirical fit and interpolation showed good agreement with experimental validation data.

Generalized Reduced Order Modeling of Aeroservoelastic Systems

NASA Astrophysics Data System (ADS)

Gariffo, James Michael

Transonic aeroelastic and aeroservoelastic (ASE) modeling presents a significant technical and computational challenge. Flow fields with a mixture of subsonic and supersonic flow, as well as moving shock waves, can only be captured through high-fidelity CFD analysis. With modern computing power, it is realtively straightforward to determine the flutter boundary for a single structural configuration at a single flight condition, but problems of larger scope remain quite costly. Some such problems include characterizing a vehicle's flutter boundary over its full flight envelope, optimizing its structural weight subject to aeroelastic constraints, and designing control laws for flutter suppression. For all of these applications, reduced-order models (ROMs) offer substantial computational savings. ROM techniques in general have existed for decades, and the methodology presented in this dissertation builds on successful previous techniques to create a powerful new scheme for modeling aeroelastic systems, and predicting and interpolating their transonic flutter boundaries. In this method, linear ASE state-space models are constructed from modal structural and actuator models coupled to state-space models of the linearized aerodynamic forces through feedback loops. Flutter predictions can be made from these models through simple eigenvalue analysis of their state-transition matrices for an appropriate set of dynamic pressures. Moreover, this analysis returns the frequency and damping trend of every aeroelastic branch. In contrast, determining the critical dynamic pressure by direct time-marching CFD requires a separate run for every dynamic pressure being analyzed simply to obtain the trend for the critical branch. The present ROM methodology also includes a new model interpolation technique that greatly enhances the benefits of these ROMs. This enables predictions of the dynamic behavior of the system for flight conditions where CFD analysis has not been explicitly performed, thus making it possible to characterize the overall flutter boundary with far fewer CFD runs. A major challenge of this research is that transonic flutter boundaries can involve multiple unstable modes of different types. Multiple ROM-based studies on the ONERA M6 wing are shown indicating that in addition to classic bending-torsion (BT) flutter modes. which become unstable above a threshold dynamic pressure after two natural modes become aerodynamically coupled, some natural modes are able to extract energy from the air and become unstable by themselves. These single-mode instabilities tend to be weaker than the BT instabilities, but have near-zero flutter boundaries (exactly zero in the absence of structural damping). Examples of hump modes, which behave like natural mode instabilities before stabilizing, are also shown, as are cases where multiple instabilities coexist at a single flight condition. The result of all these instabilities is a highly sensitive flutter boundary, where small changes in Mach number, structural stiffness, and structural damping can substantially alter not only the stability of individual aeroelastic branches, but also which branch is critical. Several studies are shown presenting how the flutter boundary varies with respect to all three of these parameters, as well as the number of structural modes used to construct the ROMs. Finally, an investigation of the effectiveness and limitations of the interpolation scheme is presented. It is found that in regions where the flutter boundary is relatively smooth, the interpolation method produces ROMs that predict the flutter characteristics of the corresponding directly computed models to a high degree of accuracy, even for relatively coarsely spaced data. On the other hand, in the transonic dip region, the interpolated ROMs show significant errors at points where the boundary changes rapidly; however, they still give a good qualitative estimate of where the largest jumps occur.

Transactions of The Army Conference on Applied Mathematics and Computing (5th) Held in West Point, New York on 15-18 June 1987

DTIC Science & Technology

1988-03-01

29 Statistical Machine Learning for the Cognitive Selection of Nonlinear Programming Algorithms in Engineering Design Optimization Toward...interpolation and Interpolation by Box Spline Surfaces Charles K. Chui, Harvey Diamond, Louise A. Raphael. 301 Knot Selection for Least Squares...West Virginia University, Morgantown, West Virginia; and Louise Raphael, National Science Foundation, Washington, DC Knot Selection for Least

Multi-Objective Optimization of Mixed Variable, Stochastic Systems Using Single-Objective Formulations

DTIC Science & Technology

2008-03-01

investigated, as well as the methodology used . Chapter IV presents the data collection and analysis procedures, and the resulting analysis and...interpolate the data, although a non-interpolating model is possible. For this research Design and Analysis of Computer Experiments (DACE) is used ...followed by the analysis . 4.1. Testing Approach The initial SMOMADS algorithm used for this research was acquired directly from Walston [70]. The

An Approach to Unbiased Subsample Interpolation for Motion Tracking

PubMed Central

McCormick, Matthew M.; Varghese, Tomy

2013-01-01

Accurate subsample displacement estimation is necessary for ultrasound elastography because of the small deformations that occur and the subsequent application of a derivative operation on local displacements. Many of the commonly used subsample estimation techniques introduce significant bias errors. This article addresses a reduced bias approach to subsample displacement estimations that consists of a two-dimensional windowed-sinc interpolation with numerical optimization. It is shown that a Welch or Lanczos window with a Nelder–Mead simplex or regular-step gradient-descent optimization is well suited for this purpose. Little improvement results from a sinc window radius greater than four data samples. The strain signal-to-noise ratio (SNR) obtained in a uniformly elastic phantom is compared with other parabolic and cosine interpolation methods; it is found that the strain SNR ratio is improved over parabolic interpolation from 11.0 to 13.6 in the axial direction and 0.7 to 1.1 in the lateral direction for an applied 1% axial deformation. The improvement was most significant for small strains and displacement tracking in the lateral direction. This approach does not rely on special properties of the image or similarity function, which is demonstrated by its effectiveness with the application of a previously described regularization technique. PMID:23493609

Ambient Ozone Exposure in Czech Forests: A GIS-Based Approach to Spatial Distribution Assessment

PubMed Central

Hůnová, I.; Horálek, J.; Schreiberová, M.; Zapletal, M.

2012-01-01

Ambient ozone (O3) is an important phytotoxic pollutant, and detailed knowledge of its spatial distribution is becoming increasingly important. The aim of the paper is to compare different spatial interpolation techniques and to recommend the best approach for producing a reliable map for O3 with respect to its phytotoxic potential. For evaluation we used real-time ambient O3 concentrations measured by UV absorbance from 24 Czech rural sites in the 2007 and 2008 vegetation seasons. We considered eleven approaches for spatial interpolation used for the development of maps for mean vegetation season O3 concentrations and the AOT40F exposure index for forests. The uncertainty of maps was assessed by cross-validation analysis. The root mean square error (RMSE) of the map was used as a criterion. Our results indicate that the optimal interpolation approach is linear regression of O3 data and altitude with subsequent interpolation of its residuals by ordinary kriging. The relative uncertainty of the map of O3 mean for the vegetation season is less than 10%, using the optimal method as for both explored years, and this is a very acceptable value. In the case of AOT40F, however, the relative uncertainty of the map is notably worse, reaching nearly 20% in both examined years. PMID:22566757

Lognormal Assimilation of Water Vapor in a WRF-GSI Cycled System

NASA Astrophysics Data System (ADS)

Fletcher, S. J.; Kliewer, A.; Jones, A. S.; Forsythe, J. M.

2015-12-01

Recent publications have shown the viability of both detecting a lognormally-distributed signal for water vapor mixing ratio and the improved quality of satellite retrievals in a 1DVAR mixed lognormal-Gaussian assimilation scheme over a Gaussian-only system. This mixed scheme is incorporated into the Gridpoint Statistical Interpolation (GSI) assimilation scheme with the goal of improving forecasts from the Weather Research and Forecasting (WRF) Model in a cycled system. Results are presented of the impact of treating water vapor as a lognormal random variable. Included in the analysis are: 1) the evolution of Tropical Storm Chris from 2006, and 2) an analysis of a "Pineapple Express" water vapor event from 2005 where a lognormal signal has been previously detected.

Newly-Developed 3D GRMHD Code and its Application to Jet Formation

NASA Technical Reports Server (NTRS)

Mizuno, Y.; Nishikawa, K.-I.; Koide, S.; Hardee, P.; Fishman, G. J.

2006-01-01

We have developed a new three-dimensional general relativistic magnetohydrodynamic code by using a conservative, high-resolution shock-capturing scheme. The numerical fluxes are calculated using the HLL approximate Riemann solver scheme. The flux-interpolated constrained transport scheme is used to maintain a divergence-free magnetic field. We have performed various 1-dimensional test problems in both special and general relativity by using several reconstruction methods and found that the new 3D GRMHD code shows substantial improvements over our previous model. The . preliminary results show the jet formations from a geometrically thin accretion disk near a non-rotating and a rotating black hole. We will discuss the jet properties depended on the rotation of a black hole and the magnetic field strength.

On-line estimation of error covariance parameters for atmospheric data assimilation

NASA Technical Reports Server (NTRS)

Dee, Dick P.

1995-01-01

A simple scheme is presented for on-line estimation of covariance parameters in statistical data assimilation systems. The scheme is based on a maximum-likelihood approach in which estimates are produced on the basis of a single batch of simultaneous observations. Simple-sample covariance estimation is reasonable as long as the number of available observations exceeds the number of tunable parameters by two or three orders of magnitude. Not much is known at present about model error associated with actual forecast systems. Our scheme can be used to estimate some important statistical model error parameters such as regionally averaged variances or characteristic correlation length scales. The advantage of the single-sample approach is that it does not rely on any assumptions about the temporal behavior of the covariance parameters: time-dependent parameter estimates can be continuously adjusted on the basis of current observations. This is of practical importance since it is likely to be the case that both model error and observation error strongly depend on the actual state of the atmosphere. The single-sample estimation scheme can be incorporated into any four-dimensional statistical data assimilation system that involves explicit calculation of forecast error covariances, including optimal interpolation (OI) and the simplified Kalman filter (SKF). The computational cost of the scheme is high but not prohibitive; on-line estimation of one or two covariance parameters in each analysis box of an operational bozed-OI system is currently feasible. A number of numerical experiments performed with an adaptive SKF and an adaptive version of OI, using a linear two-dimensional shallow-water model and artificially generated model error are described. The performance of the nonadaptive versions of these methods turns out to depend rather strongly on correct specification of model error parameters. These parameters are estimated under a variety of conditions, including uniformly distributed model error and time-dependent model error statistics.

A staggered-grid finite-difference scheme optimized in the time–space domain for modeling scalar-wave propagation in geophysical problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tan, Sirui, E-mail: siruitan@hotmail.com; Huang, Lianjie, E-mail: ljh@lanl.gov

For modeling scalar-wave propagation in geophysical problems using finite-difference schemes, optimizing the coefficients of the finite-difference operators can reduce numerical dispersion. Most optimized finite-difference schemes for modeling seismic-wave propagation suppress only spatial but not temporal dispersion errors. We develop a novel optimized finite-difference scheme for numerical scalar-wave modeling to control dispersion errors not only in space but also in time. Our optimized scheme is based on a new stencil that contains a few more grid points than the standard stencil. We design an objective function for minimizing relative errors of phase velocities of waves propagating in all directions within amore » given range of wavenumbers. Dispersion analysis and numerical examples demonstrate that our optimized finite-difference scheme is computationally up to 2.5 times faster than the optimized schemes using the standard stencil to achieve the similar modeling accuracy for a given 2D or 3D problem. Compared with the high-order finite-difference scheme using the same new stencil, our optimized scheme reduces 50 percent of the computational cost to achieve the similar modeling accuracy. This new optimized finite-difference scheme is particularly useful for large-scale 3D scalar-wave modeling and inversion.« less

Usefulness of Wave Data Assimilation to the WAVE WATCH III Modeling System

NASA Astrophysics Data System (ADS)

Choi, J. K.; Dykes, J. D.; Yaremchuk, M.; Wittmann, P.

2017-12-01

In-situ and remote-sensed wave data are more abundant currently than in years past, with excellent accuracy at global scales. Forecast skill of the WAVE WATCH III model is improved by assimilation of these measurements and they are also useful for model validation and calibration. It has been known that the impact of assimilation in wind-sea conditions is not large, but spectra that result in large swell with long term propagation are identified and assimilated, the improved accuracy of the initial conditions improve the long-term forecasts. The Navy's assimilation method started with the simple Optimal Interpolation (OI) method. Operationally, Fleet Numerical Meteorology and Oceanography Center uses the sequential 2DVar scheme, but a new approach has been tested based on an adjoint-free method to variational assimilation in WAVE WATCH III. We will present the status of wave data assimilation into the WAVE WATCH III numerical model and upcoming development of this new adjoint-free variational approach.

Effective 3-D surface modeling for geographic information systems

NASA Astrophysics Data System (ADS)

Yüksek, K.; Alparslan, M.; Mendi, E.

2013-11-01

In this work, we propose a dynamic, flexible and interactive urban digital terrain platform (DTP) with spatial data and query processing capabilities of Geographic Information Systems (GIS), multimedia database functionality and graphical modeling infrastructure. A new data element, called Geo-Node, which stores image, spatial data and 3-D CAD objects is developed using an efficient data structure. The system effectively handles data transfer of Geo-Nodes between main memory and secondary storage with an optimized Directional Replacement Policy (DRP) based buffer management scheme. Polyhedron structures are used in Digital Surface Modeling (DSM) and smoothing process is performed by interpolation. The experimental results show that our framework achieves high performance and works effectively with urban scenes independent from the amount of spatial data and image size. The proposed platform may contribute to the development of various applications such as Web GIS systems based on 3-D graphics standards (e.g. X3-D and VRML) and services which integrate multi-dimensional spatial information and satellite/aerial imagery.

Computer program documentation for a subcritical wing design code using higher order far-field drag minimization

NASA Technical Reports Server (NTRS)

Kuhlman, J. M.; Shu, J. Y.

1981-01-01

A subsonic, linearized aerodynamic theory, wing design program for one or two planforms was developed which uses a vortex lattice near field model and a higher order panel method in the far field. The theoretical development of the wake model and its implementation in the vortex lattice design code are summarized and sample results are given. Detailed program usage instructions, sample input and output data, and a program listing are presented in the Appendixes. The far field wake model assumes a wake vortex sheet whose strength varies piecewise linearly in the spanwise direction. From this model analytical expressions for lift coefficient, induced drag coefficient, pitching moment coefficient, and bending moment coefficient were developed. From these relationships a direct optimization scheme is used to determine the optimum wake vorticity distribution for minimum induced drag, subject to constraints on lift, and pitching or bending moment. Integration spanwise yields the bound circulation, which is interpolated in the near field vortex lattice to obtain the design camber surface(s).

Assimilation of glider and mooring data into a coastal ocean model

NASA Astrophysics Data System (ADS)

Jones, Emlyn M.; Oke, Peter R.; Rizwi, Farhan; Murray, Lawrence M.

We have applied an ensemble optimal interpolation (EnOI) data assimilation system to a high resolution coastal ocean model of south-east Tasmania, Australia. The region is characterised by a complex coastline with water masses influenced by riverine input and the interaction between two offshore current systems. Using a large static ensemble to estimate the systems background error covariance, data from a coastal observing network of fixed moorings and a Slocum glider are assimilated into the model at daily intervals. We demonstrate that the EnOI algorithm can successfully correct a biased high resolution coastal model. In areas with dense observations, the assimilation scheme reduces the RMS difference between the model and independent GHRSST observations by 90%, while the domain-wide RMS difference is reduced by a more modest 40%. Our findings show that errors introduced by surface forcing and boundary conditions can be identified and reduced by a relatively sparse observing array using an inexpensive ensemble-based data assimilation system.

Effective 3-D surface modeling for geographic information systems

NASA Astrophysics Data System (ADS)

Yüksek, K.; Alparslan, M.; Mendi, E.

2016-01-01

In this work, we propose a dynamic, flexible and interactive urban digital terrain platform with spatial data and query processing capabilities of geographic information systems, multimedia database functionality and graphical modeling infrastructure. A new data element, called Geo-Node, which stores image, spatial data and 3-D CAD objects is developed using an efficient data structure. The system effectively handles data transfer of Geo-Nodes between main memory and secondary storage with an optimized directional replacement policy (DRP) based buffer management scheme. Polyhedron structures are used in digital surface modeling and smoothing process is performed by interpolation. The experimental results show that our framework achieves high performance and works effectively with urban scenes independent from the amount of spatial data and image size. The proposed platform may contribute to the development of various applications such as Web GIS systems based on 3-D graphics standards (e.g., X3-D and VRML) and services which integrate multi-dimensional spatial information and satellite/aerial imagery.

Distributed optical fiber-based monitoring approach of spatial seepage behavior in dike engineering

NASA Astrophysics Data System (ADS)

Su, Huaizhi; Ou, Bin; Yang, Lifu; Wen, Zhiping

2018-07-01

The failure caused by seepage is the most common one in dike engineering. As to the characteristics of seepage in dike, such as longitudinal extension engineering, the randomness, strong concealment and small initial quantity order, by means of distributed fiber temperature sensor system (DTS), adopting an improved optical fiber layer layout scheme, the location of initial interpolation point of the saturation line is obtained. With the barycentric Lagrange interpolation collocation method (BLICM), the infiltrated surface of dike full-section is generated. Combined with linear optical fiber monitoring seepage method, BLICM is applied in an engineering case, which shows that a real-time seepage monitoring technique is presented in full-section of dike based on the combination method.

Rtop - an R package for interpolation along the stream network

NASA Astrophysics Data System (ADS)

Skøien, J. O.

2009-04-01

Rtop - an R package for interpolation along the stream network Geostatistical methods have been used to a limited extent for estimation along stream networks, with a few exceptions(Gottschalk, 1993; Gottschalk, et al., 2006; Sauquet, et al., 2000; Skøien, et al., 2006). Interpolation of runoff characteristics are more complicated than the traditional random variables estimated by geostatistical methods, as the measurements have a more complicated support, and many catchments are nested. Skøien et al. (2006) presented the model Top-kriging which takes these effects into account for interpolation of stream flow characteristics (exemplified by the 100 year flood). The method has here been implemented as a package in the statistical environment R (R Development Core Team, 2004). Taking advantage of the existing methods in R for working with spatial objects, and the extensive possibilities for visualizing the result, this makes it considerably easier to apply the method on new data sets, in comparison to earlier implementation of the method. Gottschalk, L. 1993. Interpolation of runoff applying objective methods. Stochastic Hydrology and Hydraulics, 7, 269-281. Gottschalk, L., I. Krasovskaia, E. Leblois, and E. Sauquet. 2006. Mapping mean and variance of runoff in a river basin. Hydrology and Earth System Sciences, 10, 469-484. R Development Core Team. 2004. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Sauquet, E., L. Gottschalk, and E. Leblois. 2000. Mapping average annual runoff: a hierarchical approach applying a stochastic interpolation scheme. Hydrological Sciences Journal, 45 (6), 799-815. Skøien, J. O., R. Merz, and G. Blöschl. 2006. Top-kriging - geostatistics on stream networks. Hydrology and Earth System Sciences, 10, 277-287.

An Immersed Boundary method with divergence-free velocity interpolation and force spreading

NASA Astrophysics Data System (ADS)

Bao, Yuanxun; Donev, Aleksandar; Griffith, Boyce E.; McQueen, David M.; Peskin, Charles S.

2017-10-01

The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid-structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an Eulerian representation of the fluid and a Lagrangian representation of the structure. The Lagrangian and Eulerian frames are coupled by integral transforms with delta function kernels. The discretized IB equations use approximations to these transforms with regularized delta function kernels to interpolate the fluid velocity to the structure, and to spread structural forces to the fluid. It is well-known that the conventional IB method can suffer from poor volume conservation since the interpolated Lagrangian velocity field is not generally divergence-free, and so this can cause spurious volume changes. In practice, the lack of volume conservation is especially pronounced for cases where there are large pressure differences across thin structural boundaries. The aim of this paper is to greatly reduce the volume error of the IB method by introducing velocity-interpolation and force-spreading schemes with the properties that the interpolated velocity field in which the structure moves is at least C1 and satisfies a continuous divergence-free condition, and that the force-spreading operator is the adjoint of the velocity-interpolation operator. We confirm through numerical experiments in two and three spatial dimensions that this new IB method is able to achieve substantial improvement in volume conservation compared to other existing IB methods, at the expense of a modest increase in the computational cost. Further, the new method provides smoother Lagrangian forces (tractions) than traditional IB methods. The method presented here is restricted to periodic computational domains. Its generalization to non-periodic domains is important future work.

An improved adaptive interpolation clock recovery loop based on phase splitting algorithm for coherent optical communication system

NASA Astrophysics Data System (ADS)

Liu, Xuan; Liu, Bo; Zhang, Li-jia; Xin, Xiang-jun; Zhang, Qi; Wang, Yong-jun; Tian, Qing-hua; Tian, Feng; Mao, Ya-ya

2018-01-01

Traditional clock recovery scheme achieves timing adjustment by digital interpolation, thus recovering the sampling sequence. Based on this, an improved clock recovery architecture joint channel equalization for coherent optical communication system is presented in this paper. The loop is different from the traditional clock recovery. In order to reduce the interpolation error caused by the distortion in the frequency domain of the interpolator and to suppress the spectral mirroring generated by the sampling rate change, the proposed algorithm joint equalization, improves the original interpolator in the loop, along with adaptive filtering, and makes error compensation for the original signals according to the balanced pre-filtering signals. Then the signals are adaptive interpolated through the feedback loop. Furthermore, the phase splitting timing recovery algorithm is adopted in this paper. The time error is calculated according to the improved algorithm when there is no transition between the adjacent symbols, making calculated timing error more accurate. Meanwhile, Carrier coarse synchronization module is placed before the beginning of timing recovery to eliminate the larger frequency offset interference, which effectively adjust the sampling clock phase. In this paper, the simulation results show that the timing error is greatly reduced after the loop is changed. Based on the phase splitting algorithm, the BER and MSE are better than those in the unvaried architecture. In the fiber channel, using MQAM modulation format, after 100 km-transmission of single-mode fiber, especially when ROF(roll-off factor) values tends to 0, the algorithm shows a better clock performance under different ROFs. When SNR values are less than 8, the BER could achieve 10-2 to 10-1 magnitude. Furthermore, the proposed timing recovery is more suitable for the situation with low SNR values.

A numerical scheme based on radial basis function finite difference (RBF-FD) technique for solving the high-dimensional nonlinear Schrödinger equations using an explicit time discretization: Runge-Kutta method

NASA Astrophysics Data System (ADS)

Dehghan, Mehdi; Mohammadi, Vahid

2017-08-01

In this research, we investigate the numerical solution of nonlinear Schrödinger equations in two and three dimensions. The numerical meshless method which will be used here is RBF-FD technique. The main advantage of this method is the approximation of the required derivatives based on finite difference technique at each local-support domain as Ωi. At each Ωi, we require to solve a small linear system of algebraic equations with a conditionally positive definite matrix of order 1 (interpolation matrix). This scheme is efficient and its computational cost is same as the moving least squares (MLS) approximation. A challengeable issue is choosing suitable shape parameter for interpolation matrix in this way. In order to overcome this matter, an algorithm which was established by Sarra (2012), will be applied. This algorithm computes the condition number of the local interpolation matrix using the singular value decomposition (SVD) for obtaining the smallest and largest singular values of that matrix. Moreover, an explicit method based on Runge-Kutta formula of fourth-order accuracy will be applied for approximating the time variable. It also decreases the computational costs at each time step since we will not solve a nonlinear system. On the other hand, to compare RBF-FD method with another meshless technique, the moving kriging least squares (MKLS) approximation is considered for the studied model. Our results demonstrate the ability of the present approach for solving the applicable model which is investigated in the current research work.

Theoretical oscillation frequencies for solar-type dwarfs from stellar models with 〈3D〉-atmospheres

NASA Astrophysics Data System (ADS)

Jørgensen, Andreas Christ Sølvsten; Weiss, Achim; Mosumgaard, Jakob Rørsted; Silva Aguirre, Victor; Sahlholdt, Christian Lundsgaard

2017-12-01

We present a new method for replacing the outermost layers of stellar models with interpolated atmospheres based on results from 3D simulations, in order to correct for structural inadequacies of these layers. This replacement is known as patching. Tests, based on 3D atmospheres from three different codes and interior models with different input physics, are performed. Using solar models, we investigate how different patching criteria affect the eigenfrequencies. These criteria include the depth, at which the replacement is performed, the quantity, on which the replacement is based, and the mismatch in Teff and log g between the un-patched model and patched 3D atmosphere. We find the eigenfrequencies to be unaltered by the patching depth deep within the adiabatic region, while changing the patching quantity or the employed atmosphere grid leads to frequency shifts that may exceed 1 μHz. Likewise, the eigenfrequencies are sensitive to mismatches in Teff or log g. A thorough investigation of the accuracy of a new scheme, for interpolating mean 3D stratifications within the atmosphere grids, is furthermore performed. Throughout large parts of the atmosphere grids, our interpolation scheme yields sufficiently accurate results for the purpose of asteroseismology. We apply our procedure in asteroseismic analyses of four Kepler stars and draw the same conclusions as in the solar case: Correcting for structural deficiencies lowers the eigenfrequencies, this correction is slightly sensitive to the patching criteria, and the remaining frequency discrepancy between models and observations is less frequency dependent. Our work shows the applicability and relevance of patching in asteroseismology.

A morphing-based scheme for large deformation analysis with stereo-DIC

NASA Astrophysics Data System (ADS)

Genovese, Katia; Sorgente, Donato

2018-05-01

A key step in the DIC-based image registration process is the definition of the initial guess for the non-linear optimization routine aimed at finding the parameters describing the pixel subset transformation. This initialization may result very challenging and possibly fail when dealing with pairs of largely deformed images such those obtained from two angled-views of not-flat objects or from the temporal undersampling of rapidly evolving phenomena. To address this problem, we developed a procedure that generates a sequence of intermediate synthetic images for gradually tracking the pixel subset transformation between the two extreme configurations. To this scope, a proper image warping function is defined over the entire image domain through the adoption of a robust feature-based algorithm followed by a NURBS-based interpolation scheme. This allows a fast and reliable estimation of the initial guess of the deformation parameters for the subsequent refinement stage of the DIC analysis. The proposed method is described step-by-step by illustrating the measurement of the large and heterogeneous deformation of a circular silicone membrane undergoing axisymmetric indentation. A comparative analysis of the results is carried out by taking as a benchmark a standard reference-updating approach. Finally, the morphing scheme is extended to the most general case of the correspondence search between two largely deformed textured 3D geometries. The feasibility of this latter approach is demonstrated on a very challenging case: the full-surface measurement of the severe deformation (> 150% strain) suffered by an aluminum sheet blank subjected to a pneumatic bulge test.

Minimizing Interpolation Bias and Precision Error in In Vivo μCT-based Measurements of Bone Structure and Dynamics

PubMed Central

de Bakker, Chantal M. J.; Altman, Allison R.; Li, Connie; Tribble, Mary Beth; Lott, Carina; Tseng, Wei-Ju; Liu, X. Sherry

2016-01-01

In vivo μCT imaging allows for high-resolution, longitudinal evaluation of bone properties. Based on this technology, several recent studies have developed in vivo dynamic bone histomorphometry techniques that utilize registered μCT images to identify regions of bone formation and resorption, allowing for longitudinal assessment of bone remodeling. However, this analysis requires a direct voxel-by-voxel subtraction between image pairs, necessitating rotation of the images into the same coordinate system, which introduces interpolation errors. We developed a novel image transformation scheme, matched-angle transformation (MAT), whereby the interpolation errors are minimized by equally rotating both the follow-up and baseline images instead of the standard of rotating one image while the other remains fixed. This new method greatly reduced interpolation biases caused by the standard transformation. Additionally, our study evaluated the reproducibility and precision of bone remodeling measurements made via in vivo dynamic bone histomorphometry. Although bone remodeling measurements showed moderate baseline noise, precision was adequate to measure physiologically relevant changes in bone remodeling, and measurements had relatively good reproducibility, with intra-class correlation coefficients of 0.75-0.95. This indicates that, when used in conjunction with MAT, in vivo dynamic histomorphometry provides a reliable assessment of bone remodeling. PMID:26786342

Minimizing Interpolation Bias and Precision Error in In Vivo µCT-Based Measurements of Bone Structure and Dynamics.

