Analysis of Truncation Errors and Design of Physically Optimized Discretizations

2008 ◽  
pp. 49-60 ◽  
Author(s):  
Stefan Hickel ◽  
Nikolaus A. Adams
Keyword(s):  
Truncation Errors

Enhanced Information Recovery in 2D On-and Off-Resonance Nutation NQR using the Maximum Entropy Method

1996 ◽  
Vol 51 (5-6) ◽  
pp. 337-347 ◽  
Author(s):  
Mariusz Maćkowiak ◽  
Piotr Kątowski
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Theoretical Description ◽  
Entropy Method ◽  
Zero Field ◽  
Resonance Effects ◽  
Information Recovery ◽  
Truncation Errors ◽  
Enhanced Resolution ◽  
2D Data

Abstract Two-dimensional zero-field nutation NQR spectroscopy has been used to determine the full quadrupolar tensor of spin - 3/2 nuclei in serveral molecular crystals containing the 3 5 Cl and 7 5 As nuclei. The problems of reconstructing 2D-nutation NQR spectra using conventional methods and the advantages of using implementation of the maximum entropy method (MEM) are analyzed. It is shown that the replacement of conventional Fourier transform by an alternative data processing by MEM in 2D NQR spectroscopy leads to sensitivity improvement, reduction of instrumental artefacts and truncation errors, shortened data acquisition times and suppression of noise, while at the same time increasing the resolution. The effects of off-resonance irradiation in nutation experiments are demonstrated both experimentally and theoretically. It is shown that off-resonance nutation spectroscopy is a useful extension of the conventional on-resonance experiments, thus facilitating the determination of asymmetry parameters in multiple spectrum. The theoretical description of the off-resonance effects in 2D nutation NQR spectroscopy is given, and general exact formulas for the asymmetry parameter are obtained. In off-resonance conditions, the resolution of the nutation NQR spectrum decreases with the spectrometer offset. However, an enhanced resolution can be achieved by using the maximum entropy method in 2D-data reconstruction.

The Use of Subgrid Transport Equations in a Three-Dimensional Model of Atmospheric Turbulence

1973 ◽  
Vol 95 (3) ◽  
pp. 429-438 ◽  
Author(s):  
J. W. Deardorff
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Transport Equations ◽  
Subgrid Scale ◽  
Reynolds Stresses ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Truncation Errors ◽  
Subgrid Scales ◽  
Grid Points

A three-dimensional numerical model of turbulence in an atmospheric boundary layer has been revised to utilize subgrid transport equations for the subgrid Reynolds stresses and fluxes rather than subgrid eddy coefficients. It was applied to a daytime boundary layer over heated ground in a region of horizontal area 8km square and 2km deep, utilizing 40×40×40 grid points. The constraints involved in selecting four important subgrid closure constants are discussed in some detail, along with maintenance of realizability on the subgrid scale. The results indicate that the subgrid transport equations produce subgrid Reynolds stresses and fluxes which realistically simulate the transfer of larger scale variance to subgrid scales, provided truncation errors due to advective terms are not too large. They also show the superiority of this method over the use of (nonstability dependent) nonlinear eddy coefficients in maintaining the sharpness of the inversion base which lies above the mixed layer.

Energy Efficient VLSI Based DCT Architecture with Accurate Error Compensation

2014 ◽  
Vol 626 ◽  
pp. 127-135 ◽  
Author(s):  
D. Jessintha ◽  
M. Kannan ◽  
P.L. Srinivasan
Keyword(s):  
Low Power ◽  
Energy Efficient ◽  
Time Complexity ◽  
High Performance ◽  
Low Power Consumption ◽  
Distributed Arithmetic ◽  
Technology Scaling ◽  
Truncation Errors ◽  
History Of ◽  
Technology Dependency

Discrete Cosine Transform (DCT) is commonly used in image compression. In the history of DCT, a milestone was the Distributed Arithmetic (DA) technique. Due to the technology dependency a multiplier-less computation was built with DA based technique. It occupied less area but the throughput is less. Later, due to the technology scaling, multiplier based architectures can be easily adapted for low-power and high-performance architecture. Fixed width multipliers [1]-[7] reduces hardware and time complexity. In this work, Radix 4 fixed width multiplier is adapted with DCT architecture due to low power consumption and saves 30% power. In order to reduce truncation errors caused during fixed width multiplication, an estimation circuit is designed based on conditional probability theory.