PubMed

de Bakker, Chantal M J; Altman, Allison R; Li, Connie; Tribble, Mary Beth; Lott, Carina; Tseng, Wei-Ju; Liu, X Sherry

2016-08-01

In vivo µCT imaging allows for high-resolution, longitudinal evaluation of bone properties. Based on this technology, several recent studies have developed in vivo dynamic bone histomorphometry techniques that utilize registered µCT images to identify regions of bone formation and resorption, allowing for longitudinal assessment of bone remodeling. However, this analysis requires a direct voxel-by-voxel subtraction between image pairs, necessitating rotation of the images into the same coordinate system, which introduces interpolation errors. We developed a novel image transformation scheme, matched-angle transformation (MAT), whereby the interpolation errors are minimized by equally rotating both the follow-up and baseline images instead of the standard of rotating one image while the other remains fixed. This new method greatly reduced interpolation biases caused by the standard transformation. Additionally, our study evaluated the reproducibility and precision of bone remodeling measurements made via in vivo dynamic bone histomorphometry. Although bone remodeling measurements showed moderate baseline noise, precision was adequate to measure physiologically relevant changes in bone remodeling, and measurements had relatively good reproducibility, with intra-class correlation coefficients of 0.75-0.95. This indicates that, when used in conjunction with MAT, in vivo dynamic histomorphometry provides a reliable assessment of bone remodeling.

Sensitivity Analysis of the Static Aeroelastic Response of a Wing

NASA Technical Reports Server (NTRS)

Eldred, Lloyd B.

1993-01-01

A technique to obtain the sensitivity of the static aeroelastic response of a three dimensional wing model is designed and implemented. The formulation is quite general and accepts any aerodynamic and structural analysis capability. A program to combine the discipline level, or local, sensitivities into global sensitivity derivatives is developed. A variety of representations of the wing pressure field are developed and tested to determine the most accurate and efficient scheme for representing the field outside of the aerodynamic code. Chebyshev polynomials are used to globally fit the pressure field. This approach had some difficulties in representing local variations in the field, so a variety of local interpolation polynomial pressure representations are also implemented. These panel based representations use a constant pressure value, a bilinearly interpolated value. or a biquadraticallv interpolated value. The interpolation polynomial approaches do an excellent job of reducing the numerical problems of the global approach for comparable computational effort. Regardless of the pressure representation used. sensitivity and response results with excellent accuracy have been produced for large integrated quantities such as wing tip deflection and trim angle of attack. The sensitivities of such things as individual generalized displacements have been found with fair accuracy. In general, accuracy is found to be proportional to the relative size of the derivatives to the quantity itself.

Derivative-free generation and interpolation of convex Pareto optimal IMRT plans

NASA Astrophysics Data System (ADS)

Hoffmann, Aswin L.; Siem, Alex Y. D.; den Hertog, Dick; Kaanders, Johannes H. A. M.; Huizenga, Henk

2006-12-01

In inverse treatment planning for intensity-modulated radiation therapy (IMRT), beamlet intensity levels in fluence maps of high-energy photon beams are optimized. Treatment plan evaluation criteria are used as objective functions to steer the optimization process. Fluence map optimization can be considered a multi-objective optimization problem, for which a set of Pareto optimal solutions exists: the Pareto efficient frontier (PEF). In this paper, a constrained optimization method is pursued to iteratively estimate the PEF up to some predefined error. We use the property that the PEF is convex for a convex optimization problem to construct piecewise-linear upper and lower bounds to approximate the PEF from a small initial set of Pareto optimal plans. A derivative-free Sandwich algorithm is presented in which these bounds are used with three strategies to determine the location of the next Pareto optimal solution such that the uncertainty in the estimated PEF is maximally reduced. We show that an intelligent initial solution for a new Pareto optimal plan can be obtained by interpolation of fluence maps from neighbouring Pareto optimal plans. The method has been applied to a simplified clinical test case using two convex objective functions to map the trade-off between tumour dose heterogeneity and critical organ sparing. All three strategies produce representative estimates of the PEF. The new algorithm is particularly suitable for dynamic generation of Pareto optimal plans in interactive treatment planning.

Multiple-copy state discrimination: Thinking globally, acting locally

NASA Astrophysics Data System (ADS)

Higgins, B. L.; Doherty, A. C.; Bartlett, S. D.; Pryde, G. J.; Wiseman, H. M.

2011-05-01

We theoretically investigate schemes to discriminate between two nonorthogonal quantum states given multiple copies. We consider a number of state discrimination schemes as applied to nonorthogonal, mixed states of a qubit. In particular, we examine the difference that local and global optimization of local measurements makes to the probability of obtaining an erroneous result, in the regime of finite numbers of copies N, and in the asymptotic limit as N→∞. Five schemes are considered: optimal collective measurements over all copies, locally optimal local measurements in a fixed single-qubit measurement basis, globally optimal fixed local measurements, locally optimal adaptive local measurements, and globally optimal adaptive local measurements. Here an adaptive measurement is one in which the measurement basis can depend on prior measurement results. For each of these measurement schemes we determine the probability of error (for finite N) and the scaling of this error in the asymptotic limit. In the asymptotic limit, it is known analytically (and we verify numerically) that adaptive schemes have no advantage over the optimal fixed local scheme. Here we show moreover that, in this limit, the most naive scheme (locally optimal fixed local measurements) is as good as any noncollective scheme except for states with less than 2% mixture. For finite N, however, the most sophisticated local scheme (globally optimal adaptive local measurements) is better than any other noncollective scheme for any degree of mixture.

Multiple-copy state discrimination: Thinking globally, acting locally

DOE Office of Scientific and Technical Information (OSTI.GOV)

Higgins, B. L.; Pryde, G. J.; Wiseman, H. M.

2011-05-15

We theoretically investigate schemes to discriminate between two nonorthogonal quantum states given multiple copies. We consider a number of state discrimination schemes as applied to nonorthogonal, mixed states of a qubit. In particular, we examine the difference that local and global optimization of local measurements makes to the probability of obtaining an erroneous result, in the regime of finite numbers of copies N, and in the asymptotic limit as N{yields}{infinity}. Five schemes are considered: optimal collective measurements over all copies, locally optimal local measurements in a fixed single-qubit measurement basis, globally optimal fixed local measurements, locally optimal adaptive local measurements,more » and globally optimal adaptive local measurements. Here an adaptive measurement is one in which the measurement basis can depend on prior measurement results. For each of these measurement schemes we determine the probability of error (for finite N) and the scaling of this error in the asymptotic limit. In the asymptotic limit, it is known analytically (and we verify numerically) that adaptive schemes have no advantage over the optimal fixed local scheme. Here we show moreover that, in this limit, the most naive scheme (locally optimal fixed local measurements) is as good as any noncollective scheme except for states with less than 2% mixture. For finite N, however, the most sophisticated local scheme (globally optimal adaptive local measurements) is better than any other noncollective scheme for any degree of mixture.« less

Positivity-preserving numerical schemes for multidimensional advection

NASA Technical Reports Server (NTRS)

Leonard, B. P.; Macvean, M. K.; Lock, A. P.

1993-01-01

This report describes the construction of an explicit, single time-step, conservative, finite-volume method for multidimensional advective flow, based on a uniformly third-order polynomial interpolation algorithm (UTOPIA). Particular attention is paid to the problem of flow-to-grid angle-dependent, anisotropic distortion typical of one-dimensional schemes used component-wise. The third-order multidimensional scheme automatically includes certain cross-difference terms that guarantee good isotropy (and stability). However, above first-order, polynomial-based advection schemes do not preserve positivity (the multidimensional analogue of monotonicity). For this reason, a multidimensional generalization of the first author's universal flux-limiter is sought. This is a very challenging problem. A simple flux-limiter can be found; but this introduces strong anisotropic distortion. A more sophisticated technique, limiting part of the flux and then restoring the isotropy-maintaining cross-terms afterwards, gives more satisfactory results. Test cases are confined to two dimensions; three-dimensional extensions are briefly discussed.

Boundary Closures for Fourth-order Energy Stable Weighted Essentially Non-Oscillatory Finite Difference Schemes

NASA Technical Reports Server (NTRS)

Fisher, Travis C.; Carpenter, Mark H.; Yamaleev, Nail K.; Frankel, Steven H.

2009-01-01

A general strategy exists for constructing Energy Stable Weighted Essentially Non Oscillatory (ESWENO) finite difference schemes up to eighth-order on periodic domains. These ESWENO schemes satisfy an energy norm stability proof for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, boundary closures are developed for the fourth-order ESWENO scheme that maintain wherever possible the WENO stencil biasing properties, while satisfying the summation-by-parts (SBP) operator convention, thereby ensuring stability in an L2 norm. Second-order, and third-order boundary closures are developed that achieve stability in diagonal and block norms, respectively. The global accuracy for the second-order closures is three, and for the third-order closures is four. A novel set of non-uniform flux interpolation points is necessary near the boundaries to simultaneously achieve 1) accuracy, 2) the SBP convention, and 3) WENO stencil biasing mechanics.

Gaussian process regression to accelerate geometry optimizations relying on numerical differentiation

NASA Astrophysics Data System (ADS)

Schmitz, Gunnar; Christiansen, Ove

2018-06-01

We study how with means of Gaussian Process Regression (GPR) geometry optimizations, which rely on numerical gradients, can be accelerated. The GPR interpolates a local potential energy surface on which the structure is optimized. It is found to be efficient to combine results on a low computational level (HF or MP2) with the GPR-calculated gradient of the difference between the low level method and the target method, which is a variant of explicitly correlated Coupled Cluster Singles and Doubles with perturbative Triples correction CCSD(F12*)(T) in this study. Overall convergence is achieved if both the potential and the geometry are converged. Compared to numerical gradient-based algorithms, the number of required single point calculations is reduced. Although introducing an error due to the interpolation, the optimized structures are sufficiently close to the minimum of the target level of theory meaning that the reference and predicted minimum only vary energetically in the μEh regime.

Moving template analysis of crack growth. 1: Procedure development

NASA Astrophysics Data System (ADS)

Padovan, Joe; Guo, Y. H.

1994-06-01

Based on a moving template procedure, this two part series will develop a method to follow the crack tip physics in a self-adaptive manner which provides a uniformly accurate prediction of crack growth. For multiple crack environments, this is achieved by attaching a moving template to each crack tip. The templates are each individually oriented to follow the associated growth orientation and rate. In this part, the essentials of the procedure are derived for application to fatigue crack environments. Overall the scheme derived possesses several hierarchical levels, i.e. the global model, the interpolatively tied moving template, and a multilevel element death option to simulate the crack wake. To speed up computation, the hierarchical polytree scheme is used to reorganize the global stiffness inversion process. In addition to developing the various features of the scheme, the accuracy of predictions for various crack lengths is also benchmarked. Part 2 extends the scheme to multiple crack problems. Extensive benchmarking is also presented to verify the scheme.

Evaluation of MODFLOW-LGR in connection with a synthetic regional-scale model

USGS Publications Warehouse

Vilhelmsen, T.N.; Christensen, S.; Mehl, S.W.

2012-01-01

This work studies costs and benefits of utilizing local-grid refinement (LGR) as implemented in MODFLOW-LGR to simulate groundwater flow in a buried tunnel valley interacting with a regional aquifer. Two alternative LGR methods were used: the shared-node (SN) method and the ghost-node (GN) method. To conserve flows the SN method requires correction of sources and sinks in cells at the refined/coarse-grid interface. We found that the optimal correction method is case dependent and difficult to identify in practice. However, the results showed little difference and suggest that identifying the optimal method was of minor importance in our case. The GN method does not require corrections at the models' interface, and it uses a simpler head interpolation scheme than the SN method. The simpler scheme is faster but less accurate so that more iterations may be necessary. However, the GN method solved our flow problem more efficiently than the SN method. The MODFLOW-LGR results were compared with the results obtained using a globally coarse (GC) grid. The LGR simulations required one to two orders of magnitude longer run times than the GC model. However, the improvements of the numerical resolution around the buried valley substantially increased the accuracy of simulated heads and flows compared with the GC simulation. Accuracy further increased locally around the valley flanks when improving the geological resolution using the refined grid. Finally, comparing MODFLOW-LGR simulation with a globally refined (GR) grid showed that the refinement proportion of the model should not exceed 10% to 15% in order to secure method efficiency. ?? 2011, The Author(s). Ground Water ?? 2011, National Ground Water Association.

An interpolation-free ALE scheme for unsteady inviscid flows computations with large boundary displacements over three-dimensional adaptive grids

NASA Astrophysics Data System (ADS)

Re, B.; Dobrzynski, C.; Guardone, A.

2017-07-01

A novel strategy to solve the finite volume discretization of the unsteady Euler equations within the Arbitrary Lagrangian-Eulerian framework over tetrahedral adaptive grids is proposed. The volume changes due to local mesh adaptation are treated as continuous deformations of the finite volumes and they are taken into account by adding fictitious numerical fluxes to the governing equation. This peculiar interpretation enables to avoid any explicit interpolation of the solution between different grids and to compute grid velocities so that the Geometric Conservation Law is automatically fulfilled also for connectivity changes. The solution on the new grid is obtained through standard ALE techniques, thus preserving the underlying scheme properties, such as conservativeness, stability and monotonicity. The adaptation procedure includes node insertion, node deletion, edge swapping and points relocation and it is exploited both to enhance grid quality after the boundary movement and to modify the grid spacing to increase solution accuracy. The presented approach is assessed by three-dimensional simulations of steady and unsteady flow fields. The capability of dealing with large boundary displacements is demonstrated by computing the flow around the translating infinite- and finite-span NACA 0012 wing moving through the domain at the flight speed. The proposed adaptive scheme is applied also to the simulation of a pitching infinite-span wing, where the bi-dimensional character of the flow is well reproduced despite the three-dimensional unstructured grid. Finally, the scheme is exploited in a piston-induced shock-tube problem to take into account simultaneously the large deformation of the domain and the shock wave. In all tests, mesh adaptation plays a crucial role.

Efficient Characterization of Parametric Uncertainty of Complex (Bio)chemical Networks.

PubMed

Schillings, Claudia; Sunnåker, Mikael; Stelling, Jörg; Schwab, Christoph

2015-08-01

Parametric uncertainty is a particularly challenging and relevant aspect of systems analysis in domains such as systems biology where, both for inference and for assessing prediction uncertainties, it is essential to characterize the system behavior globally in the parameter space. However, current methods based on local approximations or on Monte-Carlo sampling cope only insufficiently with high-dimensional parameter spaces associated with complex network models. Here, we propose an alternative deterministic methodology that relies on sparse polynomial approximations. We propose a deterministic computational interpolation scheme which identifies most significant expansion coefficients adaptively. We present its performance in kinetic model equations from computational systems biology with several hundred parameters and state variables, leading to numerical approximations of the parametric solution on the entire parameter space. The scheme is based on adaptive Smolyak interpolation of the parametric solution at judiciously and adaptively chosen points in parameter space. As Monte-Carlo sampling, it is "non-intrusive" and well-suited for massively parallel implementation, but affords higher convergence rates. This opens up new avenues for large-scale dynamic network analysis by enabling scaling for many applications, including parameter estimation, uncertainty quantification, and systems design.

Efficient Characterization of Parametric Uncertainty of Complex (Bio)chemical Networks

PubMed Central

Schillings, Claudia; Sunnåker, Mikael; Stelling, Jörg; Schwab, Christoph

2015-01-01

Parametric uncertainty is a particularly challenging and relevant aspect of systems analysis in domains such as systems biology where, both for inference and for assessing prediction uncertainties, it is essential to characterize the system behavior globally in the parameter space. However, current methods based on local approximations or on Monte-Carlo sampling cope only insufficiently with high-dimensional parameter spaces associated with complex network models. Here, we propose an alternative deterministic methodology that relies on sparse polynomial approximations. We propose a deterministic computational interpolation scheme which identifies most significant expansion coefficients adaptively. We present its performance in kinetic model equations from computational systems biology with several hundred parameters and state variables, leading to numerical approximations of the parametric solution on the entire parameter space. The scheme is based on adaptive Smolyak interpolation of the parametric solution at judiciously and adaptively chosen points in parameter space. As Monte-Carlo sampling, it is “non-intrusive” and well-suited for massively parallel implementation, but affords higher convergence rates. This opens up new avenues for large-scale dynamic network analysis by enabling scaling for many applications, including parameter estimation, uncertainty quantification, and systems design. PMID:26317784

Non-oscillatory central differencing for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Nessyahu, Haim; Tadmor, Eitan

1988-01-01

Many of the recently developed high resolution schemes for hyperbolic conservation laws are based on upwind differencing. The building block for these schemes is the averaging of an appropriate Godunov solver; its time consuming part involves the field-by-field decomposition which is required in order to identify the direction of the wind. Instead, the use of the more robust Lax-Friedrichs (LxF) solver is proposed. The main advantage is simplicity: no Riemann problems are solved and hence field-by-field decompositions are avoided. The main disadvantage is the excessive numerical viscosity typical to the LxF solver. This is compensated for by using high-resolution MUSCL-type interpolants. Numerical experiments show that the quality of results obtained by such convenient central differencing is comparable with those of the upwind schemes.

Efficacy of Distortion Correction on Diffusion Imaging: Comparison of FSL Eddy and Eddy_Correct Using 30 and 60 Directions Diffusion Encoding

PubMed Central

Yamada, Haruyasu; Abe, Osamu; Shizukuishi, Takashi; Kikuta, Junko; Shinozaki, Takahiro; Dezawa, Ko; Nagano, Akira; Matsuda, Masayuki; Haradome, Hiroki; Imamura, Yoshiki

2014-01-01

Diffusion imaging is a unique noninvasive tool to detect brain white matter trajectory and integrity in vivo. However, this technique suffers from spatial distortion and signal pileup or dropout originating from local susceptibility gradients and eddy currents. Although there are several methods to mitigate these problems, most techniques can be applicable either to susceptibility or eddy-current induced distortion alone with a few exceptions. The present study compared the correction efficiency of FSL tools, “eddy_correct” and the combination of “eddy” and “topup” in terms of diffusion-derived fractional anisotropy (FA). The brain diffusion images were acquired from 10 healthy subjects using 30 and 60 directions encoding schemes based on the electrostatic repulsive forces. For the 30 directions encoding, 2 sets of diffusion images were acquired with the same parameters, except for the phase-encode blips which had opposing polarities along the anteroposterior direction. For the 60 directions encoding, non–diffusion-weighted and diffusion-weighted images were obtained with forward phase-encoding blips and non–diffusion-weighted images with the same parameter, except for the phase-encode blips, which had opposing polarities. FA images without and with distortion correction were compared in a voxel-wise manner with tract-based spatial statistics. We showed that images corrected with eddy and topup possessed higher FA values than images uncorrected and corrected with eddy_correct with trilinear (FSL default setting) or spline interpolation in most white matter skeletons, using both encoding schemes. Furthermore, the 60 directions encoding scheme was superior as measured by increased FA values to the 30 directions encoding scheme, despite comparable acquisition time. This study supports the combination of eddy and topup as a superior correction tool in diffusion imaging rather than the eddy_correct tool, especially with trilinear interpolation, using 60 directions encoding scheme. PMID:25405472

Dirichlet boundary conditions for arbitrary-shaped boundaries in stellarator-like magnetic fields for the Flux-Coordinate Independent method

NASA Astrophysics Data System (ADS)

Hill, Peter; Shanahan, Brendan; Dudson, Ben

2017-04-01

We present a technique for handling Dirichlet boundary conditions with the Flux Coordinate Independent (FCI) parallel derivative operator with arbitrary-shaped material geometry in general 3D magnetic fields. The FCI method constructs a finite difference scheme for ∇∥ by following field lines between poloidal planes and interpolating within planes. Doing so removes the need for field-aligned coordinate systems that suffer from singularities in the metric tensor at null points in the magnetic field (or equivalently, when q → ∞). One cost of this method is that as the field lines are not on the mesh, they may leave the domain at any point between neighbouring planes, complicating the application of boundary conditions. The Leg Value Fill (LVF) boundary condition scheme presented here involves an extrapolation/interpolation of the boundary value onto the field line end point. The usual finite difference scheme can then be used unmodified. We implement the LVF scheme in BOUT++ and use the Method of Manufactured Solutions to verify the implementation in a rectangular domain, and show that it does not modify the error scaling of the finite difference scheme. The use of LVF for arbitrary wall geometry is outlined. We also demonstrate the feasibility of using the FCI approach in no n-axisymmetric configurations for a simple diffusion model in a "straight stellarator" magnetic field. A Gaussian blob diffuses along the field lines, tracing out flux surfaces. Dirichlet boundary conditions impose a last closed flux surface (LCFS) that confines the density. Including a poloidal limiter moves the LCFS to a smaller radius. The expected scaling of the numerical perpendicular diffusion, which is a consequence of the FCI method, in stellarator-like geometry is recovered. A novel technique for increasing the parallel resolution during post-processing, in order to reduce artefacts in visualisations, is described.

Efficacy of distortion correction on diffusion imaging: comparison of FSL eddy and eddy_correct using 30 and 60 directions diffusion encoding.

PubMed

Yamada, Haruyasu; Abe, Osamu; Shizukuishi, Takashi; Kikuta, Junko; Shinozaki, Takahiro; Dezawa, Ko; Nagano, Akira; Matsuda, Masayuki; Haradome, Hiroki; Imamura, Yoshiki

2014-01-01

Diffusion imaging is a unique noninvasive tool to detect brain white matter trajectory and integrity in vivo. However, this technique suffers from spatial distortion and signal pileup or dropout originating from local susceptibility gradients and eddy currents. Although there are several methods to mitigate these problems, most techniques can be applicable either to susceptibility or eddy-current induced distortion alone with a few exceptions. The present study compared the correction efficiency of FSL tools, "eddy_correct" and the combination of "eddy" and "topup" in terms of diffusion-derived fractional anisotropy (FA). The brain diffusion images were acquired from 10 healthy subjects using 30 and 60 directions encoding schemes based on the electrostatic repulsive forces. For the 30 directions encoding, 2 sets of diffusion images were acquired with the same parameters, except for the phase-encode blips which had opposing polarities along the anteroposterior direction. For the 60 directions encoding, non-diffusion-weighted and diffusion-weighted images were obtained with forward phase-encoding blips and non-diffusion-weighted images with the same parameter, except for the phase-encode blips, which had opposing polarities. FA images without and with distortion correction were compared in a voxel-wise manner with tract-based spatial statistics. We showed that images corrected with eddy and topup possessed higher FA values than images uncorrected and corrected with eddy_correct with trilinear (FSL default setting) or spline interpolation in most white matter skeletons, using both encoding schemes. Furthermore, the 60 directions encoding scheme was superior as measured by increased FA values to the 30 directions encoding scheme, despite comparable acquisition time. This study supports the combination of eddy and topup as a superior correction tool in diffusion imaging rather than the eddy_correct tool, especially with trilinear interpolation, using 60 directions encoding scheme.

Time-stable overset grid method for hyperbolic problems using summation-by-parts operators

NASA Astrophysics Data System (ADS)

Sharan, Nek; Pantano, Carlos; Bodony, Daniel J.

2018-05-01

A provably time-stable method for solving hyperbolic partial differential equations arising in fluid dynamics on overset grids is presented in this paper. The method uses interface treatments based on the simultaneous approximation term (SAT) penalty method and derivative approximations that satisfy the summation-by-parts (SBP) property. Time-stability is proven using energy arguments in a norm that naturally relaxes to the standard diagonal norm when the overlap reduces to a traditional multiblock arrangement. The proposed overset interface closures are time-stable for arbitrary overlap arrangements. The information between grids is transferred using Lagrangian interpolation applied to the incoming characteristics, although other interpolation schemes could also be used. The conservation properties of the method are analyzed. Several one-, two-, and three-dimensional, linear and non-linear numerical examples are presented to confirm the stability and accuracy of the method. A performance comparison between the proposed SAT-based interface treatment and the commonly-used approach of injecting the interpolated data onto each grid is performed to highlight the efficacy of the SAT method.

Computation-aware algorithm selection approach for interlaced-to-progressive conversion

NASA Astrophysics Data System (ADS)

Park, Sang-Jun; Jeon, Gwanggil; Jeong, Jechang

2010-05-01

We discuss deinterlacing results in a computationally constrained and varied environment. The proposed computation-aware algorithm selection approach (CASA) for fast interlaced to progressive conversion algorithm consists of three methods: the line-averaging (LA) method for plain regions, the modified edge-based line-averaging (MELA) method for medium regions, and the proposed covariance-based adaptive deinterlacing (CAD) method for complex regions. The proposed CASA uses two criteria, mean-squared error (MSE) and CPU time, for assigning the method. We proposed a CAD method. The principle idea of CAD is based on the correspondence between the high and low-resolution covariances. We estimated the local covariance coefficients from an interlaced image using Wiener filtering theory and then used these optimal minimum MSE interpolation coefficients to obtain a deinterlaced image. The CAD method, though more robust than most known methods, was not found to be very fast compared to the others. To alleviate this issue, we proposed an adaptive selection approach using a fast deinterlacing algorithm rather than using only one CAD algorithm. The proposed hybrid approach of switching between the conventional schemes (LA and MELA) and our CAD was proposed to reduce the overall computational load. A reliable condition to be used for switching the schemes was presented after a wide set of initial training processes. The results of computer simulations showed that the proposed methods outperformed a number of methods presented in the literature.

Sparse coded image super-resolution using K-SVD trained dictionary based on regularized orthogonal matching pursuit.

PubMed

Sajjad, Muhammad; Mehmood, Irfan; Baik, Sung Wook

2015-01-01

Image super-resolution (SR) plays a vital role in medical imaging that allows a more efficient and effective diagnosis process. Usually, diagnosing is difficult and inaccurate from low-resolution (LR) and noisy images. Resolution enhancement through conventional interpolation methods strongly affects the precision of consequent processing steps, such as segmentation and registration. Therefore, we propose an efficient sparse coded image SR reconstruction technique using a trained dictionary. We apply a simple and efficient regularized version of orthogonal matching pursuit (ROMP) to seek the coefficients of sparse representation. ROMP has the transparency and greediness of OMP and the robustness of the L1-minization that enhance the dictionary learning process to capture feature descriptors such as oriented edges and contours from complex images like brain MRIs. The sparse coding part of the K-SVD dictionary training procedure is modified by substituting OMP with ROMP. The dictionary update stage allows simultaneously updating an arbitrary number of atoms and vectors of sparse coefficients. In SR reconstruction, ROMP is used to determine the vector of sparse coefficients for the underlying patch. The recovered representations are then applied to the trained dictionary, and finally, an optimization leads to high-resolution output of high-quality. Experimental results demonstrate that the super-resolution reconstruction quality of the proposed scheme is comparatively better than other state-of-the-art schemes.

Fast dose kernel interpolation using Fourier transform with application to permanent prostate brachytherapy dosimetry.

PubMed

Liu, Derek; Sloboda, Ron S

2014-05-01

Boyer and Mok proposed a fast calculation method employing the Fourier transform (FT), for which calculation time is independent of the number of seeds but seed placement is restricted to calculation grid points. Here an interpolation method is described enabling unrestricted seed placement while preserving the computational efficiency of the original method. The Iodine-125 seed dose kernel was sampled and selected values were modified to optimize interpolation accuracy for clinically relevant doses. For each seed, the kernel was shifted to the nearest grid point via convolution with a unit impulse, implemented in the Fourier domain. The remaining fractional shift was performed using a piecewise third-order Lagrange filter. Implementation of the interpolation method greatly improved FT-based dose calculation accuracy. The dose distribution was accurate to within 2% beyond 3 mm from each seed. Isodose contours were indistinguishable from explicit TG-43 calculation. Dose-volume metric errors were negligible. Computation time for the FT interpolation method was essentially the same as Boyer's method. A FT interpolation method for permanent prostate brachytherapy TG-43 dose calculation was developed which expands upon Boyer's original method and enables unrestricted seed placement. The proposed method substantially improves the clinically relevant dose accuracy with negligible additional computation cost, preserving the efficiency of the original method.

Comparative study of numerical schemes of TVD3, UNO3-ACM and optimized compact scheme

NASA Technical Reports Server (NTRS)

Lee, Duck-Joo; Hwang, Chang-Jeon; Ko, Duck-Kon; Kim, Jae-Wook

1995-01-01

Three different schemes are employed to solve the benchmark problem. The first one is a conventional TVD-MUSCL (Monotone Upwind Schemes for Conservation Laws) scheme. The second scheme is a UNO3-ACM (Uniformly Non-Oscillatory Artificial Compression Method) scheme. The third scheme is an optimized compact finite difference scheme modified by us: the 4th order Runge Kutta time stepping, the 4th order pentadiagonal compact spatial discretization with the maximum resolution characteristics. The problems of category 1 are solved by using the second (UNO3-ACM) and third (Optimized Compact) schemes. The problems of category 2 are solved by using the first (TVD3) and second (UNO3-ACM) schemes. The problem of category 5 is solved by using the first (TVD3) scheme. It can be concluded from the present calculations that the Optimized Compact scheme and the UN03-ACM show good resolutions for category 1 and category 2 respectively.

Weighted Non-linear Compact Schemes for the Direct Numerical Simulation of Compressible, Turbulent Flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Debojyoti; Baeder, James D.

2014-01-21

A new class of compact-reconstruction weighted essentially non-oscillatory (CRWENO) schemes were introduced (Ghosh and Baeder in SIAM J Sci Comput 34(3): A1678–A1706, 2012) with high spectral resolution and essentially non-oscillatory behavior across discontinuities. The CRWENO schemes use solution-dependent weights to combine lower-order compact interpolation schemes and yield a high-order compact scheme for smooth solutions and a non-oscillatory compact scheme near discontinuities. The new schemes result in lower absolute errors, and improved resolution of discontinuities and smaller length scales, compared to the weighted essentially non-oscillatory (WENO) scheme of the same order of convergence. Several improvements to the smoothness-dependent weights, proposed inmore » the literature in the context of the WENO schemes, address the drawbacks of the original formulation. This paper explores these improvements in the context of the CRWENO schemes and compares the different formulations of the non-linear weights for flow problems with small length scales as well as discontinuities. Simplified one- and two-dimensional inviscid flow problems are solved to demonstrate the numerical properties of the CRWENO schemes and its different formulations. Canonical turbulent flow problems—the decay of isotropic turbulence and the shock-turbulence interaction—are solved to assess the performance of the schemes for the direct numerical simulation of compressible, turbulent flows« less

Higher-dimensional Wannier Interpolation for the Modern Theory of the Dzyaloshinskii-Moriya Interaction: Application to Co-based Trilayers

NASA Astrophysics Data System (ADS)

Hanke, Jan-Philipp; Freimuth, Frank; Blügel, Stefan; Mokrousov, Yuriy

2018-04-01

We present an advanced first-principles formalism to evaluate the Dzyaloshinskii-Moriya interaction (DMI) in its modern theory as well as Berry curvatures in complex spaces based on a higher-dimensional Wannier interpolation. Our method is applied to the Co-based trilayer systems IrδPt1-δ/Co/Pt and AuγPt1-γ/Co/Pt, where we gain insights into the correlations between the electronic structure and the DMI, and we uncover prominent sign changes of the chiral interaction with the overlayer composition. Beyond the discussed phenomena, the scope of applications of our Wannier-based scheme is particularly broad as it is ideally suited to study efficiently the Hamiltonian evolution under the slow variation of very general parameters.

Automatic elastic image registration by interpolation of 3D rotations and translations from discrete rigid-body transformations.

PubMed

Walimbe, Vivek; Shekhar, Raj

2006-12-01

We present an algorithm for automatic elastic registration of three-dimensional (3D) medical images. Our algorithm initially recovers the global spatial mismatch between the reference and floating images, followed by hierarchical octree-based subdivision of the reference image and independent registration of the floating image with the individual subvolumes of the reference image at each hierarchical level. Global as well as local registrations use the six-parameter full rigid-body transformation model and are based on maximization of normalized mutual information (NMI). To ensure robustness of the subvolume registration with low voxel counts, we calculate NMI using a combination of current and prior mutual histograms. To generate a smooth deformation field, we perform direct interpolation of six-parameter rigid-body subvolume transformations obtained at the last subdivision level. Our interpolation scheme involves scalar interpolation of the 3D translations and quaternion interpolation of the 3D rotational pose. We analyzed the performance of our algorithm through experiments involving registration of synthetically deformed computed tomography (CT) images. Our algorithm is general and can be applied to image pairs of any two modalities of most organs. We have demonstrated successful registration of clinical whole-body CT and positron emission tomography (PET) images using this algorithm. The registration accuracy for this application was evaluated, based on validation using expert-identified anatomical landmarks in 15 CT-PET image pairs. The algorithm's performance was comparable to the average accuracy observed for three expert-determined registrations in the same 15 image pairs.

The Structure of Optimum Interpolation Functions.

DTIC Science & Technology

1983-02-01

Daniel F. Merriam, ed., Plenum Press, 1970. 2. Hiroshi Akima, "Comments on ’Optimal Contour Mapping Using Universal Kriging’ by Ricardo 0. Olea ," (with...Kriging," Mathematical Geology 14 (1982), 249-257. 21 27. Ricardo 0. Olea , "Optimal Contour Mapping Using Universal Kriging," J. of Geophysical Res. 79

Volumetric three-dimensional intravascular ultrasound visualization using shape-based nonlinear interpolation

PubMed Central

2013-01-01

Background Intravascular ultrasound (IVUS) is a standard imaging modality for identification of plaque formation in the coronary and peripheral arteries. Volumetric three-dimensional (3D) IVUS visualization provides a powerful tool to overcome the limited comprehensive information of 2D IVUS in terms of complex spatial distribution of arterial morphology and acoustic backscatter information. Conventional 3D IVUS techniques provide sub-optimal visualization of arterial morphology or lack acoustic information concerning arterial structure due in part to low quality of image data and the use of pixel-based IVUS image reconstruction algorithms. In the present study, we describe a novel volumetric 3D IVUS reconstruction algorithm to utilize IVUS signal data and a shape-based nonlinear interpolation. Methods We developed an algorithm to convert a series of IVUS signal data into a fully volumetric 3D visualization. Intermediary slices between original 2D IVUS slices were generated utilizing the natural cubic spline interpolation to consider the nonlinearity of both vascular structure geometry and acoustic backscatter in the arterial wall. We evaluated differences in image quality between the conventional pixel-based interpolation and the shape-based nonlinear interpolation methods using both virtual vascular phantom data and in vivo IVUS data of a porcine femoral artery. Volumetric 3D IVUS images of the arterial segment reconstructed using the two interpolation methods were compared. Results In vitro validation and in vivo comparative studies with the conventional pixel-based interpolation method demonstrated more robustness of the shape-based nonlinear interpolation algorithm in determining intermediary 2D IVUS slices. Our shape-based nonlinear interpolation demonstrated improved volumetric 3D visualization of the in vivo arterial structure and more realistic acoustic backscatter distribution compared to the conventional pixel-based interpolation method. Conclusions This novel 3D IVUS visualization strategy has the potential to improve ultrasound imaging of vascular structure information, particularly atheroma determination. Improved volumetric 3D visualization with accurate acoustic backscatter information can help with ultrasound molecular imaging of atheroma component distribution. PMID:23651569

A novel forward projection-based metal artifact reduction method for flat-detector computed tomography.

PubMed

Prell, Daniel; Kyriakou, Yiannis; Beister, Marcel; Kalender, Willi A

2009-11-07

Metallic implants generate streak-like artifacts in flat-detector computed tomography (FD-CT) reconstructed volumetric images. This study presents a novel method for reducing these disturbing artifacts by inserting discarded information into the original rawdata using a three-step correction procedure and working directly with each detector element. Computation times are minimized by completely implementing the correction process on graphics processing units (GPUs). First, the original volume is corrected using a three-dimensional interpolation scheme in the rawdata domain, followed by a second reconstruction. This metal artifact-reduced volume is then segmented into three materials, i.e. air, soft-tissue and bone, using a threshold-based algorithm. Subsequently, a forward projection of the obtained tissue-class model substitutes the missing or corrupted attenuation values directly for each flat detector element that contains attenuation values corresponding to metal parts, followed by a final reconstruction. Experiments using tissue-equivalent phantoms showed a significant reduction of metal artifacts (deviations of CT values after correction compared to measurements without metallic inserts reduced typically to below 20 HU, differences in image noise to below 5 HU) caused by the implants and no significant resolution losses even in areas close to the inserts. To cover a variety of different cases, cadaver measurements and clinical images in the knee, head and spine region were used to investigate the effectiveness and applicability of our method. A comparison to a three-dimensional interpolation correction showed that the new approach outperformed interpolation schemes. Correction times are minimized, and initial and corrected images are made available at almost the same time (12.7 s for the initial reconstruction, 46.2 s for the final corrected image compared to 114.1 s and 355.1 s on central processing units (CPUs)).

Fiber orientation interpolation for the multiscale analysis of short fiber reinforced composite parts

NASA Astrophysics Data System (ADS)

Köbler, Jonathan; Schneider, Matti; Ospald, Felix; Andrä, Heiko; Müller, Ralf

2018-06-01

For short fiber reinforced plastic parts the local fiber orientation has a strong influence on the mechanical properties. To enable multiscale computations using surrogate models we advocate a two-step identification strategy. Firstly, for a number of sample orientations an effective model is derived by numerical methods available in the literature. Secondly, to cover a general orientation state, these effective models are interpolated. In this article we develop a novel and effective strategy to carry out this interpolation. Firstly, taking into account symmetry arguments, we reduce the fiber orientation phase space to a triangle in R^2 . For an associated triangulation of this triangle we furnish each node with an surrogate model. Then, we use linear interpolation on the fiber orientation triangle to equip each fiber orientation state with an effective stress. The proposed approach is quite general, and works for any physically nonlinear constitutive law on the micro-scale, as long as surrogate models for single fiber orientation states can be extracted. To demonstrate the capabilities of our scheme we study the viscoelastic creep behavior of short glass fiber reinforced PA66, and use Schapery's collocation method together with FFT-based computational homogenization to derive single orientation state effective models. We discuss the efficient implementation of our method, and present results of a component scale computation on a benchmark component by using ABAQUS ®.

Fiber orientation interpolation for the multiscale analysis of short fiber reinforced composite parts

NASA Astrophysics Data System (ADS)

Köbler, Jonathan; Schneider, Matti; Ospald, Felix; Andrä, Heiko; Müller, Ralf

2018-04-01

For short fiber reinforced plastic parts the local fiber orientation has a strong influence on the mechanical properties. To enable multiscale computations using surrogate models we advocate a two-step identification strategy. Firstly, for a number of sample orientations an effective model is derived by numerical methods available in the literature. Secondly, to cover a general orientation state, these effective models are interpolated. In this article we develop a novel and effective strategy to carry out this interpolation. Firstly, taking into account symmetry arguments, we reduce the fiber orientation phase space to a triangle in R^2 . For an associated triangulation of this triangle we furnish each node with an surrogate model. Then, we use linear interpolation on the fiber orientation triangle to equip each fiber orientation state with an effective stress. The proposed approach is quite general, and works for any physically nonlinear constitutive law on the micro-scale, as long as surrogate models for single fiber orientation states can be extracted. To demonstrate the capabilities of our scheme we study the viscoelastic creep behavior of short glass fiber reinforced PA66, and use Schapery's collocation method together with FFT-based computational homogenization to derive single orientation state effective models. We discuss the efficient implementation of our method, and present results of a component scale computation on a benchmark component by using ABAQUS ®.

Space Weather Activities of IONOLAB Group: TEC Mapping

NASA Astrophysics Data System (ADS)

Arikan, F.; Yilmaz, A.; Arikan, O.; Sayin, I.; Gurun, M.; Akdogan, K. E.; Yildirim, S. A.

2009-04-01

Being a key player in Space Weather, ionospheric variability affects the performance of both communication and navigation systems. To improve the performance of these systems, ionosphere has to be monitored. Total Electron Content (TEC), line integral of the electron density along a ray path, is an important parameter to investigate the ionospheric variability. A cost-effective way of obtaining TEC is by using dual-frequency GPS receivers. Since these measurements are sparse in space, accurate and robust interpolation techniques are needed to interpolate (or map) the TEC distribution for a given region in space. However, the TEC data derived from GPS measurements contain measurement noise, model and computational errors. Thus, it is necessary to analyze the interpolation performance of the techniques on synthetic data sets that can represent various ionospheric states. By this way, interpolation performance of the techniques can be compared over many parameters that can be controlled to represent the desired ionospheric states. In this study, Multiquadrics, Inverse Distance Weighting (IDW), Cubic Splines, Ordinary and Universal Kriging, Random Field Priors (RFP), Multi-Layer Perceptron Neural Network (MLP-NN), and Radial Basis Function Neural Network (RBF-NN) are employed as the spatial interpolation algorithms. These mapping techniques are initially tried on synthetic TEC surfaces for parameter and coefficient optimization and determination of error bounds. Interpolation performance of these methods are compared on synthetic TEC surfaces over the parameters of sampling pattern, number of samples, the variability of the surface and the trend type in the TEC surfaces. By examining the performance of the interpolation methods, it is observed that both Kriging, RFP and NN have important advantages and possible disadvantages depending on the given constraints. It is also observed that the determining parameter in the error performance is the trend in the Ionosphere. Optimization of the algorithms in terms of their performance parameters (like the choice of the semivariogram function for Kriging algorithms and the hidden layer and neuron numbers for MLP-NN) mostly depend on the behavior of the ionosphere at that given time instant for the desired region. The sampling pattern and number of samples are the other important parameters that may contribute to the higher errors in reconstruction. For example, for all of the above listed algorithms, hexagonal regular sampling of the ionosphere provides the lowest reconstruction error and the performance significantly degrades as the samples in the region become sparse and clustered. The optimized models and coefficients are applied to regional GPS-TEC mapping using the IONOLAB-TEC data (www.ionolab.org). Both Kriging combined with Kalman Filter and dynamic modeling of NN are also implemented as first trials of TEC and space weather predictions.

Optimal rotated staggered-grid finite-difference schemes for elastic wave modeling in TTI media

NASA Astrophysics Data System (ADS)

Yang, Lei; Yan, Hongyong; Liu, Hong

2015-11-01

The rotated staggered-grid finite-difference (RSFD) is an effective approach for numerical modeling to study the wavefield characteristics in tilted transversely isotropic (TTI) media. But it surfaces from serious numerical dispersion, which directly affects the modeling accuracy. In this paper, we propose two different optimal RSFD schemes based on the sampling approximation (SA) method and the least-squares (LS) method respectively to overcome this problem. We first briefly introduce the RSFD theory, based on which we respectively derive the SA-based RSFD scheme and the LS-based RSFD scheme. Then different forms of analysis are used to compare the SA-based RSFD scheme and the LS-based RSFD scheme with the conventional RSFD scheme, which is based on the Taylor-series expansion (TE) method. The contrast in numerical accuracy analysis verifies the greater accuracy of the two proposed optimal schemes, and indicates that these schemes can effectively widen the wavenumber range with great accuracy compared with the TE-based RSFD scheme. Further comparisons between these two optimal schemes show that at small wavenumbers, the SA-based RSFD scheme performs better, while at large wavenumbers, the LS-based RSFD scheme leads to a smaller error. Finally, the modeling results demonstrate that for the same operator length, the SA-based RSFD scheme and the LS-based RSFD scheme can achieve greater accuracy than the TE-based RSFD scheme, while for the same accuracy, the optimal schemes can adopt shorter difference operators to save computing time.

Continuous assimilation of simulated Geosat altimetric sea level into an eddy-resolving numerical ocean model. I - Sea level differences. II - Referenced sea level differences

NASA Technical Reports Server (NTRS)

White, Warren B.; Tai, Chang-Kou; Holland, William R.

1990-01-01

The optimal interpolation method of Lorenc (1981) was used to conduct continuous assimilation of altimetric sea level differences from the simulated Geosat exact repeat mission (ERM) into a three-layer quasi-geostrophic eddy-resolving numerical ocean box model that simulates the statistics of mesoscale eddy activity in the western North Pacific. Assimilation was conducted continuously as the Geosat tracks appeared in simulated real time/space, with each track repeating every 17 days, but occurring at different times and locations within the 17-day period, as would have occurred in a realistic nowcast situation. This interpolation method was also used to conduct the assimilation of referenced altimetric sea level differences into the same model, performing the referencing of altimetric sea sevel differences by using the simulated sea level. The results of this dynamical interpolation procedure are compared with those of a statistical (i.e., optimum) interpolation procedure.

Transfer of uncertainty of space-borne high resolution rainfall products at ungauged regions

NASA Astrophysics Data System (ADS)

Tang, Ling

Hydrologically relevant characteristics of high resolution (˜ 0.25 degree, 3 hourly) satellite rainfall uncertainty were derived as a function of season and location using a six year (2002-2007) archive of National Aeronautics and Space Administration (NASA)'s Tropical Rainfall Measuring Mission (TRMM) Multi-satellite Precipitation Analysis (TMPA) precipitation data. The Next Generation Radar (NEXRAD) Stage IV rainfall data over the continental United States was used as ground validation (GV) data. A geostatistical mapping scheme was developed and tested for transfer (i.e., spatial interpolation) of uncertainty information from GV regions to the vast non-GV regions by leveraging the error characterization work carried out in the earlier step. The open question explored here was, "If 'error' is defined on the basis of independent ground validation (GV) data, how are error metrics estimated for a satellite rainfall data product without the need for much extensive GV data?" After a quantitative analysis of the spatial and temporal structure of the satellite rainfall uncertainty, a proof-of-concept geostatistical mapping scheme (based on the kriging method) was evaluated. The idea was to understand how realistic the idea of 'transfer' is for the GPM era. It was found that it was indeed technically possible to transfer error metrics from a gauged to an ungauged location for certain error metrics and that a regionalized error metric scheme for GPM may be possible. The uncertainty transfer scheme based on a commonly used kriging method (ordinary kriging) was then assessed further at various timescales (climatologic, seasonal, monthly and weekly), and as a function of the density of GV coverage. The results indicated that if a transfer scheme for estimating uncertainty metrics was finer than seasonal scale (ranging from 3-6 hourly to weekly-monthly), the effectiveness for uncertainty transfer worsened significantly. Next, a comprehensive assessment of different kriging methods for spatial transfer (interpolation) of error metrics was performed. Three kriging methods for spatial interpolation are compared, which are: ordinary kriging (OK), indicator kriging (IK) and disjunctive kriging (DK). Additional comparison with the simple inverse distance weighting (IDW) method was also performed to quantify the added benefit (if any) of using geostatistical methods. The overall performance ranking of the kriging methods was found to be as follows: OK=DK > IDW > IK. Lastly, various metrics of satellite rainfall uncertainty were identified for two large continental landmasses that share many similar Koppen climate zones, United States and Australia. The dependence of uncertainty as a function of gauge density was then investigated. The investigation revealed that only the first and second ordered moments of error are most amenable to a Koppen-type climate type classification in different continental landmasses.

A rapid boundary integral equation technique for protein electrostatics

NASA Astrophysics Data System (ADS)

Grandison, Scott; Penfold, Robert; Vanden-Broeck, Jean-Marc

2007-06-01

A new boundary integral formulation is proposed for the solution of electrostatic field problems involving piecewise uniform dielectric continua. Direct Coulomb contributions to the total potential are treated exactly and Green's theorem is applied only to the residual reaction field generated by surface polarisation charge induced at dielectric boundaries. The implementation shows significantly improved numerical stability over alternative schemes involving the total field or its surface normal derivatives. Although strictly respecting the electrostatic boundary conditions, the partitioned scheme does introduce a jump artefact at the interface. Comparison against analytic results in canonical geometries, however, demonstrates that simple interpolation near the boundary is a cheap and effective way to circumvent this characteristic in typical applications. The new scheme is tested in a naive model to successfully predict the ground state orientation of biomolecular aggregates comprising the soybean storage protein, glycinin.

Bayesian Tracking of Emerging Epidemics Using Ensemble Optimal Statistical Interpolation

PubMed Central

Cobb, Loren; Krishnamurthy, Ashok; Mandel, Jan; Beezley, Jonathan D.

2014-01-01

We present a preliminary test of the Ensemble Optimal Statistical Interpolation (EnOSI) method for the statistical tracking of an emerging epidemic, with a comparison to its popular relative for Bayesian data assimilation, the Ensemble Kalman Filter (EnKF). The spatial data for this test was generated by a spatial susceptible-infectious-removed (S-I-R) epidemic model of an airborne infectious disease. Both tracking methods in this test employed Poisson rather than Gaussian noise, so as to handle epidemic data more accurately. The EnOSI and EnKF tracking methods worked well on the main body of the simulated spatial epidemic, but the EnOSI was able to detect and track a distant secondary focus of infection that the EnKF missed entirely. PMID:25113590

Optimization of storage tank locations in an urban stormwater drainage system using a two-stage approach.

PubMed

Wang, Mingming; Sun, Yuanxiang; Sweetapple, Chris

2017-12-15

Storage is important for flood mitigation and non-point source pollution control. However, to seek a cost-effective design scheme for storage tanks is very complex. This paper presents a two-stage optimization framework to find an optimal scheme for storage tanks using storm water management model (SWMM). The objectives are to minimize flooding, total suspended solids (TSS) load and storage cost. The framework includes two modules: (i) the analytical module, which evaluates and ranks the flooding nodes with the analytic hierarchy process (AHP) using two indicators (flood depth and flood duration), and then obtains the preliminary scheme by calculating two efficiency indicators (flood reduction efficiency and TSS reduction efficiency); (ii) the iteration module, which obtains an optimal scheme using a generalized pattern search (GPS) method based on the preliminary scheme generated by the analytical module. The proposed approach was applied to a catchment in CZ city, China, to test its capability in choosing design alternatives. Different rainfall scenarios are considered to test its robustness. The results demonstrate that the optimal framework is feasible, and the optimization is fast based on the preliminary scheme. The optimized scheme is better than the preliminary scheme for reducing runoff and pollutant loads under a given storage cost. The multi-objective optimization framework presented in this paper may be useful in finding the best scheme of storage tanks or low impact development (LID) controls. Copyright © 2017 Elsevier Ltd. All rights reserved.

Meshless Modeling of Deformable Shapes and their Motion

PubMed Central

Adams, Bart; Ovsjanikov, Maks; Wand, Michael; Seidel, Hans-Peter; Guibas, Leonidas J.

2010-01-01

We present a new framework for interactive shape deformation modeling and key frame interpolation based on a meshless finite element formulation. Starting from a coarse nodal sampling of an object’s volume, we formulate rigidity and volume preservation constraints that are enforced to yield realistic shape deformations at interactive frame rates. Additionally, by specifying key frame poses of the deforming shape and optimizing the nodal displacements while targeting smooth interpolated motion, our algorithm extends to a motion planning framework for deformable objects. This allows reconstructing smooth and plausible deformable shape trajectories in the presence of possibly moving obstacles. The presented results illustrate that our framework can handle complex shapes at interactive rates and hence is a valuable tool for animators to realistically and efficiently model and interpolate deforming 3D shapes. PMID:24839614

Near-Space TOPSAR Large-Scene Full-Aperture Imaging Scheme Based on Two-Step Processing

PubMed Central

Zhang, Qianghui; Wu, Junjie; Li, Wenchao; Huang, Yulin; Yang, Jianyu; Yang, Haiguang

2016-01-01

Free of the constraints of orbit mechanisms, weather conditions and minimum antenna area, synthetic aperture radar (SAR) equipped on near-space platform is more suitable for sustained large-scene imaging compared with the spaceborne and airborne counterparts. Terrain observation by progressive scans (TOPS), which is a novel wide-swath imaging mode and allows the beam of SAR to scan along the azimuth, can reduce the time of echo acquisition for large scene. Thus, near-space TOPS-mode SAR (NS-TOPSAR) provides a new opportunity for sustained large-scene imaging. An efficient full-aperture imaging scheme for NS-TOPSAR is proposed in this paper. In this scheme, firstly, two-step processing (TSP) is adopted to eliminate the Doppler aliasing of the echo. Then, the data is focused in two-dimensional frequency domain (FD) based on Stolt interpolation. Finally, a modified TSP (MTSP) is performed to remove the azimuth aliasing. Simulations are presented to demonstrate the validity of the proposed imaging scheme for near-space large-scene imaging application. PMID:27472341

A three-dimensional algebraic grid generation scheme for gas turbine combustors with inclined slots

NASA Technical Reports Server (NTRS)

Yang, S. L.; Cline, M. C.; Chen, R.; Chang, Y. L.

1993-01-01

A 3D algebraic grid generation scheme is presented for generating the grid points inside gas turbine combustors with inclined slots. The scheme is based on the 2D transfinite interpolation method. Since the scheme is a 2D approach, it is very efficient and can easily be extended to gas turbine combustors with either dilution hole or slot configurations. To demonstrate the feasibility and the usefulness of the technique, a numerical study of the quick-quench/lean-combustion (QQ/LC) zones of a staged turbine combustor is given. Preliminary results illustrate some of the major features of the flow and temperature fields in the QQ/LC zones. Formation of co- and counter-rotating bulk flow and shape temperature fields can be observed clearly, and the resulting patterns are consistent with experimental observations typical of the confined slanted jet-in-cross flow. Numerical solutions show the method to be an efficient and reliable tool for generating computational grids for analyzing gas turbine combustors with slanted slots.

Analysis/forecast experiments with a flow-dependent correlation function using FGGE data

NASA Technical Reports Server (NTRS)

Baker, W. E.; Bloom, S. C.; Carus, H.; Nestler, M. S.

1986-01-01

The use of a flow-dependent correlation function to improve the accuracy of an optimum interpolation (OI) scheme is examined. The development of the correlation function for the OI analysis scheme used for numerical weather prediction is described. The scheme uses a multivariate surface analysis over the oceans to model the pressure-wind error cross-correlation and it has the ability to use an error correlation function that is flow- and geographically-dependent. A series of four-day data assimilation experiments, conducted from January 5-9, 1979, were used to investigate the effect of the different features of the OI scheme (error correlation) on forecast skill for the barotropic lows and highs. The skill of the OI was compared with that of a successive correlation method (SCM) of analysis. It is observed that the largest difference in the correlation statistics occurred in barotropic and baroclinic lows and highs. The comparison reveals that the OI forecasts were more accurate than the SCM forecasts.