scholarly journals An Unconditional Positivity-Preserving Difference Scheme for Models of Cancer Migration and Invasion

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 131
Author(s):  
Mikhail K. Kolev ◽  
Miglena N. Koleva ◽  
Lubin G. Vulkov
Keyword(s):  
Difference Scheme ◽  
Nonlinear Parabolic Equations ◽  
Nonlinear Ordinary Differential Equation ◽  
Diffusion Reaction ◽  
Migration And Invasion ◽  
Reaction Type ◽  
Truncation Errors ◽  
Cancer Migration ◽  
Nonlinear Parabolic ◽  
Unconditional Positivity

In this paper, we consider models of cancer migration and invasion, which consist of two nonlinear parabolic equations (one of the convection–diffusion reaction type and the other of the diffusion–reaction type) and an additional nonlinear ordinary differential equation. The unknowns represent concentrations or densities that cannot be negative. Widely used approximations, such as difference schemes, can produce negative solutions because of truncation errors and can become unstable. We propose a new difference scheme that guarantees the positivity of the numerical solution for arbitrary mesh step sizes. It has explicit and fast performance even for nonlinear reaction terms that consist of sums of positive and negative functions. The numerical examples illustrate the simplicity and efficiency of the method. A numerical simulation of a model of cancer migration is also discussed.

scholarly journals Harmonic Modeling of a Diode-Clamped Multilevel Voltage Source Converter for Predicting Uncharacteristic Harmonics

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Tian Hao Huang ◽  
Kuo Lung Lian
Keyword(s):  
Computation Time ◽  
Voltage Source ◽  
Voltage Source Converter ◽  
Voltage Source Converters ◽  
Harmonic Model ◽  
Abcd Matrix ◽  
Truncation Errors ◽  
The Matrix ◽  
Matrix Mapping ◽  
The Time Domain

In response to the growing demand for medium- and high-power trends, multilevel voltage source converters (VSCs) have been attracting growing considerations. One of the widely used VSCs are the diode-clamped multilevel VSC (DCM-VSC). As these converters proliferate, their harmonic impact may become significant. Nevertheless, a harmonic model for the DCM-VSC is currently lacking in the literature. In this paper, the ABCD matrix, mapping the input harmonics to the output harmonics of DCM-VSC, is derived. As the matrix is formulated in the time-domain, the output harmonics are exact and do not suffer from harmonic truncation errors. As the paper will demonstrate, the derived ABCD matrix can be easily applied to a microgrid system and users can easily predict all the uncharacteristic harmonics when a microgrid is subjected to various conditions of imbalance. In addition to all the results being validated with those of PSCAD/EMTDC, the computation time of the proposed method is in contrast much shorter.

scholarly journals Errata for “Comments on Truncation Errors for Polynomial Chaos Expansions” [Jan 18 169-174]

2020 ◽  
Vol 4 (2) ◽  
pp. 504-505
Author(s):  
Tillmann Muhlpfordt ◽  
Rolf Findeisen ◽  
Veit Hagenmeyer ◽  
Timm Faulwasser
Keyword(s):  
Polynomial Chaos ◽  
Truncation Errors ◽  
Polynomial Chaos Expansions

Stability and Accuracy Analysis of Baumgarte’s Constraint Violation Stabilization Method

1995 ◽  
Vol 117 (3) ◽  
pp. 446-453 ◽  
Author(s):  
S. Yoon ◽  
R. M. Howe ◽  
D. T. Greenwood
Keyword(s):  
Equations Of Motion ◽  
Integration Step ◽  
State Variables ◽  
Stabilization Method ◽  
Lagrange Equations ◽  
Step Size ◽  
Constraint Violation ◽  
Truncation Errors ◽  
Numerical Stability Analysis ◽  
Stability And Accuracy

When Baumgarte’s Constraint Violation Stabilization Method (CVSM) is used in the simulation of Lagrange equations of motion with holonomic constraints, it is shown that, with suitable assumptions on the integration step size h and the eigenvalues (λ’s) of the linearized system, the constraint variables are effectively integrated by the same algorithm as that used for the state variables. A numerical stability analysis of the constraint violations can be performed using this so-called pseudo-integration equation. A study is also made of truncation errors and their modeling in the continuous time domain. This model can be used to determine the effectiveness of various constraint controls and integration methods in reducing the errors in the solution due to truncation errors. Examples are presented to illustrate the use of a higher-order truncation error model which leads to an accurate quantitative steady-state analysis of the constraint violations.

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