Development and validation of segmentation and interpolation techniques in sinograms for metal artifact suppression in CT.

PubMed

Veldkamp, Wouter J H; Joemai, Raoul M S; van der Molen, Aart J; Geleijns, Jacob

2010-02-01

Metal prostheses cause artifacts in computed tomography (CT) images. The purpose of this work was to design an efficient and accurate metal segmentation in raw data to achieve artifact suppression and to improve CT image quality for patients with metal hip or shoulder prostheses. The artifact suppression technique incorporates two steps: metal object segmentation in raw data and replacement of the segmented region by new values using an interpolation scheme, followed by addition of the scaled metal signal intensity. Segmentation of metal is performed directly in sinograms, making it efficient and different from current methods that perform segmentation in reconstructed images in combination with Radon transformations. Metal signal segmentation is achieved by using a Markov random field model (MRF). Three interpolation methods are applied and investigated. To provide a proof of concept, CT data of five patients with metal implants were included in the study, as well as CT data of a PMMA phantom with Teflon, PVC, and titanium inserts. Accuracy was determined quantitatively by comparing mean Hounsfield (HU) values and standard deviation (SD) as a measure of distortion in phantom images with titanium (original and suppressed) and without titanium insert. Qualitative improvement was assessed by comparing uncorrected clinical images with artifact suppressed images. Artifacts in CT data of a phantom and five patients were automatically suppressed. The general visibility of structures clearly improved. In phantom images, the technique showed reduced SD close to the SD for the case where titanium was not inserted, indicating improved image quality. HU values in corrected images were different from expected values for all interpolation methods. Subtle differences between interpolation methods were found. The new artifact suppression design is efficient, for instance, in terms of preserving spatial resolution, as it is applied directly to original raw data. It successfully reduced artifacts in CT images of five patients and in phantom images. Sophisticated interpolation methods are needed to obtain reliable HU values close to the prosthesis.

Adapting Better Interpolation Methods to Model Amphibious MT Data Along the Cascadian Subduction Zone.

NASA Astrophysics Data System (ADS)

Parris, B. A.; Egbert, G. D.; Key, K.; Livelybrooks, D.

2016-12-01

Magnetotellurics (MT) is an electromagnetic technique used to model the inner Earth's electrical conductivity structure. MT data can be analyzed using iterative, linearized inversion techniques to generate models imaging, in particular, conductive partial melts and aqueous fluids that play critical roles in subduction zone processes and volcanism. For example, the Magnetotelluric Observations of Cascadia using a Huge Array (MOCHA) experiment provides amphibious data useful for imaging subducted fluids from trench to mantle wedge corner. When using MOD3DEM(Egbert et al. 2012), a finite difference inversion package, we have encountered problems inverting, particularly, sea floor stations due to the strong, nearby conductivity gradients. As a work-around, we have found that denser, finer model grids near the land-sea interface produce better inversions, as characterized by reduced data residuals. This is partly to be due to our ability to more accurately capture topography and bathymetry. We are experimenting with improved interpolation schemes that more accurately track EM fields across cell boundaries, with an eye to enhancing the accuracy of the simulated responses and, thus, inversion results. We are adapting how MOD3DEM interpolates EM fields in two ways. The first seeks to improve weighting functions for interpolants to better address current continuity across grid boundaries. Electric fields are interpolated using a tri-linear spline technique, where the eight nearest electrical field estimates are each given weights determined by the technique, a kind of weighted average. We are modifying these weights to include cross-boundary conductivity ratios to better model current continuity. We are also adapting some of the techniques discussed in Shantsev et al (2014) to enhance the accuracy of the interpolated fields calculated by our forward solver, as well as to better approximate the sensitivities passed to the software's Jacobian that are used to generate a new forward model during each iteration of the inversion.

A fully 3D approach for metal artifact reduction in computed tomography.

PubMed

Kratz, Barbel; Weyers, Imke; Buzug, Thorsten M

2012-11-01

In computed tomography imaging metal objects in the region of interest introduce inconsistencies during data acquisition. Reconstructing these data leads to an image in spatial domain including star-shaped or stripe-like artifacts. In order to enhance the quality of the resulting image the influence of the metal objects can be reduced. Here, a metal artifact reduction (MAR) approach is proposed that is based on a recomputation of the inconsistent projection data using a fully three-dimensional Fourier-based interpolation. The success of the projection space restoration depends sensitively on a sensible continuation of neighboring structures into the recomputed area. Fortunately, structural information of the entire data is inherently included in the Fourier space of the data. This can be used for a reasonable recomputation of the inconsistent projection data. The key step of the proposed MAR strategy is the recomputation of the inconsistent projection data based on an interpolation using nonequispaced fast Fourier transforms (NFFT). The NFFT interpolation can be applied in arbitrary dimension. The approach overcomes the problem of adequate neighborhood definitions on irregular grids, since this is inherently given through the usage of higher dimensional Fourier transforms. Here, applications up to the third interpolation dimension are presented and validated. Furthermore, prior knowledge may be included by an appropriate damping of the transform during the interpolation step. This MAR method is applicable on each angular view of a detector row, on two-dimensional projection data as well as on three-dimensional projection data, e.g., a set of sequential acquisitions at different spatial positions, projection data of a spiral acquisition, or cone-beam projection data. Results of the novel MAR scheme based on one-, two-, and three-dimensional NFFT interpolations are presented. All results are compared in projection data space and spatial domain with the well-known one-dimensional linear interpolation strategy. In conclusion, it is recommended to include as much spatial information into the recomputation step as possible. This is realized by increasing the dimension of the NFFT. The resulting image quality can be enhanced considerably.

3-D ultrasound volume reconstruction using the direct frame interpolation method.

PubMed

Scheipers, Ulrich; Koptenko, Sergei; Remlinger, Rachel; Falco, Tony; Lachaine, Martin

2010-11-01

A new method for 3-D ultrasound volume reconstruction using tracked freehand 3-D ultrasound is proposed. The method is based on solving the forward volume reconstruction problem using direct interpolation of high-resolution ultrasound B-mode image frames. A series of ultrasound B-mode image frames (an image series) is acquired using the freehand scanning technique and position sensing via optical tracking equipment. The proposed algorithm creates additional intermediate image frames by directly interpolating between two or more adjacent image frames of the original image series. The target volume is filled using the original frames in combination with the additionally constructed frames. Compared with conventional volume reconstruction methods, no additional filling of empty voxels or holes within the volume is required, because the whole extent of the volume is defined by the arrangement of the original and the additionally constructed B-mode image frames. The proposed direct frame interpolation (DFI) method was tested on two different data sets acquired while scanning the head and neck region of different patients. The first data set consisted of eight B-mode 2-D frame sets acquired under optimal laboratory conditions. The second data set consisted of 73 image series acquired during a clinical study. Sample volumes were reconstructed for all 81 image series using the proposed DFI method with four different interpolation orders, as well as with the pixel nearest-neighbor method using three different interpolation neighborhoods. In addition, volumes based on a reduced number of image frames were reconstructed for comparison of the different methods' accuracy and robustness in reconstructing image data that lies between the original image frames. The DFI method is based on a forward approach making use of a priori information about the position and shape of the B-mode image frames (e.g., masking information) to optimize the reconstruction procedure and to reduce computation times and memory requirements. The method is straightforward, independent of additional input or parameters, and uses the high-resolution B-mode image frames instead of usually lower-resolution voxel information for interpolation. The DFI method can be considered as a valuable alternative to conventional 3-D ultrasound reconstruction methods based on pixel or voxel nearest-neighbor approaches, offering better quality and competitive reconstruction time.

The Mars Climate Database (MCD version 5.2)

NASA Astrophysics Data System (ADS)

Millour, E.; Forget, F.; Spiga, A.; Navarro, T.; Madeleine, J.-B.; Montabone, L.; Pottier, A.; Lefevre, F.; Montmessin, F.; Chaufray, J.-Y.; Lopez-Valverde, M. A.; Gonzalez-Galindo, F.; Lewis, S. R.; Read, P. L.; Huot, J.-P.; Desjean, M.-C.; MCD/GCM development Team

2015-10-01

The Mars Climate Database (MCD) is a database of meteorological fields derived from General Circulation Model (GCM) numerical simulations of the Martian atmosphere and validated using available observational data. The MCD includes complementary post-processing schemes such as high spatial resolution interpolation of environmental data and means of reconstructing the variability thereof. We have just completed (March 2015) the generation of a new version of the MCD, MCD version 5.2

Experimental comparison of landmark-based methods for 3D elastic registration of pre- and postoperative liver CT data

NASA Astrophysics Data System (ADS)

Lange, Thomas; Wörz, Stefan; Rohr, Karl; Schlag, Peter M.

2009-02-01

The qualitative and quantitative comparison of pre- and postoperative image data is an important possibility to validate surgical procedures, in particular, if computer assisted planning and/or navigation is performed. Due to deformations after surgery, partially caused by the removal of tissue, a non-rigid registration scheme is a prerequisite for a precise comparison. Interactive landmark-based schemes are a suitable approach, if high accuracy and reliability is difficult to achieve by automatic registration approaches. Incorporation of a priori knowledge about the anatomical structures to be registered may help to reduce interaction time and improve accuracy. Concerning pre- and postoperative CT data of oncological liver resections the intrahepatic vessels are suitable anatomical structures. In addition to using branching landmarks for registration, we here introduce quasi landmarks at vessel segments with high localization precision perpendicular to the vessels and low precision along the vessels. A comparison of interpolating thin-plate splines (TPS), interpolating Gaussian elastic body splines (GEBS) and approximating GEBS on landmarks at vessel branchings as well as approximating GEBS on the introduced vessel segment landmarks is performed. It turns out that the segment landmarks provide registration accuracies as good as branching landmarks and can improve accuracy if combined with branching landmarks. For a low number of landmarks segment landmarks are even superior.

GNSS Clock Error Impacts on Radio Occultation Retrievals

NASA Astrophysics Data System (ADS)

Weiss, Jan; Sokolovskiy, Sergey; Schreiner, Bill; Yoon, Yoke

2017-04-01

We assess the impacts of GPS and GLONASS clock errors on radio occultation retrieval of bending angle, refractivity, and temperature from low Earth orbit. The major contributing factor is the interpretation of GNSS clock offsets sampled at 30 sec or longer intervals. Using 1 Hz GNSS clock estimates as truth we apply several interpolation and fitting schemes to evaluate how they affect the accuracy of atmospheric retrieval products. The results are organized by GPS and GLONASS space vehicle and the GNSS clock interpolation/fitting scheme. We find that bending angle error is roughly similar for all current GPS transmitters (about 0.7 mcrad) but note some differences related to the type of atomic oscillator onboard the transmitter satellite. GLONASS bending angle errors show more variation over the constellation and are approximately two times larger than GPS. An investigation of the transmitter clock spectra reveals this is due to more power in periods between 2-10 sec. Retrieved refractivity and temperature products show clear differences between GNSS satellite generations, and indicate that GNSS clocks sampled at intervals smaller than 5 sec significantly improve accuracy, particularly for GLONASS. We conclude by summarizing the tested GNSS clock estimation and application strategies in the context of current and future radio occultation missions.

High-quality slab-based intermixing method for fusion rendering of multiple medical objects.

PubMed

Kim, Dong-Joon; Kim, Bohyoung; Lee, Jeongjin; Shin, Juneseuk; Kim, Kyoung Won; Shin, Yeong-Gil

2016-01-01

The visualization of multiple 3D objects has been increasingly required for recent applications in medical fields. Due to the heterogeneity in data representation or data configuration, it is difficult to efficiently render multiple medical objects in high quality. In this paper, we present a novel intermixing scheme for fusion rendering of multiple medical objects while preserving the real-time performance. First, we present an in-slab visibility interpolation method for the representation of subdivided slabs. Second, we introduce virtual zSlab, which extends an infinitely thin boundary (such as polygonal objects) into a slab with a finite thickness. Finally, based on virtual zSlab and in-slab visibility interpolation, we propose a slab-based visibility intermixing method with the newly proposed rendering pipeline. Experimental results demonstrate that the proposed method delivers more effective multiple-object renderings in terms of rendering quality, compared to conventional approaches. And proposed intermixing scheme provides high-quality intermixing results for the visualization of intersecting and overlapping surfaces by resolving aliasing and z-fighting problems. Moreover, two case studies are presented that apply the proposed method to the real clinical applications. These case studies manifest that the proposed method has the outstanding advantages of the rendering independency and reusability. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Optimal updating magnitude in adaptive flat-distribution sampling

NASA Astrophysics Data System (ADS)

Zhang, Cheng; Drake, Justin A.; Ma, Jianpeng; Pettitt, B. Montgomery

2017-11-01

We present a study on the optimization of the updating magnitude for a class of free energy methods based on flat-distribution sampling, including the Wang-Landau (WL) algorithm and metadynamics. These methods rely on adaptive construction of a bias potential that offsets the potential of mean force by histogram-based updates. The convergence of the bias potential can be improved by decreasing the updating magnitude with an optimal schedule. We show that while the asymptotically optimal schedule for the single-bin updating scheme (commonly used in the WL algorithm) is given by the known inverse-time formula, that for the Gaussian updating scheme (commonly used in metadynamics) is often more complex. We further show that the single-bin updating scheme is optimal for very long simulations, and it can be generalized to a class of bandpass updating schemes that are similarly optimal. These bandpass updating schemes target only a few long-range distribution modes and their optimal schedule is also given by the inverse-time formula. Constructed from orthogonal polynomials, the bandpass updating schemes generalize the WL and Langfeld-Lucini-Rago algorithms as an automatic parameter tuning scheme for umbrella sampling.

Optimal updating magnitude in adaptive flat-distribution sampling.

PubMed

Zhang, Cheng; Drake, Justin A; Ma, Jianpeng; Pettitt, B Montgomery

2017-11-07

We present a study on the optimization of the updating magnitude for a class of free energy methods based on flat-distribution sampling, including the Wang-Landau (WL) algorithm and metadynamics. These methods rely on adaptive construction of a bias potential that offsets the potential of mean force by histogram-based updates. The convergence of the bias potential can be improved by decreasing the updating magnitude with an optimal schedule. We show that while the asymptotically optimal schedule for the single-bin updating scheme (commonly used in the WL algorithm) is given by the known inverse-time formula, that for the Gaussian updating scheme (commonly used in metadynamics) is often more complex. We further show that the single-bin updating scheme is optimal for very long simulations, and it can be generalized to a class of bandpass updating schemes that are similarly optimal. These bandpass updating schemes target only a few long-range distribution modes and their optimal schedule is also given by the inverse-time formula. Constructed from orthogonal polynomials, the bandpass updating schemes generalize the WL and Langfeld-Lucini-Rago algorithms as an automatic parameter tuning scheme for umbrella sampling.

Comparison of different wind data interpolation methods for a region with complex terrain in Central Asia

NASA Astrophysics Data System (ADS)

Reinhardt, Katja; Samimi, Cyrus

2018-01-01

While climatological data of high spatial resolution are largely available in most developed countries, the network of climatological stations in many other regions of the world still constitutes large gaps. Especially for those regions, interpolation methods are important tools to fill these gaps and to improve the data base indispensible for climatological research. Over the last years, new hybrid methods of machine learning and geostatistics have been developed which provide innovative prospects in spatial predictive modelling. This study will focus on evaluating the performance of 12 different interpolation methods for the wind components \\overrightarrow{u} and \\overrightarrow{v} in a mountainous region of Central Asia. Thereby, a special focus will be on applying new hybrid methods on spatial interpolation of wind data. This study is the first evaluating and comparing the performance of several of these hybrid methods. The overall aim of this study is to determine whether an optimal interpolation method exists, which can equally be applied for all pressure levels, or whether different interpolation methods have to be used for the different pressure levels. Deterministic (inverse distance weighting) and geostatistical interpolation methods (ordinary kriging) were explored, which take into account only the initial values of \\overrightarrow{u} and \\overrightarrow{v} . In addition, more complex methods (generalized additive model, support vector machine and neural networks as single methods and as hybrid methods as well as regression-kriging) that consider additional variables were applied. The analysis of the error indices revealed that regression-kriging provided the most accurate interpolation results for both wind components and all pressure heights. At 200 and 500 hPa, regression-kriging is followed by the different kinds of neural networks and support vector machines and for 850 hPa it is followed by the different types of support vector machine and ordinary kriging. Overall, explanatory variables improve the interpolation results.

Directional kriging implementation for gridded data interpolation and comparative study with common methods

NASA Astrophysics Data System (ADS)

Mahmoudabadi, H.; Briggs, G.

2016-12-01

Gridded data sets, such as geoid models or datum shift grids, are commonly used in coordinate transformation algorithms. Grid files typically contain known or measured values at regular fixed intervals. The process of computing a value at an unknown location from the values in the grid data set is called "interpolation". Generally, interpolation methods predict a value at a given point by computing a weighted average of the known values in the neighborhood of the point. Geostatistical Kriging is a widely used interpolation method for irregular networks. Kriging interpolation first analyzes the spatial structure of the input data, then generates a general model to describe spatial dependencies. This model is used to calculate values at unsampled locations by finding direction, shape, size, and weight of neighborhood points. Because it is based on a linear formulation for the best estimation, Kriging it the optimal interpolation method in statistical terms. The Kriging interpolation algorithm produces an unbiased prediction, as well as the ability to calculate the spatial distribution of uncertainty, allowing you to estimate the errors in an interpolation for any particular point. Kriging is not widely used in geospatial applications today, especially applications that run on low power devices or deal with large data files. This is due to the computational power and memory requirements of standard Kriging techniques. In this paper, improvements are introduced in directional kriging implementation by taking advantage of the structure of the grid files. The regular spacing of points simplifies finding the neighborhood points and computing their pairwise distances, reducing the the complexity and improving the execution time of the Kriging algorithm. Also, the proposed method iteratively loads small portion of interest areas in different directions to reduce the amount of required memory. This makes the technique feasible on almost any computer processor. Comparison between kriging and other standard interpolation methods demonstrated more accurate estimations in less denser data files.

Merging Multi-model CMIP5/PMIP3 Past-1000 Ensemble Simulations with Tree Ring Proxy Data by Optimal Interpolation Approach

NASA Astrophysics Data System (ADS)

Chen, Xin; Luo, Yong; Xing, Pei; Nie, Suping; Tian, Qinhua

2015-04-01

Two sets of gridded annual mean surface air temperature in past millennia over the Northern Hemisphere was constructed employing optimal interpolation (OI) method so as to merge the tree ring proxy records with the simulations from CMIP5 (the fifth phase of the Climate Model Intercomparison Project). Both the uncertainties in proxy reconstruction and model simulations can be taken into account applying OI algorithm. For better preservation of physical coordinated features and spatial-temporal completeness of climate variability in 7 copies of model results, we perform the Empirical Orthogonal Functions (EOF) analysis to truncate the ensemble mean field as the first guess (background field) for OI. 681 temperature sensitive tree-ring chronologies are collected and screened from International Tree Ring Data Bank (ITRDB) and Past Global Changes (PAGES-2k) project. Firstly, two methods (variance matching and linear regression) are employed to calibrate the tree ring chronologies with instrumental data (CRUTEM4v) individually. In addition, we also remove the bias of both the background field and proxy records relative to instrumental dataset. Secondly, time-varying background error covariance matrix (B) and static "observation" error covariance matrix (R) are calculated for OI frame. In our scheme, matrix B was calculated locally, and "observation" error covariance are partially considered in R matrix (the covariance value between the pairs of tree ring sites that are very close to each other would be counted), which is different from the traditional assumption that R matrix should be diagonal. Comparing our results, it turns out that regional averaged series are not sensitive to the selection for calibration methods. The Quantile-Quantile plots indicate regional climatologies based on both methods are tend to be more agreeable with regional reconstruction of PAGES-2k in 20th century warming period than in little ice age (LIA). Lager volcanic cooling response over Asia and Europe in context of recent millennium are detected in our datasets than that revealed in regional reconstruction from PAGES-2k network. Verification experiments have showed that the merging approach really reconcile the proxy data and model ensemble simulations in an optimal way (with smaller errors than both of them). Further research is needed to improve the error estimation on them.

GENIE - Generation of computational geometry-grids for internal-external flow configurations

NASA Technical Reports Server (NTRS)

Soni, B. K.

1988-01-01

Progress realized in the development of a master geometry-grid generation code GENIE is presented. The grid refinement process is enhanced by developing strategies to utilize bezier curves/surfaces and splines along with weighted transfinite interpolation technique and by formulating new forcing function for the elliptic solver based on the minimization of a non-orthogonality functional. A two step grid adaptation procedure is developed by optimally blending adaptive weightings with weighted transfinite interpolation technique. Examples of 2D-3D grids are provided to illustrate the success of these methods.

Methods for finding transition states on reduced potential energy surfaces

NASA Astrophysics Data System (ADS)

Burger, Steven K.; Ayers, Paul W.

2010-06-01

Three new algorithms are presented for determining transition state (TS) structures on the reduced potential energy surface, that is, for problems in which a few important degrees of freedom can be isolated. All three methods use constrained optimization to rapidly find the TS without an initial Hessian evaluation. The algorithms highlight how efficiently the TS can be located on a reduced surface, where the rest of the degrees of freedom are minimized. The first method uses a nonpositive definite quasi-Newton update for the reduced degrees of freedom. The second uses Shepard interpolation to fit the Hessian and starts from a set of points that bound the TS. The third directly uses a finite difference scheme to calculate the reduced degrees of freedom of the Hessian of the entire system, and searches for the TS on the full potential energy surface. All three methods are tested on an epoxide hydrolase cluster, and the ring formations of cyclohexane and cyclobutenone. The results indicate that all the methods are able to converge quite rapidly to the correct TS, but that the finite difference approach is the most efficient.

Methods for finding transition states on reduced potential energy surfaces.

PubMed

Burger, Steven K; Ayers, Paul W

2010-06-21

Three new algorithms are presented for determining transition state (TS) structures on the reduced potential energy surface, that is, for problems in which a few important degrees of freedom can be isolated. All three methods use constrained optimization to rapidly find the TS without an initial Hessian evaluation. The algorithms highlight how efficiently the TS can be located on a reduced surface, where the rest of the degrees of freedom are minimized. The first method uses a nonpositive definite quasi-Newton update for the reduced degrees of freedom. The second uses Shepard interpolation to fit the Hessian and starts from a set of points that bound the TS. The third directly uses a finite difference scheme to calculate the reduced degrees of freedom of the Hessian of the entire system, and searches for the TS on the full potential energy surface. All three methods are tested on an epoxide hydrolase cluster, and the ring formations of cyclohexane and cyclobutenone. The results indicate that all the methods are able to converge quite rapidly to the correct TS, but that the finite difference approach is the most efficient.

Practical Implementation of Prestack Kirchhoff Time Migration on a General Purpose Graphics Processing Unit

NASA Astrophysics Data System (ADS)

Liu, Guofeng; Li, Chun

2016-08-01

In this study, we present a practical implementation of prestack Kirchhoff time migration (PSTM) on a general purpose graphic processing unit. First, we consider the three main optimizations of the PSTM GPU code, i.e., designing a configuration based on a reasonable execution, using the texture memory for velocity interpolation, and the application of an intrinsic function in device code. This approach can achieve a speedup of nearly 45 times on a NVIDIA GTX 680 GPU compared with CPU code when a larger imaging space is used, where the PSTM output is a common reflection point that is gathered as I[ nx][ ny][ nh][ nt] in matrix format. However, this method requires more memory space so the limited imaging space cannot fully exploit the GPU sources. To overcome this problem, we designed a PSTM scheme with multi-GPUs for imaging different seismic data on different GPUs using an offset value. This process can achieve the peak speedup of GPU PSTM code and it greatly increases the efficiency of the calculations, but without changing the imaging result.

An efficient and accurate molecular alignment and docking technique using ab initio quality scoring

PubMed Central

Füsti-Molnár, László; Merz, Kenneth M.

2008-01-01

An accurate and efficient molecular alignment technique is presented based on first principle electronic structure calculations. This new scheme maximizes quantum similarity matrices in the relative orientation of the molecules and uses Fourier transform techniques for two purposes. First, building up the numerical representation of true ab initio electronic densities and their Coulomb potentials is accelerated by the previously described Fourier transform Coulomb method. Second, the Fourier convolution technique is applied for accelerating optimizations in the translational coordinates. In order to avoid any interpolation error, the necessary analytical formulas are derived for the transformation of the ab initio wavefunctions in rotational coordinates. The results of our first implementation for a small test set are analyzed in detail and compared with published results of the literature. A new way of refinement of existing shape based alignments is also proposed by using Fourier convolutions of ab initio or other approximate electron densities. This new alignment technique is generally applicable for overlap, Coulomb, kinetic energy, etc., quantum similarity measures and can be extended to a genuine docking solution with ab initio scoring. PMID:18624561

The Use of Daily Geodetic UT1 and LOD Data in the Optimal Estimation of UT1 and LOD With the JPL Kalman Earth Orientation Filter

NASA Technical Reports Server (NTRS)

Freedman, A. P.; Steppe, J. A.

1995-01-01

The Jet Propulsion Laboratory Kalman Earth Orientation Filter (KEOF) uses several of the Earth rotation data sets available to generate optimally interpolated UT1 and LOD series to support spacecraft navigation. This paper compares use of various data sets within KEOF.

A general-purpose optimization program for engineering design

NASA Technical Reports Server (NTRS)

Vanderplaats, G. N.; Sugimoto, H.

1986-01-01

A new general-purpose optimization program for engineering design is described. ADS (Automated Design Synthesis) is a FORTRAN program for nonlinear constrained (or unconstrained) function minimization. The optimization process is segmented into three levels: Strategy, Optimizer, and One-dimensional search. At each level, several options are available so that a total of nearly 100 possible combinations can be created. An example of available combinations is the Augmented Lagrange Multiplier method, using the BFGS variable metric unconstrained minimization together with polynomial interpolation for the one-dimensional search.

Elastic-wave-mode separation in TTI media with inverse-distance weighted interpolation involving position shading

NASA Astrophysics Data System (ADS)

Wang, Jian; Meng, Xiaohong; Zheng, Wanqiu

2017-10-01

The elastic-wave reverse-time migration of inhomogeneous anisotropic media is becoming the hotspot of research today. In order to ensure the accuracy of the migration, it is necessary to separate the wave mode into P-wave and S-wave before migration. For inhomogeneous media, the Kelvin-Christoffel equation can be solved in the wave-number domain by using the anisotropic parameters of the mesh nodes, and the polarization vector of the P-wave and S-wave at each node can be calculated and transformed into the space domain to obtain the quasi-differential operators. However, this method is computationally expensive, especially for the process of quasi-differential operators. In order to reduce the computational complexity, the wave-mode separation of mixed domain can be realized on the basis of a reference model in the wave-number domain. But conventional interpolation methods and reference model selection methods reduce the separation accuracy. In order to further improve the separation effect, this paper introduces an inverse-distance interpolation method involving position shading and uses the reference model selection method of random points scheme. This method adds the spatial weight coefficient K, which reflects the orientation of the reference point on the conventional IDW algorithm, and the interpolation process takes into account the combined effects of the distance and azimuth of the reference points. Numerical simulation shows that the proposed method can separate the wave mode more accurately using fewer reference models and has better practical value.

Chemical association in simple models of molecular and ionic fluids. III. The cavity function

NASA Astrophysics Data System (ADS)

Zhou, Yaoqi; Stell, George

1992-01-01

Exact equations which relate the cavity function to excess solvation free energies and equilibrium association constants are rederived by using a thermodynamic cycle. A zeroth-order approximation, derived previously by us as a simple interpolation scheme, is found to be very accurate if the associative bonding occurs on or near the surface of the repulsive core of the interaction potential. If the bonding radius is substantially less than the core radius, the approximation overestimates the association degree and the association constant. For binary association, the zeroth-order approximation is equivalent to the first-order thermodynamic perturbation theory (TPT) of Wertheim. For n-particle association, the combination of the zeroth-order approximation with a ``linear'' approximation (for n-particle distribution functions in terms of the two-particle function) yields the first-order TPT result. Using our exact equations to go beyond TPT, near-exact analytic results for binary hard-sphere association are obtained. Solvent effects on binary hard-sphere association and ionic association are also investigated. A new rule which generalizes Le Chatelier's principle is used to describe the three distinct forms of behaviors involving solvent effects that we find. The replacement of the dielectric-continuum solvent model by a dipolar hard-sphere model leads to improved agreement with an experimental observation. Finally, equation of state for an n-particle flexible linear-chain fluid is derived on the basis of a one-parameter approximation that interpolates between the generalized Kirkwood superposition approximation and the linear approximation. A value of the parameter that appears to be near optimal in the context of this application is obtained from comparison with computer-simulation data.

Interpolated memory tests reduce mind wandering and improve learning of online lectures.

PubMed

Szpunar, Karl K; Khan, Novall Y; Schacter, Daniel L

2013-04-16

The recent emergence and popularity of online educational resources brings with it challenges for educators to optimize the dissemination of online content. Here we provide evidence that points toward a solution for the difficulty that students frequently report in sustaining attention to online lectures over extended periods. In two experiments, we demonstrate that the simple act of interpolating online lectures with memory tests can help students sustain attention to lecture content in a manner that discourages task-irrelevant mind wandering activities, encourages task-relevant note-taking activities, and improves learning. Importantly, frequent testing was associated with reduced anxiety toward a final cumulative test and also with reductions in subjective estimates of cognitive demand. Our findings suggest a potentially key role for interpolated testing in the development and dissemination of online educational content.

Interpolated memory tests reduce mind wandering and improve learning of online lectures

PubMed Central

Szpunar, Karl K.; Khan, Novall Y.; Schacter, Daniel L.

2013-01-01

The recent emergence and popularity of online educational resources brings with it challenges for educators to optimize the dissemination of online content. Here we provide evidence that points toward a solution for the difficulty that students frequently report in sustaining attention to online lectures over extended periods. In two experiments, we demonstrate that the simple act of interpolating online lectures with memory tests can help students sustain attention to lecture content in a manner that discourages task-irrelevant mind wandering activities, encourages task-relevant note-taking activities, and improves learning. Importantly, frequent testing was associated with reduced anxiety toward a final cumulative test and also with reductions in subjective estimates of cognitive demand. Our findings suggest a potentially key role for interpolated testing in the development and dissemination of online educational content. PMID:23576743

Progress in Grid Generation: From Chimera to DRAGON Grids

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing; Kao, Kai-Hsiung

1994-01-01

Hybrid grids, composed of structured and unstructured grids, combines the best features of both. The chimera method is a major stepstone toward a hybrid grid from which the present approach is evolved. The chimera grid composes a set of overlapped structured grids which are independently generated and body-fitted, yielding a high quality grid readily accessible for efficient solution schemes. The chimera method has been shown to be efficient to generate a grid about complex geometries and has been demonstrated to deliver accurate aerodynamic prediction of complex flows. While its geometrical flexibility is attractive, interpolation of data in the overlapped regions - which in today's practice in 3D is done in a nonconservative fashion, is not. In the present paper we propose a hybrid grid scheme that maximizes the advantages of the chimera scheme and adapts the strengths of the unstructured grid while at the same time keeps its weaknesses minimal. Like the chimera method, we first divide up the physical domain by a set of structured body-fitted grids which are separately generated and overlaid throughout a complex configuration. To eliminate any pure data manipulation which does not necessarily follow governing equations, we use non-structured grids only to directly replace the region of the arbitrarily overlapped grids. This new adaptation to the chimera thinking is coined the DRAGON grid. The nonstructured grid region sandwiched between the structured grids is limited in size, resulting in only a small increase in memory and computational effort. The DRAGON method has three important advantages: (1) preserving strengths of the chimera grid; (2) eliminating difficulties sometimes encountered in the chimera scheme, such as the orphan points and bad quality of interpolation stencils; and (3) making grid communication in a fully conservative and consistent manner insofar as the governing equations are concerned. To demonstrate its use, the governing equations are discretized using the newly proposed flux scheme, AUSM+, which will be briefly described herein. Numerical tests on representative 2D inviscid flows are given for demonstration. Finally, extension to 3D is underway, only paced by the availability of the 3D unstructured grid generator.

Interpretation of atomic mass systematics in terms of the valence shells and a simple scheme for predicting masses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haustein, P.E.; Brenner, D.S.; Casten, R.F.

1988-07-01

A new semiempirical method that significantly simplifies atomic mass systematics and which provides a method for making mass predictions by linear interpolation is discussed in the context of the nuclear valence space. In certain regions complicated patterns of mass systematics in traditional plots versus Z, N, or isospin are consolidated and transformed into linear ones extending over long isotopic and isotonic sequences.

Spatial interpolation of solar global radiation

NASA Astrophysics Data System (ADS)

Lussana, C.; Uboldi, F.; Antoniazzi, C.

2010-09-01

Solar global radiation is defined as the radiant flux incident onto an area element of the terrestrial surface. Its direct knowledge plays a crucial role in many applications, from agrometeorology to environmental meteorology. The ARPA Lombardia's meteorological network includes about one hundred of pyranometers, mostly distributed in the southern part of the Alps and in the centre of the Po Plain. A statistical interpolation method based on an implementation of the Optimal Interpolation is applied to the hourly average of the solar global radiation observations measured by the ARPA Lombardia's network. The background field is obtained using SMARTS (The Simple Model of the Atmospheric Radiative Transfer of Sunshine, Gueymard, 2001). The model is initialised by assuming clear sky conditions and it takes into account the solar position and orography related effects (shade and reflection). The interpolation of pyranometric observations introduces in the analysis fields information about cloud presence and influence. A particular effort is devoted to prevent observations affected by large errors of different kinds (representativity errors, systematic errors, gross errors) from entering the analysis procedure. The inclusion of direct cloud information from satellite observations is also planned.

[Study of spatial stratified sampling strategy of Oncomelania hupensis snail survey based on plant abundance].

PubMed

Xun-Ping, W; An, Z

2017-07-27

Objective To optimize and simplify the survey method of Oncomelania hupensis snails in marshland endemic regions of schistosomiasis, so as to improve the precision, efficiency and economy of the snail survey. Methods A snail sampling strategy (Spatial Sampling Scenario of Oncomelania based on Plant Abundance, SOPA) which took the plant abundance as auxiliary variable was explored and an experimental study in a 50 m×50 m plot in a marshland in the Poyang Lake region was performed. Firstly, the push broom surveyed data was stratified into 5 layers by the plant abundance data; then, the required numbers of optimal sampling points of each layer through Hammond McCullagh equation were calculated; thirdly, every sample point in the line with the Multiple Directional Interpolation (MDI) placement scheme was pinpointed; and finally, the comparison study among the outcomes of the spatial random sampling strategy, the traditional systematic sampling method, the spatial stratified sampling method, Sandwich spatial sampling and inference and SOPA was performed. Results The method (SOPA) proposed in this study had the minimal absolute error of 0.213 8; and the traditional systematic sampling method had the largest estimate, and the absolute error was 0.924 4. Conclusion The snail sampling strategy (SOPA) proposed in this study obtains the higher estimation accuracy than the other four methods.

5-D interpolation with wave-front attributes

NASA Astrophysics Data System (ADS)

Xie, Yujiang; Gajewski, Dirk

2017-11-01

Most 5-D interpolation and regularization techniques reconstruct the missing data in the frequency domain by using mathematical transforms. An alternative type of interpolation methods uses wave-front attributes, that is, quantities with a specific physical meaning like the angle of emergence and wave-front curvatures. In these attributes structural information of subsurface features like dip and strike of a reflector are included. These wave-front attributes work on 5-D data space (e.g. common-midpoint coordinates in x and y, offset, azimuth and time), leading to a 5-D interpolation technique. Since the process is based on stacking next to the interpolation a pre-stack data enhancement is achieved, improving the signal-to-noise ratio (S/N) of interpolated and recorded traces. The wave-front attributes are determined in a data-driven fashion, for example, with the Common Reflection Surface (CRS method). As one of the wave-front-attribute-based interpolation techniques, the 3-D partial CRS method was proposed to enhance the quality of 3-D pre-stack data with low S/N. In the past work on 3-D partial stacks, two potential problems were still unsolved. For high-quality wave-front attributes, we suggest a global optimization strategy instead of the so far used pragmatic search approach. In previous works, the interpolation of 3-D data was performed along a specific azimuth which is acceptable for narrow azimuth acquisition but does not exploit the potential of wide-, rich- or full-azimuth acquisitions. The conventional 3-D partial CRS method is improved in this work and we call it as a wave-front-attribute-based 5-D interpolation (5-D WABI) as the two problems mentioned above are addressed. Data examples demonstrate the improved performance by the 5-D WABI method when compared with the conventional 3-D partial CRS approach. A comparison of the rank-reduction-based 5-D seismic interpolation technique with the proposed 5-D WABI method is given. The comparison reveals that there are significant advantages for steep dipping events using the 5-D WABI method when compared to the rank-reduction-based 5-D interpolation technique. Diffraction tails substantially benefit from this improved performance of the partial CRS stacking approach while the CPU time is comparable to the CPU time consumed by the rank-reduction-based method.

Some results on numerical methods for hyperbolic conservation laws

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang Huanan.

1989-01-01

This dissertation contains some results on the numerical solutions of hyperbolic conservation laws. (1) The author introduced an artificial compression method as a correction to the basic ENO schemes. The method successfully prevents contact discontinuities from being smeared. This is achieved by increasing the slopes of the ENO reconstructions in such a way that the essentially non-oscillatory property of the schemes is kept. He analyzes the non-oscillatory property of the new artificial compression method by applying it to the UNO scheme which is a second order accurate ENO scheme, and proves that the resulting scheme is indeed non-oscillatory. Extensive 1-Dmore » numerical results and some preliminary 2-D ones are provided to show the strong performance of the method. (2) He combines the ENO schemes and the centered difference schemes into self-adjusting hybrid schemes which will be called the localized ENO schemes. At or near the jumps, he uses the ENO schemes with the field by field decompositions, otherwise he simply uses the centered difference schemes without the field by field decompositions. The method involves a new interpolation analysis. In the numerical experiments on several standard test problems, the quality of the numerical results of this method is close to that of the pure ENO results. The localized ENO schemes can be equipped with the above artificial compression method. In this way, he dramatically improves the resolutions of the contact discontinuities at very little additional costs. (3) He introduces a space-time mesh refinement method for time dependent problems.« less

The concurrent multiplicative-additive approach for gauge-radar/satellite multisensor precipitation estimates

NASA Astrophysics Data System (ADS)

Garcia-Pintado, J.; Barberá, G. G.; Erena Arrabal, M.; Castillo, V. M.

2010-12-01

Objective analysis schemes (OAS), also called ``succesive correction methods'' or ``observation nudging'', have been proposed for multisensor precipitation estimation combining remote sensing data (meteorological radar or satellite) with data from ground-based raingauge networks. However, opposite to the more complex geostatistical approaches, the OAS techniques for this use are not optimized. On the other hand, geostatistical techniques ideally require, at the least, modelling the covariance from the rain gauge data at every time step evaluated, which commonly cannot be soundly done. Here, we propose a new procedure (concurrent multiplicative-additive objective analysis scheme [CMA-OAS]) for operational rainfall estimation using rain gauges and meteorological radar, which does not require explicit modelling of spatial covariances. On the basis of a concurrent multiplicative-additive (CMA) decomposition of the spatially nonuniform radar bias, within-storm variability of rainfall and fractional coverage of rainfall are taken into account. Thus both spatially nonuniform radar bias, given that rainfall is detected, and bias in radar detection of rainfall are handled. The interpolation procedure of CMA-OAS is built on the OAS, whose purpose is to estimate a filtered spatial field of the variable of interest through a successive correction of residuals resulting from a Gaussian kernel smoother applied on spatial samples. The CMA-OAS, first, poses an optimization problem at each gauge-radar support point to obtain both a local multiplicative-additive radar bias decomposition and a regionalization parameter. Second, local biases and regionalization parameters are integrated into an OAS to estimate the multisensor rainfall at the ground level. The approach considers radar estimates as background a priori information (first guess), so that nudging to observations (gauges) may be relaxed smoothly to the first guess, and the relaxation shape is obtained from the sequential optimization. The procedure is suited to relatively sparse rain gauge networks. To show the procedure, six storms are analyzed at hourly steps over 10,663 km2. Results generally indicated an improved quality with respect to other methods evaluated: a standard mean-field bias adjustment, an OAS spatially variable adjustment with multiplicative factors, ordinary cokriging, and kriging with external drift. In theory, it could be equally applicable to gauge-satellite estimates and other hydrometeorological variables.

Numerical analysis of a high-order unstructured overset grid method for compressible LES of turbomachinery

NASA Astrophysics Data System (ADS)

de Laborderie, J.; Duchaine, F.; Gicquel, L.; Vermorel, O.; Wang, G.; Moreau, S.

2018-06-01

Large-Eddy Simulation (LES) is recognized as a promising method for high-fidelity flow predictions in turbomachinery applications. The presented approach consists of the coupling of several instances of the same LES unstructured solver through an overset grid method. A high-order interpolation, implemented within this coupling method, is introduced and evaluated on several test cases. It is shown to be third order accurate, to preserve the accuracy of various second and third order convective schemes and to ensure the continuity of diffusive fluxes and subgrid scale tensors even in detrimental interface configurations. In this analysis, three types of spurious waves generated at the interface are identified. They are significantly reduced by the high-order interpolation at the interface. The latter having the same cost as the original lower order method, the high-order overset grid method appears as a promising alternative to be used in all the applications.

A fast simulation method for radiation maps using interpolation in a virtual environment.

PubMed

Li, Meng-Kun; Liu, Yong-Kuo; Peng, Min-Jun; Xie, Chun-Li; Yang, Li-Qun

2018-05-10

In nuclear decommissioning, virtual simulation technology is a useful tool to achieve an effective work process by using virtual environments to represent the physical and logical scheme of a real decommissioning project. This technology is cost-saving and time-saving, with the capacity to develop various decommissioning scenarios and reduce the risk of retrofitting. The method utilises a radiation map in a virtual simulation as the basis for the assessment of exposure to a virtual human. In this paper, we propose a fast simulation method using a known radiation source. The method has a unique advantage over point kernel and Monte Carlo methods because it generates the radiation map using interpolation in a virtual environment. The simulation of the radiation map including the calculation and the visualisation were realised using UNITY and MATLAB. The feasibility of the proposed method was tested on a hypothetical case and the results obtained are discussed in this paper.

An interpolated activity during the knowledge-of-results delay interval eliminates the learning advantages of self-controlled feedback schedules.

PubMed

Carter, Michael J; Ste-Marie, Diane M

2017-03-01

The learning advantages of self-controlled knowledge-of-results (KR) schedules compared to yoked schedules have been linked to the optimization of the informational value of the KR received for the enhancement of one's error-detection capabilities. This suggests that information-processing activities that occur after motor execution, but prior to receiving KR (i.e., the KR-delay interval) may underlie self-controlled KR learning advantages. The present experiment investigated whether self-controlled KR learning benefits would be eliminated if an interpolated activity was performed during the KR-delay interval. Participants practiced a waveform matching task that required two rapid elbow extension-flexion reversals in one of four groups using a factorial combination of choice (self-controlled, yoked) and KR-delay interval (empty, interpolated). The waveform had specific spatial and temporal constraints, and an overall movement time goal. The results indicated that the self-controlled + empty group had superior retention and transfer scores compared to all other groups. Moreover, the self-controlled + interpolated and yoked + interpolated groups did not differ significantly in retention and transfer; thus, the interpolated activity eliminated the typically found learning benefits of self-controlled KR. No significant differences were found between the two yoked groups. We suggest the interpolated activity interfered with information-processing activities specific to self-controlled KR conditions that occur during the KR-delay interval and that these activities are vital for reaping the associated learning benefits. These findings add to the growing evidence that challenge the motivational account of self-controlled KR learning advantages and instead highlights informational factors associated with the KR-delay interval as an important variable for motor learning under self-controlled KR schedules.

Optimization of the scheme for natural ecology planning of urban rivers based on ANP (analytic network process) model.

PubMed

Zhang, Yichuan; Wang, Jiangping

2015-07-01

Rivers serve as a highly valued component in ecosystem and urban infrastructures. River planning should follow basic principles of maintaining or reconstructing the natural landscape and ecological functions of rivers. Optimization of planning scheme is a prerequisite for successful construction of urban rivers. Therefore, relevant studies on optimization of scheme for natural ecology planning of rivers is crucial. In the present study, four planning schemes for Zhaodingpal River in Xinxiang City, Henan Province were included as the objects for optimization. Fourteen factors that influenced the natural ecology planning of urban rivers were selected from five aspects so as to establish the ANP model. The data processing was done using Super Decisions software. The results showed that important degree of scheme 3 was highest. A scientific, reasonable and accurate evaluation of schemes could be made by ANP method on natural ecology planning of urban rivers. This method could be used to provide references for sustainable development and construction of urban rivers. ANP method is also suitable for optimization of schemes for urban green space planning and design.

An optimized data fusion method and its application to improve lateral boundary conditions in winter for Pearl River Delta regional PM2.5 modeling, China

NASA Astrophysics Data System (ADS)

Huang, Zhijiong; Hu, Yongtao; Zheng, Junyu; Zhai, Xinxin; Huang, Ran

2018-05-01

Lateral boundary conditions (LBCs) are essential for chemical transport models to simulate regional transport; however they often contain large uncertainties. This study proposes an optimized data fusion approach to reduce the bias of LBCs by fusing gridded model outputs, from which the daughter domain's LBCs are derived, with ground-level measurements. The optimized data fusion approach follows the framework of a previous interpolation-based fusion method but improves it by using a bias kriging method to correct the spatial bias in gridded model outputs. Cross-validation shows that the optimized approach better estimates fused fields in areas with a large number of observations compared to the previous interpolation-based method. The optimized approach was applied to correct LBCs of PM2.5 concentrations for simulations in the Pearl River Delta (PRD) region as a case study. Evaluations show that the LBCs corrected by data fusion improve in-domain PM2.5 simulations in terms of the magnitude and temporal variance. Correlation increases by 0.13-0.18 and fractional bias (FB) decreases by approximately 3%-15%. This study demonstrates the feasibility of applying data fusion to improve regional air quality modeling.

Time optimal control of a jet engine using a quasi-Hermite interpolation model. M.S. Thesis

NASA Technical Reports Server (NTRS)

Comiskey, J. G.

1979-01-01

This work made preliminary efforts to generate nonlinear numerical models of a two-spooled turbofan jet engine, and subject these models to a known method of generating global, nonlinear, time optimal control laws. The models were derived numerically, directly from empirical data, as a first step in developing an automatic modelling procedure.

Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling

NASA Astrophysics Data System (ADS)

Liu, Youshan; Teng, Jiwen; Xu, Tao; Badal, José

2017-05-01

The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant-Friedrichs-Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational efficiency, the OTSEM is more efficient than the Fekete-based TSEM, although it is slightly costlier than the QSEM when a comparable numerical accuracy is required.

Intel Xeon Phi accelerated Weather Research and Forecasting (WRF) Goddard microphysics scheme

NASA Astrophysics Data System (ADS)

Mielikainen, J.; Huang, B.; Huang, A. H.-L.

2014-12-01

The Weather Research and Forecasting (WRF) model is a numerical weather prediction system designed to serve both atmospheric research and operational forecasting needs. The WRF development is a done in collaboration around the globe. Furthermore, the WRF is used by academic atmospheric scientists, weather forecasters at the operational centers and so on. The WRF contains several physics components. The most time consuming one is the microphysics. One microphysics scheme is the Goddard cloud microphysics scheme. It is a sophisticated cloud microphysics scheme in the Weather Research and Forecasting (WRF) model. The Goddard microphysics scheme is very suitable for massively parallel computation as there are no interactions among horizontal grid points. Compared to the earlier microphysics schemes, the Goddard scheme incorporates a large number of improvements. Thus, we have optimized the Goddard scheme code. In this paper, we present our results of optimizing the Goddard microphysics scheme on Intel Many Integrated Core Architecture (MIC) hardware. The Intel Xeon Phi coprocessor is the first product based on Intel MIC architecture, and it consists of up to 61 cores connected by a high performance on-die bidirectional interconnect. The Intel MIC is capable of executing a full operating system and entire programs rather than just kernels as the GPU does. The MIC coprocessor supports all important Intel development tools. Thus, the development environment is one familiar to a vast number of CPU developers. Although, getting a maximum performance out of MICs will require using some novel optimization techniques. Those optimization techniques are discussed in this paper. The results show that the optimizations improved performance of Goddard microphysics scheme on Xeon Phi 7120P by a factor of 4.7×. In addition, the optimizations reduced the Goddard microphysics scheme's share of the total WRF processing time from 20.0 to 7.5%. Furthermore, the same optimizations improved performance on Intel Xeon E5-2670 by a factor of 2.8× compared to the original code.

Numerical simulation of large-scale ocean-atmosphere coupling and the ocean's role in climate

NASA Technical Reports Server (NTRS)

Gates, W. L.

1983-01-01

The problem of reducing model generated sigma coordinate data to pressure levels is considered. A mass consistent scheme for performing budget analyses is proposed, wherein variables interpolated to a given pressure level are weighted according to the mass between a nominal pressure level above and either a nominal pressure level below or the Earth's surface, whichever is closer. The method is applied to the atmospheric energy cycle as simulated by the OSU two level atmospheric general circulation model. The results are more realistic than sigma coordinate analyses with respect to eddy decomposition, and are in agreement with the sigma coordinate evaluation of the numerical energy sink. Comparison with less sophisticated budget schemes indicates superiority locally, but not globally.

Flow solution on a dual-block grid around an airplane

NASA Technical Reports Server (NTRS)

Eriksson, Lars-Erik

1987-01-01

The compressible flow around a complex fighter-aircraft configuration (fuselage, cranked delta wing, canard, and inlet) is simulated numerically using a novel grid scheme and a finite-volume Euler solver. The patched dual-block grid is generated by an algebraic procedure based on transfinite interpolation, and the explicit Runge-Kutta time-stepping Euler solver is implemented with a high degree of vectorization on a Cyber 205 processor. Results are presented in extensive graphs and diagrams and characterized in detail. The concentration of grid points near the wing apex in the present scheme is shown to facilitate capture of the vortex generated by the leading edge at high angles of attack and modeling of its interaction with the canard wake.

A Method for Extracting Road Boundary Information from Crowdsourcing Vehicle GPS Trajectories.

PubMed

Yang, Wei; Ai, Tinghua; Lu, Wei

2018-04-19

Crowdsourcing trajectory data is an important approach for accessing and updating road information. In this paper, we present a novel approach for extracting road boundary information from crowdsourcing vehicle traces based on Delaunay triangulation (DT). First, an optimization and interpolation method is proposed to filter abnormal trace segments from raw global positioning system (GPS) traces and interpolate the optimization segments adaptively to ensure there are enough tracking points. Second, constructing the DT and the Voronoi diagram within interpolated tracking lines to calculate road boundary descriptors using the area of Voronoi cell and the length of triangle edge. Then, the road boundary detection model is established integrating the boundary descriptors and trajectory movement features (e.g., direction) by DT. Third, using the boundary detection model to detect road boundary from the DT constructed by trajectory lines, and a regional growing method based on seed polygons is proposed to extract the road boundary. Experiments were conducted using the GPS traces of taxis in Beijing, China, and the results show that the proposed method is suitable for extracting the road boundary from low-frequency GPS traces, multi-type road structures, and different time intervals. Compared with two existing methods, the automatically extracted boundary information was proved to be of higher quality.

A Method for Extracting Road Boundary Information from Crowdsourcing Vehicle GPS Trajectories

PubMed Central

Yang, Wei

2018-01-01

Crowdsourcing trajectory data is an important approach for accessing and updating road information. In this paper, we present a novel approach for extracting road boundary information from crowdsourcing vehicle traces based on Delaunay triangulation (DT). First, an optimization and interpolation method is proposed to filter abnormal trace segments from raw global positioning system (GPS) traces and interpolate the optimization segments adaptively to ensure there are enough tracking points. Second, constructing the DT and the Voronoi diagram within interpolated tracking lines to calculate road boundary descriptors using the area of Voronoi cell and the length of triangle edge. Then, the road boundary detection model is established integrating the boundary descriptors and trajectory movement features (e.g., direction) by DT. Third, using the boundary detection model to detect road boundary from the DT constructed by trajectory lines, and a regional growing method based on seed polygons is proposed to extract the road boundary. Experiments were conducted using the GPS traces of taxis in Beijing, China, and the results show that the proposed method is suitable for extracting the road boundary from low-frequency GPS traces, multi-type road structures, and different time intervals. Compared with two existing methods, the automatically extracted boundary information was proved to be of higher quality. PMID:29671792

Development of adaptive observation strategy using retrospective optimal interpolation

NASA Astrophysics Data System (ADS)

Noh, N.; Kim, S.; Song, H.; Lim, G.

2011-12-01

Retrospective optimal interpolation (ROI) is a method that is used to minimize cost functions with multiple minima without using adjoint models. Song and Lim (2011) perform the experiments to reduce the computational costs for implementing ROI by transforming the control variables into eigenvectors of background error covariance. We adapt the ROI algorithm to compute sensitivity estimates of severe weather events over the Korean peninsula. The eigenvectors of the ROI algorithm is modified every time the observations are assimilated. This implies that the modified eigenvectors shows the error distribution of control variables which are updated by assimilating observations. So, We can estimate the effects of the specific observations. In order to verify the adaptive observation strategy, High-impact weather over the Korean peninsula is simulated and interpreted using WRF modeling system and sensitive regions for each high-impact weather is calculated. The effects of assimilation for each observation type is discussed.

Ocean data assimilation using optimal interpolation with a quasi-geostrophic model

NASA Technical Reports Server (NTRS)

Rienecker, Michele M.; Miller, Robert N.

1991-01-01

A quasi-geostrophic (QG) stream function is analyzed by optimal interpolation (OI) over a 59-day period in a 150-km-square domain off northern California. Hydrographic observations acquired over five surveys were assimilated into a QG open boundary ocean model. Assimilation experiments were conducted separately for individual surveys to investigate the sensitivity of the OI analyses to parameters defining the decorrelation scale of an assumed error covariance function. The analyses were intercompared through dynamical hindcasts between surveys. The best hindcast was obtained using the smooth analyses produced with assumed error decorrelation scales identical to those of the observed stream function. The rms difference between the hindcast stream function and the final analysis was only 23 percent of the observation standard deviation. The two sets of OI analyses were temporally smoother than the fields from statistical objective analysis and in good agreement with the only independent data available for comparison.

Efficient and accurate time-stepping schemes for integrate-and-fire neuronal networks.

PubMed

Shelley, M J; Tao, L

2001-01-01

To avoid the numerical errors associated with resetting the potential following a spike in simulations of integrate-and-fire neuronal networks, Hansel et al. and Shelley independently developed a modified time-stepping method. Their particular scheme consists of second-order Runge-Kutta time-stepping, a linear interpolant to find spike times, and a recalibration of postspike potential using the spike times. Here we show analytically that such a scheme is second order, discuss the conditions under which efficient, higher-order algorithms can be constructed to treat resets, and develop a modified fourth-order scheme. To support our analysis, we simulate a system of integrate-and-fire conductance-based point neurons with all-to-all coupling. For six-digit accuracy, our modified Runge-Kutta fourth-order scheme needs a time-step of Delta(t) = 0.5 x 10(-3) seconds, whereas to achieve comparable accuracy using a recalibrated second-order or a first-order algorithm requires time-steps of 10(-5) seconds or 10(-9) seconds, respectively. Furthermore, since the cortico-cortical conductances in standard integrate-and-fire neuronal networks do not depend on the value of the membrane potential, we can attain fourth-order accuracy with computational costs normally associated with second-order schemes.

AN ADVANCED LEAKAGE SCHEME FOR NEUTRINO TREATMENT IN ASTROPHYSICAL SIMULATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perego, A.; Cabezón, R. M.; Käppeli, R., E-mail: albino.perego@physik.tu-darmstadt.de

We present an Advanced Spectral Leakage (ASL) scheme to model neutrinos in the context of core-collapse supernovae (CCSNe) and compact binary mergers. Based on previous gray leakage schemes, the ASL scheme computes the neutrino cooling rates by interpolating local production and diffusion rates (relevant in optically thin and thick regimes, respectively) separately for discretized values of the neutrino energy. Neutrino trapped components are also modeled, based on equilibrium and timescale arguments. The better accuracy achieved by the spectral treatment allows a more reliable computation of neutrino heating rates in optically thin conditions. The scheme has been calibrated and tested against Boltzmannmore » transport in the context of Newtonian spherically symmetric models of CCSNe. ASL shows a very good qualitative and a partial quantitative agreement for key quantities from collapse to a few hundreds of milliseconds after core bounce. We have proved the adaptability and flexibility of our ASL scheme, coupling it to an axisymmetric Eulerian and to a three-dimensional smoothed particle hydrodynamics code to simulate core collapse. Therefore, the neutrino treatment presented here is ideal for large parameter-space explorations, parametric studies, high-resolution tests, code developments, and long-term modeling of asymmetric configurations, where more detailed neutrino treatments are not available or are currently computationally too expensive.« less

Randomized interpolative decomposition of separated representations

NASA Astrophysics Data System (ADS)

Biagioni, David J.; Beylkin, Daniel; Beylkin, Gregory

2015-01-01

We introduce an algorithm to compute tensor interpolative decomposition (dubbed CTD-ID) for the reduction of the separation rank of Canonical Tensor Decompositions (CTDs). Tensor ID selects, for a user-defined accuracy ɛ, a near optimal subset of terms of a CTD to represent the remaining terms via a linear combination of the selected terms. CTD-ID can be used as an alternative to or in combination with the Alternating Least Squares (ALS) algorithm. We present examples of its use within a convergent iteration to compute inverse operators in high dimensions. We also briefly discuss the spectral norm as a computational alternative to the Frobenius norm in estimating approximation errors of tensor ID. We reduce the problem of finding tensor IDs to that of constructing interpolative decompositions of certain matrices. These matrices are generated via randomized projection of the terms of the given tensor. We provide cost estimates and several examples of the new approach to the reduction of separation rank.

Application of Allan Deviation to Assessing Uncertainties of Continuous-measurement Instruments, and Optimizing Calibration Schemes

NASA Astrophysics Data System (ADS)

Jacobson, Gloria; Rella, Chris; Farinas, Alejandro

2014-05-01

Technological advancement of instrumentation in atmospheric and other geoscience disciplines over the past decade has lead to a shift from discrete sample analysis to continuous, in-situ monitoring. Standard error analysis used for discrete measurements is not sufficient to assess and compare the error contribution of noise and drift from continuous-measurement instruments, and a different statistical analysis approach should be applied. The Allan standard deviation analysis technique developed for atomic clock stability assessment by David W. Allan [1] can be effectively and gainfully applied to continuous measurement instruments. As an example, P. Werle et al has applied these techniques to look at signal averaging for atmospheric monitoring by Tunable Diode-Laser Absorption Spectroscopy (TDLAS) [2]. This presentation will build on, and translate prior foundational publications to provide contextual definitions and guidelines for the practical application of this analysis technique to continuous scientific measurements. The specific example of a Picarro G2401 Cavity Ringdown Spectroscopy (CRDS) analyzer used for continuous, atmospheric monitoring of CO2, CH4 and CO will be used to define the basics features the Allan deviation, assess factors affecting the analysis, and explore the time-series to Allan deviation plot translation for different types of instrument noise (white noise, linear drift, and interpolated data). In addition, the useful application of using an Allan deviation to optimize and predict the performance of different calibration schemes will be presented. Even though this presentation will use the specific example of the Picarro G2401 CRDS Analyzer for atmospheric monitoring, the objective is to present the information such that it can be successfully applied to other instrument sets and disciplines. [1] D.W. Allan, "Statistics of Atomic Frequency Standards," Proc, IEEE, vol. 54, pp 221-230, Feb 1966 [2] P. Werle, R. Miicke, F. Slemr, "The Limits of Signal Averaging in Atmospheric Trace-Gas Monitoring by Tunable Diode-Laser Absorption Spectroscopy (TDLAS)," Applied Physics, B57, pp 131-139, April 1993

Selecting registration schemes in case of interstitial lung disease follow-up in CT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vlachopoulos, Georgios; Korfiatis, Panayiotis; Skiadopoulos, Spyros

Purpose: Primary goal of this study is to select optimal registration schemes in the framework of interstitial lung disease (ILD) follow-up analysis in CT. Methods: A set of 128 multiresolution schemes composed of multiresolution nonrigid and combinations of rigid and nonrigid registration schemes are evaluated, utilizing ten artificially warped ILD follow-up volumes, originating from ten clinical volumetric CT scans of ILD affected patients, to select candidate optimal schemes. Specifically, all combinations of four transformation models (three rigid: rigid, similarity, affine and one nonrigid: third order B-spline), four cost functions (sum-of-square distances, normalized correlation coefficient, mutual information, and normalized mutual information),more » four gradient descent optimizers (standard, regular step, adaptive stochastic, and finite difference), and two types of pyramids (recursive and Gaussian-smoothing) were considered. The selection process involves two stages. The first stage involves identification of schemes with deformation field singularities, according to the determinant of the Jacobian matrix. In the second stage, evaluation methodology is based on distance between corresponding landmark points in both normal lung parenchyma (NLP) and ILD affected regions. Statistical analysis was performed in order to select near optimal registration schemes per evaluation metric. Performance of the candidate registration schemes was verified on a case sample of ten clinical follow-up CT scans to obtain the selected registration schemes. Results: By considering near optimal schemes common to all ranking lists, 16 out of 128 registration schemes were initially selected. These schemes obtained submillimeter registration accuracies in terms of average distance errors 0.18 ± 0.01 mm for NLP and 0.20 ± 0.01 mm for ILD, in case of artificially generated follow-up data. Registration accuracy in terms of average distance error in clinical follow-up data was in the range of 1.985–2.156 mm and 1.966–2.234 mm, for NLP and ILD affected regions, respectively, excluding schemes with statistically significant lower performance (Wilcoxon signed-ranks test, p < 0.05), resulting in 13 finally selected registration schemes. Conclusions: Selected registration schemes in case of ILD CT follow-up analysis indicate the significance of adaptive stochastic gradient descent optimizer, as well as the importance of combined rigid and nonrigid schemes providing high accuracy and time efficiency. The selected optimal deformable registration schemes are equivalent in terms of their accuracy and thus compatible in terms of their clinical outcome.« less

Maximum likelihood convolutional decoding (MCD) performance due to system losses

NASA Technical Reports Server (NTRS)

Webster, L.

1976-01-01

A model for predicting the computational performance of a maximum likelihood convolutional decoder (MCD) operating in a noisy carrier reference environment is described. This model is used to develop a subroutine that will be utilized by the Telemetry Analysis Program to compute the MCD bit error rate. When this computational model is averaged over noisy reference phase errors using a high-rate interpolation scheme, the results are found to agree quite favorably with experimental measurements.

Computation of Acoustic Waves Through Sliding-Zone Interfaces Using an Euler/Navier-Stokes Code

NASA Technical Reports Server (NTRS)

Rumsey, Christopher L.

1996-01-01

The effect of a patched sliding-zone interface on the transmission of acoustic waves is examined for two- and three-dimensional model problems. A simple but general interpolation scheme at the patched boundary passes acoustic waves without distortion, provided that a sufficiently small time step is taken. A guideline is provided for the maximum permissible time step or zone speed that gives an acceptable error introduced by the sliding-zone interface.

Three-Dimensional Unsteady Separation at Low Reynolds Numbers

DTIC Science & Technology

1990-07-01

novel, robust adaptive- grid technique for incompressible flow (Shen & Reed 1990a "Shepard’s Interpolation for Solution-Adaptive Methods" submitted to...3-D adaptive- grid schemes developed for flat plate for full, unsteady, incompressible Navier Stokes. 4. 2-D and 3-D unsteady, vortex-lattice code...perforated to tailor suction through wall. Honeycomb and contractiong uide flow uniformly crons "a dn muwet a m Fiur32 c ic R n R ev lving -disc seals

Equalizing resolution in smoothed-particle hydrodynamics calculations using self-adaptive sinc kernels

NASA Astrophysics Data System (ADS)

García-Senz, Domingo; Cabezón, Rubén M.; Escartín, José A.; Ebinger, Kevin

2014-10-01

Context. The smoothed-particle hydrodynamics (SPH) technique is a numerical method for solving gas-dynamical problems. It has been applied to simulate the evolution of a wide variety of astrophysical systems. The method has a second-order accuracy, with a resolution that is usually much higher in the compressed regions than in the diluted zones of the fluid. Aims: We propose and check a method to balance and equalize the resolution of SPH between high- and low-density regions. This method relies on the versatility of a family of interpolators called sinc kernels, which allows increasing the interpolation quality by varying only a single parameter (the exponent of the sinc function). Methods: The proposed method was checked and validated through a number of numerical tests, from standard one-dimensional Riemann problems in shock tubes, to multidimensional simulations of explosions, hydrodynamic instabilities, and the collapse of a Sun-like polytrope. Results: The analysis of the hydrodynamical simulations suggests that the scheme devised to equalize the accuracy improves the treatment of the post-shock regions and, in general, of the rarefacted zones of fluids while causing no harm to the growth of hydrodynamic instabilities. The method is robust and easy to implement with a low computational overload. It conserves mass, energy, and momentum and reduces to the standard SPH scheme in regions of the fluid that have smooth density gradients.

Full Multigrid Flow Solver

NASA Technical Reports Server (NTRS)

Mineck, Raymond E.; Thomas, James L.; Biedron, Robert T.; Diskin, Boris

2005-01-01

FMG3D (full multigrid 3 dimensions) is a pilot computer program that solves equations of fluid flow using a finite difference representation on a structured grid. Infrastructure exists for three dimensions but the current implementation treats only two dimensions. Written in Fortran 90, FMG3D takes advantage of the recursive subroutine feature, dynamic memory allocation, and structured-programming constructs of that language. FMG3D supports multi-block grids with three types of block-to-block interfaces: periodic, C-zero, and C-infinity. For all three types, grid points must match at interfaces. For periodic and C-infinity types, derivatives of grid metrics must be continuous at interfaces. The available equation sets are as follows: scalar elliptic equations, scalar convection equations, and the pressure-Poisson formulation of the Navier-Stokes equations for an incompressible fluid. All the equation sets are implemented with nonzero forcing functions to enable the use of user-specified solutions to assist in verification and validation. The equations are solved with a full multigrid scheme using a full approximation scheme to converge the solution on each succeeding grid level. Restriction to the next coarser mesh uses direct injection for variables and full weighting for residual quantities; prolongation of the coarse grid correction from the coarse mesh to the fine mesh uses bilinear interpolation; and prolongation of the coarse grid solution uses bicubic interpolation.

Revisiting Intel Xeon Phi optimization of Thompson cloud microphysics scheme in Weather Research and Forecasting (WRF) model

NASA Astrophysics Data System (ADS)

Mielikainen, Jarno; Huang, Bormin; Huang, Allen

2015-10-01

The Thompson cloud microphysics scheme is a sophisticated cloud microphysics scheme in the Weather Research and Forecasting (WRF) model. The scheme is very suitable for massively parallel computation as there are no interactions among horizontal grid points. Compared to the earlier microphysics schemes, the Thompson scheme incorporates a large number of improvements. Thus, we have optimized the speed of this important part of WRF. Intel Many Integrated Core (MIC) ushers in a new era of supercomputing speed, performance, and compatibility. It allows the developers to run code at trillions of calculations per second using the familiar programming model. In this paper, we present our results of optimizing the Thompson microphysics scheme on Intel Many Integrated Core Architecture (MIC) hardware. The Intel Xeon Phi coprocessor is the first product based on Intel MIC architecture, and it consists of up to 61 cores connected by a high performance on-die bidirectional interconnect. The coprocessor supports all important Intel development tools. Thus, the development environment is familiar one to a vast number of CPU developers. Although, getting a maximum performance out of MICs will require using some novel optimization techniques. New optimizations for an updated Thompson scheme are discusses in this paper. The optimizations improved the performance of the original Thompson code on Xeon Phi 7120P by a factor of 1.8x. Furthermore, the same optimizations improved the performance of the Thompson on a dual socket configuration of eight core Intel Xeon E5-2670 CPUs by a factor of 1.8x compared to the original Thompson code.

Rtop - an R package for interpolation of data with a variable spatial support - examples from river networks

NASA Astrophysics Data System (ADS)

Olav Skøien, Jon; Laaha, Gregor; Koffler, Daniel; Blöschl, Günter; Pebesma, Edzer; Parajka, Juraj; Viglione, Alberto

2013-04-01

Geostatistical methods have been applied only to a limited extent for spatial interpolation in applications where the observations have an irregular support, such as runoff characteristics or population health data. Several studies have shown the potential of such methods (Gottschalk 1993, Sauquet et al. 2000, Gottschalk et al. 2006, Skøien et al. 2006, Goovaerts 2008), but these developments have so far not led to easily accessible, versatile, easy to apply and open source software. Based on the top-kriging approach suggested by Skøien et al. (2006), we will here present the package rtop, which has been implemented in the statistical environment R (R Core Team 2012). Taking advantage of the existing methods in R for analysis of spatial objects (Bivand et al. 2008), and the extensive possibilities for visualizing the results, rtop makes it easy to apply geostatistical interpolation methods when observations have a non-point spatial support. Although the package is flexible regarding data input, the main application so far has been for interpolation along river networks. We will present some examples showing how the package can easily be used for such interpolation. The model will soon be uploaded to CRAN, but is in the meantime also available from R-forge and can be installed by: > install.packages("rtop", repos="http://R-Forge.R-project.org") Bivand, R.S., Pebesma, E.J. & Gómez-Rubio, V., 2008. Applied spatial data analysis with r: Springer. Goovaerts, P., 2008. Kriging and semivariogram deconvolution in the presence of irregular geographical units. Mathematical Geosciences, 40 (1), 101-128. Gottschalk, L., 1993. Interpolation of runoff applying objective methods. Stochastic Hydrology and Hydraulics, 7, 269-281. Gottschalk, L., Krasovskaia, I., Leblois, E. & Sauquet, E., 2006. Mapping mean and variance of runoff in a river basin. Hydrology and Earth System Sciences, 10, 469-484. R Core Team, 2012. R: A language and environment for statistical computing. Vienna, Austria, ISBN 3-900051-07-0. Sauquet, E., Gottschalk, L. & Leblois, E., 2000. Mapping average annual runoff: A hierarchical approach applying a stochastic interpolation scheme. Hydrological Sciences Journal, 45 (6), 799-815. Skøien, J.O., Merz, R. & Blöschl, G., 2006. Top-kriging - geostatistics on stream networks. Hydrology and Earth System Sciences, 10, 277-287.

The Canadian Precipitation Analysis (CaPA): Evaluation of the statistical interpolation scheme

NASA Astrophysics Data System (ADS)

Evans, Andrea; Rasmussen, Peter; Fortin, Vincent

2013-04-01

CaPA (Canadian Precipitation Analysis) is a data assimilation system which employs statistical interpolation to combine observed precipitation with gridded precipitation fields produced by Environment Canada's Global Environmental Multiscale (GEM) climate model into a final gridded precipitation analysis. Precipitation is important in many fields and applications, including agricultural water management projects, flood control programs, and hydroelectric power generation planning. Precipitation is a key input to hydrological models, and there is a desire to have access to the best available information about precipitation in time and space. The principal goal of CaPA is to produce this type of information. In order to perform the necessary statistical interpolation, CaPA requires the estimation of a semi-variogram. This semi-variogram is used to describe the spatial correlations between precipitation innovations, defined as the observed precipitation amounts minus the GEM forecasted amounts predicted at the observation locations. Currently, CaPA uses a single isotropic variogram across the entire analysis domain. The present project investigates the implications of this choice by first conducting a basic variographic analysis of precipitation innovation data across the Canadian prairies, with specific interest in identifying and quantifying potential anisotropy within the domain. This focus is further expanded by identifying the effect of storm type on the variogram. The ultimate goal of the variographic analysis is to develop improved semi-variograms for CaPA that better capture the spatial complexities of precipitation over the Canadian prairies. CaPA presently applies a Box-Cox data transformation to both the observations and the GEM data, prior to the calculation of the innovations. The data transformation is necessary to satisfy the normal distribution assumption, but introduces a significant bias. The second part of the investigation aims at devising a bias correction scheme based on a moving-window averaging technique. For both the variogram and bias correction components of this investigation, a series of trial runs are conducted to evaluate the impact of these changes on the resulting CaPA precipitation analyses.

Optimal design of compact spur gear reductions

NASA Technical Reports Server (NTRS)

Savage, M.; Lattime, S. B.; Kimmel, J. A.; Coe, H. H.

1992-01-01

The optimal design of compact spur gear reductions includes the selection of bearing and shaft proportions in addition to gear mesh parameters. Designs for single mesh spur gear reductions are based on optimization of system life, system volume, and system weight including gears, support shafts, and the four bearings. The overall optimization allows component properties to interact, yielding the best composite design. A modified feasible directions search algorithm directs the optimization through a continuous design space. Interpolated polynomials expand the discrete bearing properties and proportions into continuous variables for optimization. After finding the continuous optimum, the designer can analyze near optimal designs for comparison and selection. Design examples show the influence of the bearings on the optimal configurations.

Targeted ENO schemes with tailored resolution property for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Fu, Lin; Hu, Xiangyu Y.; Adams, Nikolaus A.

2017-11-01

In this paper, we extend the range of targeted ENO (TENO) schemes (Fu et al. (2016) [18]) by proposing an eighth-order TENO8 scheme. A general formulation to construct the high-order undivided difference τK within the weighting strategy is proposed. With the underlying scale-separation strategy, sixth-order accuracy for τK in the smooth solution regions is designed for good performance and robustness. Furthermore, a unified framework to optimize independently the dispersion and dissipation properties of high-order finite-difference schemes is proposed. The new framework enables tailoring of dispersion and dissipation as function of wavenumber. The optimal linear scheme has minimum dispersion error and a dissipation error that satisfies a dispersion-dissipation relation. Employing the optimal linear scheme, a sixth-order TENO8-opt scheme is constructed. A set of benchmark cases involving strong discontinuities and broadband fluctuations is computed to demonstrate the high-resolution properties of the new schemes.

Gaussian process regression for geometry optimization

NASA Astrophysics Data System (ADS)

Denzel, Alexander; Kästner, Johannes

2018-03-01

We implemented a geometry optimizer based on Gaussian process regression (GPR) to find minimum structures on potential energy surfaces. We tested both a two times differentiable form of the Matérn kernel and the squared exponential kernel. The Matérn kernel performs much better. We give a detailed description of the optimization procedures. These include overshooting the step resulting from GPR in order to obtain a higher degree of interpolation vs. extrapolation. In a benchmark against the Limited-memory Broyden-Fletcher-Goldfarb-Shanno optimizer of the DL-FIND library on 26 test systems, we found the new optimizer to generally reduce the number of required optimization steps.

Application of data assimilation methods for analysis and integration of observed and modeled Arctic Sea ice motions

NASA Astrophysics Data System (ADS)

Meier, Walter Neil

This thesis demonstrates the applicability of data assimilation methods to improve observed and modeled ice motion fields and to demonstrate the effects of assimilated motion on Arctic processes important to the global climate and of practical concern to human activities. Ice motions derived from 85 GHz and 37 GHz SSM/I imagery and estimated from two-dimensional dynamic-thermodynamic sea ice models are compared to buoy observations. Mean error, error standard deviation, and correlation with buoys are computed for the model domain. SSM/I motions generally have a lower bias, but higher error standard deviations and lower correlation with buoys than model motions. There are notable variations in the statistics depending on the region of the Arctic, season, and ice characteristics. Assimilation methods are investigated and blending and optimal interpolation strategies are implemented. Blending assimilation improves error statistics slightly, but the effect of the assimilation is reduced due to noise in the SSM/I motions and is thus not an effective method to improve ice motion estimates. However, optimal interpolation assimilation reduces motion errors by 25--30% over modeled motions and 40--45% over SSM/I motions. Optimal interpolation assimilation is beneficial in all regions, seasons and ice conditions, and is particularly effective in regimes where modeled and SSM/I errors are high. Assimilation alters annual average motion fields. Modeled ice products of ice thickness, ice divergence, Fram Strait ice volume export, transport across the Arctic and interannual basin averages are also influenced by assimilated motions. Assimilation improves estimates of pollutant transport and corrects synoptic-scale errors in the motion fields caused by incorrect forcings or errors in model physics. The portability of the optimal interpolation assimilation method is demonstrated by implementing the strategy in an ice thickness distribution (ITD) model. This research presents an innovative method of combining a new data set of SSM/I-derived ice motions with three different sea ice models via two data assimilation methods. The work described here is the first example of assimilating remotely-sensed data within high-resolution and detailed dynamic-thermodynamic sea ice models. The results demonstrate that assimilation is a valuable resource for determining accurate ice motion in the Arctic.

General MoM Solutions for Large Arrays

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fasenfest, B; Capolino, F; Wilton, D R

2003-07-22

This paper focuses on a numerical procedure that addresses the difficulties of dealing with large, finite arrays while preserving the generality and robustness of full-wave methods. We present a fast method based on approximating interactions between sufficiently separated array elements via a relatively coarse interpolation of the Green's function on a uniform grid commensurate with the array's periodicity. The interaction between the basis and testing functions is reduced to a three-stage process. The first stage is a projection of standard (e.g., RWG) subdomain bases onto a set of interpolation functions that interpolate the Green's function on the array face. Thismore » projection, which is used in a matrix/vector product for each array cell in an iterative solution process, need only be carried out once for a single cell and results in a low-rank matrix. An intermediate stage matrix/vector product computation involving the uniformly sampled Green's function is of convolutional form in the lateral (transverse) directions so that a 2D FFT may be used. The final stage is a third matrix/vector product computation involving a matrix resulting from projecting testing functions onto the Green's function interpolation functions; the low-rank matrix is either identical to (using Galerkin's method) or similar to that for the bases projection. An effective MoM solution scheme is developed for large arrays using a modification of the AIM (Adaptive Integral Method) method. The method permits the analysis of arrays with arbitrary contours and nonplanar elements. Both fill and solve times within the MoM method are improved with respect to more standard MoM solvers.« less

An adaptive multi-moment FVM approach for incompressible flows

NASA Astrophysics Data System (ADS)

Liu, Cheng; Hu, Changhong

2018-04-01

In this study, a multi-moment finite volume method (FVM) based on block-structured adaptive Cartesian mesh is proposed for simulating incompressible flows. A conservative interpolation scheme following the idea of the constrained interpolation profile (CIP) method is proposed for the prolongation operation of the newly created mesh. A sharp immersed boundary (IB) method is used to model the immersed rigid body. A moving least squares (MLS) interpolation approach is applied for reconstruction of the velocity field around the solid surface. An efficient method for discretization of Laplacian operators on adaptive meshes is proposed. Numerical simulations on several test cases are carried out for validation of the proposed method. For the case of viscous flow past an impulsively started cylinder (Re = 3000 , 9500), the computed surface vorticity coincides with the result of the body-fitted method. For the case of a fast pitching NACA 0015 airfoil at moderate Reynolds numbers (Re = 10000 , 45000), the predicted drag coefficient (CD) and lift coefficient (CL) agree well with other numerical or experimental results. For 2D and 3D simulations of viscous flow past a pitching plate with prescribed motions (Re = 5000 , 40000), the predicted CD, CL and CM (moment coefficient) are in good agreement with those obtained by other numerical methods.

Quantum Optimal Multiple Assignment Scheme for Realizing General Access Structure of Secret Sharing

NASA Astrophysics Data System (ADS)

Matsumoto, Ryutaroh

The multiple assignment scheme is to assign one or more shares to single participant so that any kind of access structure can be realized by classical secret sharing schemes. We propose its quantum version including ramp secret sharing schemes. Then we propose an integer optimization approach to minimize the average share size.

Energy-Aware Multipath Routing Scheme Based on Particle Swarm Optimization in Mobile Ad Hoc Networks

PubMed Central

Robinson, Y. Harold; Rajaram, M.

2015-01-01

Mobile ad hoc network (MANET) is a collection of autonomous mobile nodes forming an ad hoc network without fixed infrastructure. Dynamic topology property of MANET may degrade the performance of the network. However, multipath selection is a great challenging task to improve the network lifetime. We proposed an energy-aware multipath routing scheme based on particle swarm optimization (EMPSO) that uses continuous time recurrent neural network (CTRNN) to solve optimization problems. CTRNN finds the optimal loop-free paths to solve link disjoint paths in a MANET. The CTRNN is used as an optimum path selection technique that produces a set of optimal paths between source and destination. In CTRNN, particle swarm optimization (PSO) method is primly used for training the RNN. The proposed scheme uses the reliability measures such as transmission cost, energy factor, and the optimal traffic ratio between source and destination to increase routing performance. In this scheme, optimal loop-free paths can be found using PSO to seek better link quality nodes in route discovery phase. PSO optimizes a problem by iteratively trying to get a better solution with regard to a measure of quality. The proposed scheme discovers multiple loop-free paths by using PSO technique. PMID:26819966

Research on connection structure of aluminumbody bus using multi-objective topology optimization

NASA Astrophysics Data System (ADS)

Peng, Q.; Ni, X.; Han, F.; Rhaman, K.; Ulianov, C.; Fang, X.

2018-01-01

For connecting Aluminum Alloy bus body aluminum components often occur the problem of failure, a new aluminum alloy connection structure is designed based on multi-objective topology optimization method. Determining the shape of the outer contour of the connection structure with topography optimization, establishing a topology optimization model of connections based on SIMP density interpolation method, going on multi-objective topology optimization, and improving the design of the connecting piece according to the optimization results. The results show that the quality of the aluminum alloy connector after topology optimization is reduced by 18%, and the first six natural frequencies are improved and the strength performance and stiffness performance are obviously improved.

Satellite radiothermovision of atmospheric mesoscale processes: case study of tropical cyclones

NASA Astrophysics Data System (ADS)

Ermakov, D. M.; Sharkov, E. A.; Chernushich, A. P.

2015-04-01

Satellite radiothermovision is a set of processing techniques applicable for multisource data of radiothermal monitoring of oceanatmosphere system, which allows creating dynamic description of mesoscale and synoptic atmospheric processes and estimating physically meaningful integral characteristics of the observed processes (like avdective flow of the latent heat through a given border). The approach is based on spatiotemporal interpolation of the satellite measurements which allows reconstructing the radiothermal fields (as well as the fields of geophysical parameters) of the ocean-atmosphere system at global scale with spatial resolution of about 0.125° and temporal resolution of 1.5 hour. The accuracy of spatiotemporal interpolation was estimated by direct comparison of interpolated data with the data of independent asynchronous measurements and was shown to correspond to the best achievable as reported in literature (for total precipitable water fields the accuracy is about 0.8 mm). The advantages of the implemented interpolation scheme are: closure under input radiothermal data, homogeneity in time scale (all data are interpolated through the same time intervals), automatic estimation of both the intermediate states of scalar field of the studied geophysical parameter and of vector field of effective velocity of advection (horizontal movements). Using this pair of fields one can calculate the flow of a given geophysical quantity though any given border. For example, in case of total precipitable water field, this flow (under proper calibration) has the meaning of latent heat advective flux. This opportunity was used to evaluate the latent heat flux though a set of circular contours, enclosing a tropical cyclone and drifting with it during its evolution. A remarkable interrelation was observed between the calculated magnitude and sign of advective latent flux and the intensity of a tropical cyclone. This interrelation is demonstrated in several examples of hurricanes and tropical cyclones of August, 2000, and typhoons of November, 2013, including super typhoon Haiyan.

Optimizing the Betts-Miller-Janjic cumulus parameterization with Intel Many Integrated Core (MIC) architecture

NASA Astrophysics Data System (ADS)

Huang, Melin; Huang, Bormin; Huang, Allen H.-L.

2015-10-01

The schemes of cumulus parameterization are responsible for the sub-grid-scale effects of convective and/or shallow clouds, and intended to represent vertical fluxes due to unresolved updrafts and downdrafts and compensating motion outside the clouds. Some schemes additionally provide cloud and precipitation field tendencies in the convective column, and momentum tendencies due to convective transport of momentum. The schemes all provide the convective component of surface rainfall. Betts-Miller-Janjic (BMJ) is one scheme to fulfill such purposes in the weather research and forecast (WRF) model. National Centers for Environmental Prediction (NCEP) has tried to optimize the BMJ scheme for operational application. As there are no interactions among horizontal grid points, this scheme is very suitable for parallel computation. With the advantage of Intel Xeon Phi Many Integrated Core (MIC) architecture, efficient parallelization and vectorization essentials, it allows us to optimize the BMJ scheme. If compared to the original code respectively running on one CPU socket (eight cores) and on one CPU core with Intel Xeon E5-2670, the MIC-based optimization of this scheme running on Xeon Phi coprocessor 7120P improves the performance by 2.4x and 17.0x, respectively.

Optimal design of the first stage of the plate-fin heat exchanger for the EAST cryogenic system

NASA Astrophysics Data System (ADS)

Qingfeng, JIANG; Zhigang, ZHU; Qiyong, ZHANG; Ming, ZHUANG; Xiaofei, LU

2018-03-01

The size of the heat exchanger is an important factor determining the dimensions of the cold box in helium cryogenic systems. In this paper, a counter-flow multi-stream plate-fin heat exchanger is optimized by means of a spatial interpolation method coupled with a hybrid genetic algorithm. Compared with empirical correlations, this spatial interpolation algorithm based on a kriging model can be adopted to more precisely predict the Colburn heat transfer factors and Fanning friction factors of offset-strip fins. Moreover, strict computational fluid dynamics simulations can be carried out to predict the heat transfer and friction performance in the absence of reliable experimental data. Within the constraints of heat exchange requirements, maximum allowable pressure drop, existing manufacturing techniques and structural strength, a mathematical model of an optimized design with discrete and continuous variables based on a hybrid genetic algorithm is established in order to minimize the volume. The results show that for the first-stage heat exchanger in the EAST refrigerator, the structural size could be decreased from the original 2.200 × 0.600 × 0.627 (m3) to the optimized 1.854 × 0.420 × 0.340 (m3), with a large reduction in volume. The current work demonstrates that the proposed method could be a useful tool to achieve optimization in an actual engineering project during the practical design process.

Systematic design of 3D auxetic lattice materials with programmable Poisson's ratio for finite strains

NASA Astrophysics Data System (ADS)

Wang, Fengwen

2018-05-01

This paper presents a systematic approach for designing 3D auxetic lattice materials, which exhibit constant negative Poisson's ratios over large strain intervals. A unit cell model mimicking tensile tests is established and based on the proposed model, the secant Poisson's ratio is defined as the negative ratio between the lateral and the longitudinal engineering strains. The optimization problem for designing a material unit cell with a target Poisson's ratio is formulated to minimize the average lateral engineering stresses under the prescribed deformations. Numerical results demonstrate that 3D auxetic lattice materials with constant Poisson's ratios can be achieved by the proposed optimization formulation and that two sets of material architectures are obtained by imposing different symmetry on the unit cell. Moreover, inspired by the topology-optimized material architecture, a subsequent shape optimization is proposed by parametrizing material architectures using super-ellipsoids. By designing two geometrical parameters, simple optimized material microstructures with different target Poisson's ratios are obtained. By interpolating these two parameters as polynomial functions of Poisson's ratios, material architectures for any Poisson's ratio in the interval of ν ∈ [ - 0.78 , 0.00 ] are explicitly presented. Numerical evaluations show that interpolated auxetic lattice materials exhibit constant Poisson's ratios in the target strain interval of [0.00, 0.20] and that 3D auxetic lattice material architectures with programmable Poisson's ratio are achievable.

Computer-intensive simulation of solid-state NMR experiments using SIMPSON.

PubMed

Tošner, Zdeněk; Andersen, Rasmus; Stevensson, Baltzar; Edén, Mattias; Nielsen, Niels Chr; Vosegaard, Thomas

2014-09-01

Conducting large-scale solid-state NMR simulations requires fast computer software potentially in combination with efficient computational resources to complete within a reasonable time frame. Such simulations may involve large spin systems, multiple-parameter fitting of experimental spectra, or multiple-pulse experiment design using parameter scan, non-linear optimization, or optimal control procedures. To efficiently accommodate such simulations, we here present an improved version of the widely distributed open-source SIMPSON NMR simulation software package adapted to contemporary high performance hardware setups. The software is optimized for fast performance on standard stand-alone computers, multi-core processors, and large clusters of identical nodes. We describe the novel features for fast computation including internal matrix manipulations, propagator setups and acquisition strategies. For efficient calculation of powder averages, we implemented interpolation method of Alderman, Solum, and Grant, as well as recently introduced fast Wigner transform interpolation technique. The potential of the optimal control toolbox is greatly enhanced by higher precision gradients in combination with the efficient optimization algorithm known as limited memory Broyden-Fletcher-Goldfarb-Shanno. In addition, advanced parallelization can be used in all types of calculations, providing significant time reductions. SIMPSON is thus reflecting current knowledge in the field of numerical simulations of solid-state NMR experiments. The efficiency and novel features are demonstrated on the representative simulations. Copyright © 2014 Elsevier Inc. All rights reserved.

A genetic fuzzy analytical hierarchy process based projection pursuit method for selecting schemes of water transportation projects

NASA Astrophysics Data System (ADS)

Jin, Juliang; Li, Lei; Wang, Wensheng; Zhang, Ming

2006-10-01

The optimal selection of schemes of water transportation projects is a process of choosing a relatively optimal scheme from a number of schemes of water transportation programming and management projects, which is of importance in both theory and practice in water resource systems engineering. In order to achieve consistency and eliminate the dimensions of fuzzy qualitative and fuzzy quantitative evaluation indexes, to determine the weights of the indexes objectively, and to increase the differences among the comprehensive evaluation index values of water transportation project schemes, a projection pursuit method, named FPRM-PP for short, was developed in this work for selecting the optimal water transportation project scheme based on the fuzzy preference relation matrix. The research results show that FPRM-PP is intuitive and practical, the correction range of the fuzzy preference relation matrix A it produces is relatively small, and the result obtained is both stable and accurate; therefore FPRM-PP can be widely used in the optimal selection of different multi-factor decision-making schemes.

A new solution-adaptive grid generation method for transonic airfoil flow calculations

NASA Technical Reports Server (NTRS)

Nakamura, S.; Holst, T. L.

1981-01-01

The clustering algorithm is controlled by a second-order, ordinary differential equation which uses the airfoil surface density gradient as a forcing function. The solution to this differential equation produces a surface grid distribution which is automatically clustered in regions with large gradients. The interior grid points are established from this surface distribution by using an interpolation scheme which is fast and retains the desirable properties of the original grid generated from the standard elliptic equation approach.

An efficient transport solver for tokamak plasmas

DOE PAGES

Park, Jin Myung; Murakami, Masanori; St. John, H. E.; ...

2017-01-03

A simple approach to efficiently solve a coupled set of 1-D diffusion-type transport equations with a stiff transport model for tokamak plasmas is presented based on the 4th order accurate Interpolated Differential Operator scheme along with a nonlinear iteration method derived from a root-finding algorithm. Here, numerical tests using the Trapped Gyro-Landau-Fluid model show that the presented high order method provides an accurate transport solution using a small number of grid points with robust nonlinear convergence.

A data base and analysis program for shuttle main engine dynamic pressure measurements. Appendix F: Data base plots for SSME tests 750-120 through 750-200

NASA Technical Reports Server (NTRS)

Coffin, T.

1986-01-01

A dynamic pressure data base and data base management system developed to characterize the Space Shuttle Main Engine (SSME) dynamic pressure environment is presented. The data base represents dynamic pressure measurements obtained during single engine hot firing tests of the SSME. Software is provided to permit statistical evaluation of selected measurements under specified operating conditions. An interpolation scheme is also included to estimate spectral trends with SSME power level.

Thickness Gauging of Single-Layer Conductive Materials with Two-Point Non Linear Calibration Algorithm

NASA Technical Reports Server (NTRS)

Fulton, James P. (Inventor); Namkung, Min (Inventor); Simpson, John W. (Inventor); Wincheski, Russell A. (Inventor); Nath, Shridhar C. (Inventor)

1998-01-01

A thickness gauging instrument uses a flux focusing eddy current probe and two-point nonlinear calibration algorithm. The instrument is small and portable due to the simple interpretation and operational characteristics of the probe. A nonlinear interpolation scheme incorporated into the instrument enables a user to make highly accurate thickness measurements over a fairly wide calibration range from a single side of nonferromagnetic conductive metals. The instrument is very easy to use and can be calibrated quickly.

The Effect of Multigrid Parameters in a 3D Heat Diffusion Equation

NASA Astrophysics Data System (ADS)

Oliveira, F. De; Franco, S. R.; Pinto, M. A. Villela

2018-02-01

The aim of this paper is to reduce the necessary CPU time to solve the three-dimensional heat diffusion equation using Dirichlet boundary conditions. The finite difference method (FDM) is used to discretize the differential equations with a second-order accuracy central difference scheme (CDS). The algebraic equations systems are solved using the lexicographical and red-black Gauss-Seidel methods, associated with the geometric multigrid method with a correction scheme (CS) and V-cycle. Comparisons are made between two types of restriction: injection and full weighting. The used prolongation process is the trilinear interpolation. This work is concerned with the study of the influence of the smoothing value (v), number of mesh levels (L) and number of unknowns (N) on the CPU time, as well as the analysis of algorithm complexity.

Current Saturation Avoidance with Real-Time Control using DPCS

NASA Astrophysics Data System (ADS)

Ferrara, M.; Hutchinson, I.; Wolfe, S.; Stillerman, J.; Fredian, T.

2008-11-01

Tokamak ohmic-transformer and equilibrium-field coils need to be able to operate near their maximum current capabilities. However if they reach their upper limit during high-performance discharges or in the presence of a strong off-normal event, shape control is compromised, and instability, even plasma disruptions can result. On Alcator C-Mod we designed and tested an anti-saturation routine which detects the impending saturation of OH and EF currents and interpolates to a neighboring safe equilibrium in real-time. The routine was implemented with a multi-processor, multi-time-scale control scheme, which is based on a master process and multiple asynchronous slave processes. The scheme is general and can be used for any computationally-intensive algorithm. USDoE award DE- FC02-99ER545512.

The Linear Bicharacteristic Scheme for Computational Electromagnetics

NASA Technical Reports Server (NTRS)

Beggs, John H.; Chan, Siew-Loong

2000-01-01

The upwind leapfrog or Linear Bicharacteristic Scheme (LBS) has previously been implemented and demonstrated on electromagnetic wave propagation problems. This paper extends the Linear Bicharacteristic Scheme for computational electromagnetics to treat lossy dielectric and magnetic materials and perfect electrical conductors. This is accomplished by proper implementation of the LBS for homogeneous lossy dielectric and magnetic media, and treatment of perfect electrical conductors (PECs) are shown to follow directly in the limit of high conductivity. Heterogeneous media are treated through implementation of surface boundary conditions and no special extrapolations or interpolations at dielectric material boundaries are required. Results are presented for one-dimensional model problems on both uniform and nonuniform grids, and the FDTD algorithm is chosen as a convenient reference algorithm for comparison. The results demonstrate that the explicit LBS is a dissipation-free, second-order accurate algorithm which uses a smaller stencil than the FDTD algorithm, yet it has approximately one-third the phase velocity error. The LBS is also more accurate on nonuniform grids.

Cost-effective accurate coarse-grid method for highly convective multidimensional unsteady flows

NASA Technical Reports Server (NTRS)

Leonard, B. P.; Niknafs, H. S.

1991-01-01

A fundamentally multidimensional convection scheme is described based on vector transient interpolation modeling rewritten in conservative control-volume form. Vector third-order upwinding is used as the basis of the algorithm; this automatically introduces important cross-difference terms that are absent from schemes using component-wise one-dimensional formulas. Third-order phase accuracy is good; this is important for coarse-grid large-eddy or full simulation. Potential overshoots or undershoots are avoided by using a recently developed universal limiter. Higher order accuracy is obtained locally, where needed, by the cost-effective strategy of adaptive stencil expansion in a direction normal to each control-volume face; this is controlled by monitoring the absolute normal gradient and curvature across the face. Higher (than third) order cross-terms do not appear to be needed. Since the wider stencil is used only in isolated narrow regions (near discontinuities), extremely high (in this case, seventh) order accuracy can be achieved for little more than the cost of a globally third-order scheme.

A Two-Dimensional Linear Bicharacteristic Scheme for Electromagnetics

NASA Technical Reports Server (NTRS)

Beggs, John H.

2002-01-01

The upwind leapfrog or Linear Bicharacteristic Scheme (LBS) has previously been implemented and demonstrated on one-dimensional electromagnetic wave propagation problems. This memorandum extends the Linear Bicharacteristic Scheme for computational electromagnetics to model lossy dielectric and magnetic materials and perfect electrical conductors in two dimensions. This is accomplished by proper implementation of the LBS for homogeneous lossy dielectric and magnetic media and for perfect electrical conductors. Both the Transverse Electric and Transverse Magnetic polarizations are considered. Computational requirements and a Fourier analysis are also discussed. Heterogeneous media are modeled through implementation of surface boundary conditions and no special extrapolations or interpolations at dielectric material boundaries are required. Results are presented for two-dimensional model problems on uniform grids, and the Finite Difference Time Domain (FDTD) algorithm is chosen as a convenient reference algorithm for comparison. The results demonstrate that the two-dimensional explicit LBS is a dissipation-free, second-order accurate algorithm which uses a smaller stencil than the FDTD algorithm, yet it has less phase velocity error.

Investigation of Advanced Counterrotation Blade Configuration Concepts for High Speed Turboprop Systems. Task 3: Advanced Fan Section Grid Generator Final Report and Computer Program User's Manual

NASA Technical Reports Server (NTRS)

Crook, Andrew J.; Delaney, Robert A.

1991-01-01

A procedure is studied for generating three-dimensional grids for advanced turbofan engine fan section geometries. The procedure constructs a discrete mesh about engine sections containing the fan stage, an arbitrary number of axisymmetric radial flow splitters, a booster stage, and a bifurcated core/bypass flow duct with guide vanes. The mesh is an h-type grid system, the points being distributed with a transfinite interpolation scheme with axial and radial spacing being user specified. Elliptic smoothing of the grid in the meridional plane is a post-process option. The grid generation scheme is consistent with aerodynamic analyses utilizing the average-passage equation system developed by Dr. John Adamczyk of NASA Lewis. This flow solution scheme requires a series of blade specific grids each having a common axisymmetric mesh, but varying in the circumferential direction according to the geometry of the specific blade row.

Enhanced Conformational Sampling in Molecular Dynamics Simulations of Solvated Peptides: Fragment-Based Local Elevation Umbrella Sampling.

PubMed

Hansen, Halvor S; Daura, Xavier; Hünenberger, Philippe H

2010-09-14

A new method, fragment-based local elevation umbrella sampling (FB-LEUS), is proposed to enhance the conformational sampling in explicit-solvent molecular dynamics (MD) simulations of solvated polymers. The method is derived from the local elevation umbrella sampling (LEUS) method [ Hansen and Hünenberger , J. Comput. Chem. 2010 , 31 , 1 - 23 ], which combines the local elevation (LE) conformational searching and the umbrella sampling (US) conformational sampling approaches into a single scheme. In LEUS, an initial (relatively short) LE build-up (searching) phase is used to construct an optimized (grid-based) biasing potential within a subspace of conformationally relevant degrees of freedom, which is then frozen and used in a (comparatively longer) US sampling phase. This combination dramatically enhances the sampling power of MD simulations but, due to computational and memory costs, is only applicable to relevant subspaces of low dimensionalities. As an attempt to expand the scope of the LEUS approach to solvated polymers with more than a few relevant degrees of freedom, the FB-LEUS scheme involves an US sampling phase that relies on a superposition of low-dimensionality biasing potentials optimized using LEUS at the fragment level. The feasibility of this approach is tested using polyalanine (poly-Ala) and polyvaline (poly-Val) oligopeptides. Two-dimensional biasing potentials are preoptimized at the monopeptide level, and subsequently applied to all dihedral-angle pairs within oligopeptides of 4,  6,  8, or 10 residues. Two types of fragment-based biasing potentials are distinguished: (i) the basin-filling (BF) potentials act so as to "fill" free-energy basins up to a prescribed free-energy level above the global minimum; (ii) the valley-digging (VD) potentials act so as to "dig" valleys between the (four) free-energy minima of the two-dimensional maps, preserving barriers (relative to linearly interpolated free-energy changes) of a prescribed magnitude. The application of these biasing potentials may lead to an impressive enhancement of the searching power (volume of conformational space visited in a given amount of simulation time). However, this increase is largely offset by a deterioration of the statistical efficiency (representativeness of the biased ensemble in terms of the conformational distribution appropriate for the physical ensemble). As a result, it appears difficult to engineer FB-LEUS schemes representing a significant improvement over plain MD, at least for the systems considered here.

An Interpolation Approach to Optimal Trajectory Planning for Helicopter Unmanned Aerial Vehicles

DTIC Science & Technology

2012-06-01

Armament Data Line DOF Degree of Freedom PS Pseudospectral LGL Legendre -Gauss-Lobatto quadrature nodes ODE Ordinary Differential Equation xiv...low order polynomials patched together in such away so that the resulting trajectory has several continuous derivatives at all points. In [7], Murray...claims that splines are ideal for optimal control problems because each segment of the spline’s piecewise polynomials approximate the trajectory

Fast exploration of an optimal path on the multidimensional free energy surface

PubMed Central

Chen, Changjun

2017-01-01

In a reaction, determination of an optimal path with a high reaction rate (or a low free energy barrier) is important for the study of the reaction mechanism. This is a complicated problem that involves lots of degrees of freedom. For simple models, one can build an initial path in the collective variable space by the interpolation method first and then update the whole path constantly in the optimization. However, such interpolation method could be risky in the high dimensional space for large molecules. On the path, steric clashes between neighboring atoms could cause extremely high energy barriers and thus fail the optimization. Moreover, performing simulations for all the snapshots on the path is also time-consuming. In this paper, we build and optimize the path by a growing method on the free energy surface. The method grows a path from the reactant and extends its length in the collective variable space step by step. The growing direction is determined by both the free energy gradient at the end of the path and the direction vector pointing at the product. With fewer snapshots on the path, this strategy can let the path avoid the high energy states in the growing process and save the precious simulation time at each iteration step. Applications show that the presented method is efficient enough to produce optimal paths on either the two-dimensional or the twelve-dimensional free energy surfaces of different small molecules. PMID:28542475

Multiobjective hyper heuristic scheme for system design and optimization

NASA Astrophysics Data System (ADS)

Rafique, Amer Farhan

2012-11-01

As system design is becoming more and more multifaceted, integrated, and complex, the traditional single objective optimization trends of optimal design are becoming less and less efficient and effective. Single objective optimization methods present a unique optimal solution whereas multiobjective methods present pareto front. The foremost intent is to predict a reasonable distributed pareto-optimal solution set independent of the problem instance through multiobjective scheme. Other objective of application of intended approach is to improve the worthiness of outputs of the complex engineering system design process at the conceptual design phase. The process is automated in order to provide the system designer with the leverage of the possibility of studying and analyzing a large multiple of possible solutions in a short time. This article presents Multiobjective Hyper Heuristic Optimization Scheme based on low level meta-heuristics developed for the application in engineering system design. Herein, we present a stochastic function to manage meta-heuristics (low-level) to augment surety of global optimum solution. Generic Algorithm, Simulated Annealing and Swarm Intelligence are used as low-level meta-heuristics in this study. Performance of the proposed scheme is investigated through a comprehensive empirical analysis yielding acceptable results. One of the primary motives for performing multiobjective optimization is that the current engineering systems require simultaneous optimization of conflicting and multiple. Random decision making makes the implementation of this scheme attractive and easy. Injecting feasible solutions significantly alters the search direction and also adds diversity of population resulting in accomplishment of pre-defined goals set in the proposed scheme.

The MusIC method: a fast and quasi-optimal solution to the muscle forces estimation problem.

PubMed

Muller, A; Pontonnier, C; Dumont, G

2018-02-01

The present paper aims at presenting a fast and quasi-optimal method of muscle forces estimation: the MusIC method. It consists in interpolating a first estimation in a database generated offline thanks to a classical optimization problem, and then correcting it to respect the motion dynamics. Three different cost functions - two polynomial criteria and a min/max criterion - were tested on a planar musculoskeletal model. The MusIC method provides a computation frequency approximately 10 times higher compared to a classical optimization problem with a relative mean error of 4% on cost function evaluation.

PEGASUS 5: An Automated Pre-Processor for Overset-Grid CFD

NASA Technical Reports Server (NTRS)

Suhs, Norman E.; Rogers, Stuart E.; Dietz, William E.; Kwak, Dochan (Technical Monitor)

2002-01-01

An all new, automated version of the PEGASUS software has been developed and tested. PEGASUS provides the hole-cutting and connectivity information between overlapping grids, and is used as the final part of the grid generation process for overset-grid computational fluid dynamics approaches. The new PEGASUS code (Version 5) has many new features: automated hole cutting; a projection scheme for fixing gaps in overset surfaces; more efficient interpolation search methods using an alternating digital tree; hole-size optimization based on adding additional layers of fringe points; and an automatic restart capability. The new code has also been parallelized using the Message Passing Interface standard. The parallelization performance provides efficient speed-up of the execution time by an order of magnitude, and up to a factor of 30 for very large problems. The results of three example cases are presented: a three-element high-lift airfoil, a generic business jet configuration, and a complete Boeing 777-200 aircraft in a high-lift landing configuration. Comparisons of the computed flow fields for the airfoil and 777 test cases between the old and new versions of the PEGASUS codes show excellent agreement with each other and with experimental results.

Spatial interpolation of GPS PWV and meteorological variables over the west coast of Peninsular Malaysia during 2013 Klang Valley Flash Flood

NASA Astrophysics Data System (ADS)

Suparta, Wayan; Rahman, Rosnani

2016-02-01

Global Positioning System (GPS) receivers are widely installed throughout the Peninsular Malaysia, but the implementation for monitoring weather hazard system such as flash flood is still not optimal. To increase the benefit for meteorological applications, the GPS system should be installed in collocation with meteorological sensors so the precipitable water vapor (PWV) can be measured. The distribution of PWV is a key element to the Earth's climate for quantitative precipitation improvement as well as flash flood forecasts. The accuracy of this parameter depends on a large extent on the number of GPS receiver installations and meteorological sensors in the targeted area. Due to cost constraints, a spatial interpolation method is proposed to address these issues. In this paper, we investigated spatial distribution of GPS PWV and meteorological variables (surface temperature, relative humidity, and rainfall) by using thin plate spline (tps) and ordinary kriging (Krig) interpolation techniques over the Klang Valley in Peninsular Malaysia (longitude: 99.5°-102.5°E and latitude: 2.0°-6.5°N). Three flash flood cases in September, October, and December 2013 were studied. The analysis was performed using mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R2) to determine the accuracy and reliability of the interpolation techniques. Results at different phases (pre, onset, and post) that were evaluated showed that tps interpolation technique is more accurate, reliable, and highly correlated in estimating GPS PWV and relative humidity, whereas Krig is more reliable for predicting temperature and rainfall during pre-flash flood events. During the onset of flash flood events, both methods showed good interpolation in estimating all meteorological parameters with high accuracy and reliability. The finding suggests that the proposed method of spatial interpolation techniques are capable of handling limited data sources with high accuracy, which in turn can be used to predict future floods.

Optimal estimation of suspended-sediment concentrations in streams

USGS Publications Warehouse

Holtschlag, D.J.

2001-01-01

Optimal estimators are developed for computation of suspended-sediment concentrations in streams. The estimators are a function of parameters, computed by use of generalized least squares, which simultaneously account for effects of streamflow, seasonal variations in average sediment concentrations, a dynamic error component, and the uncertainty in concentration measurements. The parameters are used in a Kalman filter for on-line estimation and an associated smoother for off-line estimation of suspended-sediment concentrations. The accuracies of the optimal estimators are compared with alternative time-averaging interpolators and flow-weighting regression estimators by use of long-term daily-mean suspended-sediment concentration and streamflow data from 10 sites within the United States. For sampling intervals from 3 to 48 days, the standard errors of on-line and off-line optimal estimators ranged from 52.7 to 107%, and from 39.5 to 93.0%, respectively. The corresponding standard errors of linear and cubic-spline interpolators ranged from 48.8 to 158%, and from 50.6 to 176%, respectively. The standard errors of simple and multiple regression estimators, which did not vary with the sampling interval, were 124 and 105%, respectively. Thus, the optimal off-line estimator (Kalman smoother) had the lowest error characteristics of those evaluated. Because suspended-sediment concentrations are typically measured at less than 3-day intervals, use of optimal estimators will likely result in significant improvements in the accuracy of continuous suspended-sediment concentration records. Additional research on the integration of direct suspended-sediment concentration measurements and optimal estimators applied at hourly or shorter intervals is needed.

Dental implant customization using numerical optimization design and 3-dimensional printing fabrication of zirconia ceramic.

PubMed

Cheng, Yung-Chang; Lin, Deng-Huei; Jiang, Cho-Pei; Lin, Yuan-Min

2017-05-01

This study proposes a new methodology for dental implant customization consisting of numerical geometric optimization and 3-dimensional printing fabrication of zirconia ceramic. In the numerical modeling, exogenous factors for implant shape include the thread pitch, thread depth, maximal diameter of implant neck, and body size. Endogenous factors are bone density, cortical bone thickness, and non-osseointegration. An integration procedure, including uniform design method, Kriging interpolation and genetic algorithm, is applied to optimize the geometry of dental implants. The threshold of minimal micromotion for optimization evaluation was 100 μm. The optimized model is imported to the 3-dimensional slurry printer to fabricate the zirconia green body (powder is bonded by polymer weakly) of the implant. The sintered implant is obtained using a 2-stage sintering process. Twelve models are constructed according to uniform design method and simulated the micromotion behavior using finite element modeling. The result of uniform design models yields a set of exogenous factors that can provide the minimal micromotion (30.61 μm), as a suitable model. Kriging interpolation and genetic algorithm modified the exogenous factor of the suitable model, resulting in 27.11 μm as an optimization model. Experimental results show that the 3-dimensional slurry printer successfully fabricated the green body of the optimization model, but the accuracy of sintered part still needs to be improved. In addition, the scanning electron microscopy morphology is a stabilized t-phase microstructure, and the average compressive strength of the sintered part is 632.1 MPa. Copyright © 2016 John Wiley & Sons, Ltd.

Optical realization of optimal symmetric real state quantum cloning machine

NASA Astrophysics Data System (ADS)

Hu, Gui-Yu; Zhang, Wen-Hai; Ye, Liu

2010-01-01

We present an experimentally uniform linear optical scheme to implement the optimal 1→2 symmetric and optimal 1→3 symmetric economical real state quantum cloning machine of the polarization state of the single photon. This scheme requires single-photon sources and two-photon polarization entangled state as input states. It also involves linear optical elements and three-photon coincidence. Then we consider the realistic realization of the scheme by using the parametric down-conversion as photon resources. It is shown that under certain condition, the scheme is feasible by current experimental technology.

Using optimal interpolation to assimilate surface measurements and satellite AOD for ozone and PM2.5: A case study for July 2011.

PubMed

Tang, Youhua; Chai, Tianfeng; Pan, Li; Lee, Pius; Tong, Daniel; Kim, Hyun-Cheol; Chen, Weiwei

2015-10-01

We employed an optimal interpolation (OI) method to assimilate AIRNow ozone/PM2.5 and MODIS (Moderate Resolution Imaging Spectroradiometer) aerosol optical depth (AOD) data into the Community Multi-scale Air Quality (CMAQ) model to improve the ozone and total aerosol concentration for the CMAQ simulation over the contiguous United States (CONUS). AIRNow data assimilation was applied to the boundary layer, and MODIS AOD data were used to adjust total column aerosol. Four OI cases were designed to examine the effects of uncertainty setting and assimilation time; two of these cases used uncertainties that varied in time and location, or "dynamic uncertainties." More frequent assimilation and higher model uncertainties pushed the modeled results closer to the observation. Our comparison over a 24-hr period showed that ozone and PM2.5 mean biases could be reduced from 2.54 ppbV to 1.06 ppbV and from -7.14 µg/m³ to -0.11 µg/m³, respectively, over CONUS, while their correlations were also improved. Comparison to DISCOVER-AQ 2011 aircraft measurement showed that surface ozone assimilation applied to the CMAQ simulation improves regional low-altitude (below 2 km) ozone simulation. This paper described an application of using optimal interpolation method to improve the model's ozone and PM2.5 estimation using surface measurement and satellite AOD. It highlights the usage of the operational AIRNow data set, which is available in near real time, and the MODIS AOD. With a similar method, we can also use other satellite products, such as the latest VIIRS products, to improve PM2.5 prediction.

A Neural Network Aero Design System for Advanced Turbo-Engines

NASA Technical Reports Server (NTRS)

Sanz, Jose M.

1999-01-01

An inverse design method calculates the blade shape that produces a prescribed input pressure distribution. By controlling this input pressure distribution the aerodynamic design objectives can easily be met. Because of the intrinsic relationship between pressure distribution and airfoil physical properties, a Neural Network can be trained to choose the optimal pressure distribution that would meet a set of physical requirements. Neural network systems have been attempted in the context of direct design methods. From properties ascribed to a set of blades the neural network is trained to infer the properties of an 'interpolated' blade shape. The problem is that, especially in transonic regimes where we deal with intrinsically non linear and ill posed problems, small perturbations of the blade shape can produce very large variations of the flow parameters. It is very unlikely that, under these circumstances, a neural network will be able to find the proper solution. The unique situation in the present method is that the neural network can be trained to extract the required input pressure distribution from a database of pressure distributions while the inverse method will still compute the exact blade shape that corresponds to this 'interpolated' input pressure distribution. In other words, the interpolation process is transferred to a smoother problem, namely, finding what pressure distribution would produce the required flow conditions and, once this is done, the inverse method will compute the exact solution for this problem. The use of neural network is, in this context, highly related to the use of proper optimization techniques. The optimization is used essentially as an automation procedure to force the input pressure distributions to achieve the required aero and structural design parameters. A multilayered feed forward network with back-propagation is used to train the system for pattern association and classification.

Quantification of soil water retention parameters using multi-section TDR-waveform analysis

NASA Astrophysics Data System (ADS)

Baviskar, S. M.; Heimovaara, T. J.

2017-06-01

Soil water retention parameters are important for describing flow in variably saturated soils. TDR is one of the standard methods used for determining water content in soil samples. In this study, we present an approach to estimate water retention parameters of a sample which is initially saturated and subjected to an incremental decrease in boundary head causing it to drain in a multi-step fashion. TDR waveforms are measured along the height of the sample at assumed different hydrostatic conditions at daily interval. The cumulative discharge outflow drained from the sample is also recorded. The saturated water content is obtained using volumetric analysis after the final step involved in multi-step drainage. The equation obtained by coupling the unsaturated parametric function and the apparent dielectric permittivity is fitted to a TDR wave propagation forward model. The unsaturated parametric function is used to spatially interpolate the water contents along TDR probe. The cumulative discharge outflow data is fitted with cumulative discharge estimated using the unsaturated parametric function. The weight of water inside the sample estimated at the first and final boundary head in multi-step drainage is fitted with the corresponding weights calculated using unsaturated parametric function. A Bayesian optimization scheme is used to obtain optimized water retention parameters for these different objective functions. This approach can be used for samples with long heights and is especially suitable for characterizing sands with a uniform particle size distribution at low capillary heads.

A stabilized element-based finite volume method for poroelastic problems

NASA Astrophysics Data System (ADS)

Honório, Hermínio T.; Maliska, Clovis R.; Ferronato, Massimiliano; Janna, Carlo

2018-07-01

The coupled equations of Biot's poroelasticity, consisting of stress equilibrium and fluid mass balance in deforming porous media, are numerically solved. The governing partial differential equations are discretized by an Element-based Finite Volume Method (EbFVM), which can be used in three dimensional unstructured grids composed of elements of different types. One of the difficulties for solving these equations is the numerical pressure instability that can arise when undrained conditions take place. In this paper, a stabilization technique is developed to overcome this problem by employing an interpolation function for displacements that considers also the pressure gradient effect. The interpolation function is obtained by the so-called Physical Influence Scheme (PIS), typically employed for solving incompressible fluid flows governed by the Navier-Stokes equations. Classical problems with analytical solutions, as well as three-dimensional realistic cases are addressed. The results reveal that the proposed stabilization technique is able to eliminate the spurious pressure instabilities arising under undrained conditions at a low computational cost.

Poisson Coordinates.

PubMed

Li, Xian-Ying; Hu, Shi-Min

2013-02-01

Harmonic functions are the critical points of a Dirichlet energy functional, the linear projections of conformal maps. They play an important role in computer graphics, particularly for gradient-domain image processing and shape-preserving geometric computation. We propose Poisson coordinates, a novel transfinite interpolation scheme based on the Poisson integral formula, as a rapid way to estimate a harmonic function on a certain domain with desired boundary values. Poisson coordinates are an extension of the Mean Value coordinates (MVCs) which inherit their linear precision, smoothness, and kernel positivity. We give explicit formulas for Poisson coordinates in both continuous and 2D discrete forms. Superior to MVCs, Poisson coordinates are proved to be pseudoharmonic (i.e., they reproduce harmonic functions on n-dimensional balls). Our experimental results show that Poisson coordinates have lower Dirichlet energies than MVCs on a number of typical 2D domains (particularly convex domains). As well as presenting a formula, our approach provides useful insights for further studies on coordinates-based interpolation and fast estimation of harmonic functions.

A refined characterization of the alluvial geology of yucca flat and its effect on bulk hydraulic conductivity

USGS Publications Warehouse

Phelps, G.A.; Halford, K.J.

2011-01-01

In Yucca Flat, on the Nevada National Security Site in southern Nevada, the migration of radionuclides from tests located in the alluvial deposits into the Paleozoic carbonate aquifer involves passage through a thick, heterogeneous section of late Tertiary and Quaternary alluvial sediments. An understanding of the lateral and vertical changes in the material properties of the alluvial sediments will aid in the further development of the hydrogeologic framework and the delineation of hydrostratigraphic units and hydraulic properties required for simulating groundwater flow in the Yucca Flat area. Previously published geologic models for the alluvial sediments within Yucca Flat are based on extensive examination and categorization of drill-hole data, combined with a simple, data-driven interpolation scheme. The U.S. Geological Survey, in collaboration with Stanford University, is researching improvements to the modeling of the alluvial section, incorporating prior knowledge of geologic structure into the interpolation method and estimating the uncertainty of the modeled hydrogeologic units.

The concentration dependence of the galaxy–halo connection: Modeling assembly bias with abundance matching

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lehmann, Benjamin V.; Mao, Yao -Yuan; Becker, Matthew R.

Empirical methods for connecting galaxies to their dark matter halos have become essential for interpreting measurements of the spatial statistics of galaxies. In this work, we present a novel approach for parameterizing the degree of concentration dependence in the abundance matching method. Furthermore, this new parameterization provides a smooth interpolation between two commonly used matching proxies: the peak halo mass and the peak halo maximal circular velocity. This parameterization controls the amount of dependence of galaxy luminosity on halo concentration at a fixed halo mass. Effectively this interpolation scheme enables abundance matching models to have adjustable assembly bias in the resulting galaxy catalogs. With the newmore » $$400\\,\\mathrm{Mpc}\\,{h}^{-1}$$ DarkSky Simulation, whose larger volume provides lower sample variance, we further show that low-redshift two-point clustering and satellite fraction measurements from SDSS can already provide a joint constraint on this concentration dependence and the scatter within the abundance matching framework.« less

The concentration dependence of the galaxy–halo connection: Modeling assembly bias with abundance matching

DOE PAGES

Lehmann, Benjamin V.; Mao, Yao -Yuan; Becker, Matthew R.; ...

2016-12-28

Empirical methods for connecting galaxies to their dark matter halos have become essential for interpreting measurements of the spatial statistics of galaxies. In this work, we present a novel approach for parameterizing the degree of concentration dependence in the abundance matching method. Furthermore, this new parameterization provides a smooth interpolation between two commonly used matching proxies: the peak halo mass and the peak halo maximal circular velocity. This parameterization controls the amount of dependence of galaxy luminosity on halo concentration at a fixed halo mass. Effectively this interpolation scheme enables abundance matching models to have adjustable assembly bias in the resulting galaxy catalogs. With the newmore » $$400\\,\\mathrm{Mpc}\\,{h}^{-1}$$ DarkSky Simulation, whose larger volume provides lower sample variance, we further show that low-redshift two-point clustering and satellite fraction measurements from SDSS can already provide a joint constraint on this concentration dependence and the scatter within the abundance matching framework.« less

An online replanning method using warm start optimization and aperture morphing for flattening-filter-free beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahunbay, Ergun E., E-mail: eahunbay@mcw.edu; Ates,

Purpose: In a situation where a couch shift for patient positioning is not preferred or prohibited (e.g., MR-linac), segment aperture morphing (SAM) can address target dislocation and deformation. For IMRT/VMAT with flattening-filter-free (FFF) beams, however, SAM method would lead to an adverse translational dose effect due to the beam unflattening. Here the authors propose a new two-step process to address both the translational effect of FFF beams and the target deformation. Methods: The replanning method consists of an offline and an online step. The offline step is to create a series of preshifted-plans (PSPs) obtained by a so-called “warm start”more » optimization (starting optimization from the original plan, rather than from scratch) at a series of isocenter shifts. The PSPs all have the same number of segments with very similar shapes, since the warm start optimization only adjusts the MLC positions instead of regenerating them. In the online step, a new plan is obtained by picking the closest PSP or linearly interpolating the MLC positions and the monitor units of the closest PSPs for the shift determined from the image of the day. This two-step process is completely automated and almost instantaneous (no optimization or dose calculation needed). The previously developed SAM algorithm is then applied for daily deformation. The authors tested the method on sample prostate and pancreas cases. Results: The two-step interpolation method can account for the adverse dose effects from FFF beams, while SAM corrects for the target deformation. Plan interpolation method is effective in diminishing the unflat beam effect and may allow reducing the required number of PSPs. The whole process takes the same time as the previously reported SAM process (5–10 min). Conclusions: The new two-step method plus SAM can address both the translation effects of FFF beams and target deformation, and can be executed in full automation except the delineation of target contour required by the SAM process.« less

Influence of ultrasound speckle tracking strategies for motion and strain estimation.

PubMed

Curiale, Ariel H; Vegas-Sánchez-Ferrero, Gonzalo; Aja-Fernández, Santiago

2016-08-01

Speckle Tracking is one of the most prominent techniques used to estimate the regional movement of the heart based on ultrasound acquisitions. Many different approaches have been proposed, proving their suitability to obtain quantitative and qualitative information regarding myocardial deformation, motion and function assessment. New proposals to improve the basic algorithm usually focus on one of these three steps: (1) the similarity measure between images and the speckle model; (2) the transformation model, i.e. the type of motion considered between images; (3) the optimization strategies, such as the use of different optimization techniques in the transformation step or the inclusion of structural information. While many contributions have shown their good performance independently, it is not always clear how they perform when integrated in a whole pipeline. Every step will have a degree of influence over the following and hence over the final result. Thus, a Speckle Tracking pipeline must be analyzed as a whole when developing novel methods, since improvements in a particular step might be undermined by the choices taken in further steps. This work presents two main contributions: (1) We provide a complete analysis of the influence of the different steps in a Speckle Tracking pipeline over the motion and strain estimation accuracy. (2) The study proposes a methodology for the analysis of Speckle Tracking systems specifically designed to provide an easy and systematic way to include other strategies. We close the analysis with some conclusions and recommendations that can be used as an orientation of the degree of influence of the models for speckle, the transformation models, interpolation schemes and optimization strategies over the estimation of motion features. They can be further use to evaluate and design new strategy into a Speckle Tracking system. Copyright © 2016 Elsevier B.V. All rights reserved.

Technical note: RabbitCT--an open platform for benchmarking 3D cone-beam reconstruction algorithms.

PubMed

Rohkohl, C; Keck, B; Hofmann, H G; Hornegger, J

2009-09-01

Fast 3D cone beam reconstruction is mandatory for many clinical workflows. For that reason, researchers and industry work hard on hardware-optimized 3D reconstruction. Backprojection is a major component of many reconstruction algorithms that require a projection of each voxel onto the projection data, including data interpolation, before updating the voxel value. This step is the bottleneck of most reconstruction algorithms and the focus of optimization in recent publications. A crucial limitation, however, of these publications is that the presented results are not comparable to each other. This is mainly due to variations in data acquisitions, preprocessing, and chosen geometries and the lack of a common publicly available test dataset. The authors provide such a standardized dataset that allows for substantial comparison of hardware accelerated backprojection methods. They developed an open platform RabbitCT (www.rabbitCT.com) for worldwide comparison in backprojection performance and ranking on different architectures using a specific high resolution C-arm CT dataset of a rabbit. This includes a sophisticated benchmark interface, a prototype implementation in C++, and image quality measures. At the time of writing, six backprojection implementations are already listed on the website. Optimizations include multithreading using Intel threading building blocks and OpenMP, vectorization using SSE, and computation on the GPU using CUDA 2.0. There is a need for objectively comparing backprojection implementations for reconstruction algorithms. RabbitCT aims to provide a solution to this problem by offering an open platform with fair chances for all participants. The authors are looking forward to a growing community and await feedback regarding future evaluations of novel software- and hardware-based acceleration schemes.

Combining geostatistics with Moran's I analysis for mapping soil heavy metals in Beijing, China.

PubMed

Huo, Xiao-Ni; Li, Hong; Sun, Dan-Feng; Zhou, Lian-Di; Li, Bao-Guo

2012-03-01

Production of high quality interpolation maps of heavy metals is important for risk assessment of environmental pollution. In this paper, the spatial correlation characteristics information obtained from Moran's I analysis was used to supplement the traditional geostatistics. According to Moran's I analysis, four characteristics distances were obtained and used as the active lag distance to calculate the semivariance. Validation of the optimality of semivariance demonstrated that using the two distances where the Moran's I and the standardized Moran's I, Z(I) reached a maximum as the active lag distance can improve the fitting accuracy of semivariance. Then, spatial interpolation was produced based on the two distances and their nested model. The comparative analysis of estimation accuracy and the measured and predicted pollution status showed that the method combining geostatistics with Moran's I analysis was better than traditional geostatistics. Thus, Moran's I analysis is a useful complement for geostatistics to improve the spatial interpolation accuracy of heavy metals.

Combining Geostatistics with Moran’s I Analysis for Mapping Soil Heavy Metals in Beijing, China

PubMed Central

Huo, Xiao-Ni; Li, Hong; Sun, Dan-Feng; Zhou, Lian-Di; Li, Bao-Guo

2012-01-01

Production of high quality interpolation maps of heavy metals is important for risk assessment of environmental pollution. In this paper, the spatial correlation characteristics information obtained from Moran’s I analysis was used to supplement the traditional geostatistics. According to Moran’s I analysis, four characteristics distances were obtained and used as the active lag distance to calculate the semivariance. Validation of the optimality of semivariance demonstrated that using the two distances where the Moran’s I and the standardized Moran’s I, Z(I) reached a maximum as the active lag distance can improve the fitting accuracy of semivariance. Then, spatial interpolation was produced based on the two distances and their nested model. The comparative analysis of estimation accuracy and the measured and predicted pollution status showed that the method combining geostatistics with Moran’s I analysis was better than traditional geostatistics. Thus, Moran’s I analysis is a useful complement for geostatistics to improve the spatial interpolation accuracy of heavy metals. PMID:22690179

Spatial interpolation of pesticide drift from hand-held knapsack sprayers used in potato production

NASA Astrophysics Data System (ADS)

Garcia-Santos, Glenda; Pleschberger, Martin; Scheiber, Michael; Pilz, Jürgen

2017-04-01

Tropical mountainous regions in developing countries are often neglected in research and policy but represent key areas to be considered if sustainable agricultural and rural development is to be promoted. One example is the lack of information of pesticide drift soil deposition, which can support pesticide risk assessment for soil, surface water, bystanders and off-target plants and fauna. This is considered a serious gap, given the evidence of pesticide-related poisoning in those regions. Empirical data of drift deposition of a pesticide surrogate, Uranine tracer, were obtained within one of the highest potato producing regions in Colombia. Based on the empirical data, different spatial interpolation techniques i.e. Thiessen, inverse distance squared weighting, co-kriging, pair-copulas and drift curves depending on distance and wind speed were tested and optimized. Results of the best performing spatial interpolation methods, suitable curves to assess mean relative drift and implications on risk assessment studies will be presented.

Application of a derivative-free global optimization algorithm to the derivation of a new time integration scheme for the simulation of incompressible turbulence

NASA Astrophysics Data System (ADS)

Alimohammadi, Shahrouz; Cavaglieri, Daniele; Beyhaghi, Pooriya; Bewley, Thomas R.

2016-11-01

This work applies a recently developed Derivative-free optimization algorithm to derive a new mixed implicit-explicit (IMEX) time integration scheme for Computational Fluid Dynamics (CFD) simulations. This algorithm allows imposing a specified order of accuracy for the time integration and other important stability properties in the form of nonlinear constraints within the optimization problem. In this procedure, the coefficients of the IMEX scheme should satisfy a set of constraints simultaneously. Therefore, the optimization process, at each iteration, estimates the location of the optimal coefficients using a set of global surrogates, for both the objective and constraint functions, as well as a model of the uncertainty function of these surrogates based on the concept of Delaunay triangulation. This procedure has been proven to converge to the global minimum of the constrained optimization problem provided the constraints and objective functions are twice differentiable. As a result, a new third-order, low-storage IMEX Runge-Kutta time integration scheme is obtained with remarkably fast convergence. Numerical tests are then performed leveraging the turbulent channel flow simulations to validate the theoretical order of accuracy and stability properties of the new scheme.

Exact subthreshold integration with continuous spike times in discrete-time neural network simulations.

PubMed

Morrison, Abigail; Straube, Sirko; Plesser, Hans Ekkehard; Diesmann, Markus

2007-01-01

Very large networks of spiking neurons can be simulated efficiently in parallel under the constraint that spike times are bound to an equidistant time grid. Within this scheme, the subthreshold dynamics of a wide class of integrate-and-fire-type neuron models can be integrated exactly from one grid point to the next. However, the loss in accuracy caused by restricting spike times to the grid can have undesirable consequences, which has led to interest in interpolating spike times between the grid points to retrieve an adequate representation of network dynamics. We demonstrate that the exact integration scheme can be combined naturally with off-grid spike events found by interpolation. We show that by exploiting the existence of a minimal synaptic propagation delay, the need for a central event queue is removed, so that the precision of event-driven simulation on the level of single neurons is combined with the efficiency of time-driven global scheduling. Further, for neuron models with linear subthreshold dynamics, even local event queuing can be avoided, resulting in much greater efficiency on the single-neuron level. These ideas are exemplified by two implementations of a widely used neuron model. We present a measure for the efficiency of network simulations in terms of their integration error and show that for a wide range of input spike rates, the novel techniques we present are both more accurate and faster than standard techniques.

Intel Many Integrated Core (MIC) architecture optimization strategies for a memory-bound Weather Research and Forecasting (WRF) Goddard microphysics scheme

NASA Astrophysics Data System (ADS)

Mielikainen, Jarno; Huang, Bormin; Huang, Allen H.

2014-10-01

The Goddard cloud microphysics scheme is a sophisticated cloud microphysics scheme in the Weather Research and Forecasting (WRF) model. The WRF is a widely used weather prediction system in the world. It development is a done in collaborative around the globe. The Goddard microphysics scheme is very suitable for massively parallel computation as there are no interactions among horizontal grid points. Compared to the earlier microphysics schemes, the Goddard scheme incorporates a large number of improvements. Thus, we have optimized the code of this important part of WRF. In this paper, we present our results of optimizing the Goddard microphysics scheme on Intel Many Integrated Core Architecture (MIC) hardware. The Intel Xeon Phi coprocessor is the first product based on Intel MIC architecture, and it consists of up to 61 cores connected by a high performance on-die bidirectional interconnect. The Intel MIC is capable of executing a full operating system and entire programs rather than just kernels as the GPU do. The MIC coprocessor supports all important Intel development tools. Thus, the development environment is familiar one to a vast number of CPU developers. Although, getting a maximum performance out of MICs will require using some novel optimization techniques. Those optimization techniques are discusses in this paper. The results show that the optimizations improved performance of the original code on Xeon Phi 7120P by a factor of 4.7x. Furthermore, the same optimizations improved performance on a dual socket Intel Xeon E5-2670 system by a factor of 2.8x compared to the original code.

Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part I: numerical scheme

NASA Astrophysics Data System (ADS)

Rõõm, Rein; Männik, Aarne; Luhamaa, Andres

2007-10-01

Two-time-level, semi-implicit, semi-Lagrangian (SISL) scheme is applied to the non-hydrostatic pressure coordinate equations, constituting a modified Miller-Pearce-White model, in hybrid-coordinate framework. Neutral background is subtracted in the initial continuous dynamics, yielding modified equations for geopotential, temperature and logarithmic surface pressure fluctuation. Implicit Lagrangian marching formulae for single time-step are derived. A disclosure scheme is presented, which results in an uncoupled diagnostic system, consisting of 3-D Poisson equation for omega velocity and 2-D Helmholtz equation for logarithmic pressure fluctuation. The model is discretized to create a non-hydrostatic extension to numerical weather prediction model HIRLAM. The discretization schemes, trajectory computation algorithms and interpolation routines, as well as the physical parametrization package are maintained from parent hydrostatic HIRLAM. For stability investigation, the derived SISL model is linearized with respect to the initial, thermally non-equilibrium resting state. Explicit residuals of the linear model prove to be sensitive to the relative departures of temperature and static stability from the reference state. Relayed on the stability study, the semi-implicit term in the vertical momentum equation is replaced to the implicit term, which results in stability increase of the model.

Accurate Adaptive Level Set Method and Sharpening Technique for Three Dimensional Deforming Interfaces

NASA Technical Reports Server (NTRS)

Kim, Hyoungin; Liou, Meng-Sing

2011-01-01

In this paper, we demonstrate improved accuracy of the level set method for resolving deforming interfaces by proposing two key elements: (1) accurate level set solutions on adapted Cartesian grids by judiciously choosing interpolation polynomials in regions of different grid levels and (2) enhanced reinitialization by an interface sharpening procedure. The level set equation is solved using a fifth order WENO scheme or a second order central differencing scheme depending on availability of uniform stencils at each grid point. Grid adaptation criteria are determined so that the Hamiltonian functions at nodes adjacent to interfaces are always calculated by the fifth order WENO scheme. This selective usage between the fifth order WENO and second order central differencing schemes is confirmed to give more accurate results compared to those in literature for standard test problems. In order to further improve accuracy especially near thin filaments, we suggest an artificial sharpening method, which is in a similar form with the conventional re-initialization method but utilizes sign of curvature instead of sign of the level set function. Consequently, volume loss due to numerical dissipation on thin filaments is remarkably reduced for the test problems

Receiver-Coupling Schemes Based On Optimal-Estimation Theory

NASA Technical Reports Server (NTRS)

Kumar, Rajendra

1992-01-01

Two schemes for reception of weak radio signals conveying digital data via phase modulation provide for mutual coupling of multiple receivers, and coherent combination of outputs of receivers. In both schemes, optimal mutual-coupling weights computed according to Kalman-filter theory, but differ in manner of transmission and combination of outputs of receivers.

Eulerian and Lagrangian approaches to multidimensional condensation and collection

NASA Astrophysics Data System (ADS)

Li, Xiang-Yu; Brandenburg, A.; Haugen, N. E. L.; Svensson, G.

2017-06-01

Turbulence is argued to play a crucial role in cloud droplet growth. The combined problem of turbulence and cloud droplet growth is numerically challenging. Here an Eulerian scheme based on the Smoluchowski equation is compared with two Lagrangian superparticle (or superdroplet) schemes in the presence of condensation and collection. The growth processes are studied either separately or in combination using either two-dimensional turbulence, a steady flow or just gravitational acceleration without gas flow. Good agreement between the different schemes for the time evolution of the size spectra is observed in the presence of gravity or turbulence. The Lagrangian superparticle schemes are found to be superior over the Eulerian one in terms of computational performance. However, it is shown that the use of interpolation schemes such as the cloud-in-cell algorithm is detrimental in connection with superparticle or superdroplet approaches. Furthermore, the use of symmetric over asymmetric collection schemes is shown to reduce the amount of scatter in the results. For the Eulerian scheme, gravitational collection is rather sensitive to the mass bin resolution, but not so in the case with turbulence.