Numerical Experiments Using Modified POM WAD with Computing Time Saving Technique

2015 ◽  
Vol 21 (1) ◽  
pp. 72-82
Author(s):  
Il Heum Park ◽  
◽  
Heung Bae Choi
Keyword(s):  
Numerical Experiments ◽  
Computing Time ◽  
Time Saving

A Novel Technique for Analyzing Hydraulic Transients by Method of Characteristics

2003 ◽  
Author(s):  
Jianing Pu
Keyword(s):  
Numerical Experiments ◽  
Method Of Characteristics ◽  
Numerical Accuracy ◽  
Hydraulic Transients ◽  
Time Saving ◽  
Simulation Accuracy ◽  
Novel Technique ◽  
The Common ◽  
Usage Flexibility ◽  
Computation Speed

In analyzing hydraulic transients in complex pipeline systems by method of characteristics, existing approaches can not be fully satisfactory regard to numerical accuracy, computation speed, and application flexibility and simplicity. Trying to overcome this shortcomings, the paper puts forward a novel technique: in node computations, variable time steps are used, the common for boundaries and the different for lines; in every computation cycle, analyses of boundary nodes are always prior to that of interior ones, while simulation times of interior nodes are always prior to that of boundary ones; in solution of boundaries, only interpolation is used. Explanations and numerical experiments demonstrate its usage flexibility and simplicity, simulation accuracy, and executing time saving. It is specially suitable to analyses of complex systems.

scholarly journals Technical Note: An efficient method for accelerating the spin-up process for process-based biogeochemistry models

2018 ◽  
Author(s):  
Yang Qu ◽  
Shamil Maksyutov ◽  
Qianlai Zhuang
Keyword(s):  
Global Climate ◽  
Computing Time ◽  
Terrestrial Ecosystem ◽  
Terrestrial Ecosystems ◽  
Ecosystem Model ◽  
Original Method ◽  
Technical Note ◽  
Time Saving ◽  
Spatial And Temporal Scales ◽  
Terrestrial Ecosystem Model

Abstract. To better understand the role of terrestrial ecosystems in the global carbon cycle and their feedbacks to the global climate system, process-based biogeochemistry models need to be improved with respect to model parameterization and model structure. To achieve these improvements, the spin-up time for those differential equation-based models needs to be shortened. Here, an algorithm for a fast spin-up was developed and implemented in a biogeochemistry model, the Terrestrial Ecosystem Model (TEM). With the new spin-up algorithm, we showed that the model reached a steady state in less than 10 years of computing time, while the original method requires more than 200 years on average of model run. For the test sites with five different plant function types, the new method saves over 90 % of the original spin-up time in site-level simulations. In North America simulations, average spin-up time saving for all grid cells is 85 % for either daily or monthly version of TEM. The developed spin-up method shall greatly facilitate our future quantification of carbon dynamics at fine spatial and temporal scales.

scholarly journals Efficient k-Step Linear Block Methods to Solve Second Order Initial Value Problems Directly

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1752
Author(s):  
Higinio Ramos ◽  
Samuel N. Jator ◽  
Mark I. Modebei
Keyword(s):  
Computational Efficiency ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
Computing Time ◽  
Approximate Solutions ◽  
Second Order ◽  
Initial Value ◽  
Special Equation ◽  
Block Methods ◽  
Grid Points

There are dozens of block methods in literature intended for solving second order initial-value problems. This article aimed at the analysis of the efficiency of k-step block methods for directly solving general second-order initial-value problems. Each of these methods consists of a set of 2k multi-step formulas (although we will see that this number can be reduced to k+1 in case of a special equation) that provides approximate solutions at k grid points at once. The usual way to obtain these formulas is by using collocation and interpolation at different points, which are not all necessarily in the mesh (it may also be considered intra-step or off-step points). An important issue is that for each k, all of them are essentially the same method, although they can adopt different formulations. Nevertheless, the performance of those formulations is not the same. The analysis of the methods presented give some clues as how to select the most appropriate ones in terms of computational efficiency. The numerical experiments show that using the proposed formulations, the computing time can be reduced to less than half.

A New Approach to the Dynamic Characteristic of Undamped Rotor-Bearing Systems

1989 ◽  
Vol 111 (4) ◽  
pp. 379-385 ◽  
Author(s):  
Ting Nung Shiau ◽  
Jon Li Hwang
Keyword(s):  
Finite Element ◽  
Dynamic Characteristic ◽  
Computing Time ◽  
Present Approach ◽  
Order System ◽  
System Response ◽  
Time Saving ◽  
New Approach ◽  
Rotor Bearing ◽  
Bearing System

A new approach to the dynamic characteristic of undamped rotor-bearing systems is presented. The dynamic behavior of a rotor bearing system is usually studied using finite element approach and/or transfer matrix approach. In this paper, the assumed mode method is first employed to describe the system response and the properties of Rayleigh quotient are applied to analyze the critical speeds of a rotor-bearing system. Three examples are used to illustrate the efficiency and the accuracy of the present approach. The numerical results, based on the present approach, stand with very good agreement with those using the finite element method. Moreover, the present approach will provide a significant computing time saving for a relative large order system. It may be a more effective way to analyze the dynamic characteristic for most of the rotor bearing systems.

scholarly journals Parameter learning and fractional differential operators: Applications in regularized image denoising and decomposition problems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Sören Bartels ◽  
Nico Weber
Keyword(s):  
Image Denoising ◽  
Numerical Experiments ◽  
Fractional Laplacian ◽  
Differential Operators ◽  
Riesz Potential ◽  
Regularization Parameter ◽  
Computing Time ◽  
Bilevel Optimization ◽  
Learning Approaches ◽  
Decomposition Models

<p style='text-indent:20px;'>In this paper, we focus on learning optimal parameters for PDE-based image denoising and decomposition models. First, we learn the regularization parameter and the differential operator for gray-scale image denoising using the fractional Laplacian in combination with a bilevel optimization problem. In our setting the fractional Laplacian allows the use of Fourier transform, which enables the optimization of the denoising operator. We prove stable and explainable results as an advantage in comparison to machine learning approaches. The numerical experiments correlate with our theoretical model settings and show a reduction of computing time in contrast to the Rudin-Osher-Fatemi model. Second, we introduce a new regularized image decomposition model with the fractional Laplacian and the Riesz potential. We provide an explicit formula for the unique solution and the numerical experiments illustrate the efficiency.</p>

Infinite boundary element absorbing boundary for wave propagation simulations

Geophysics ◽  
2000 ◽  
Vol 65 (2) ◽  
pp. 596-602 ◽  
Author(s):  
Li‐Yun Fu ◽  
Ru‐Shan Wu
Keyword(s):  
Wave Propagation ◽  
Boundary Element ◽  
Numerical Experiments ◽  
Computing Time ◽  
Computational Effort ◽  
Shape Functions ◽  
Absorbing Boundary ◽  
Perfect Absorption ◽  
Memory Space ◽  
Absorbing Elements

In the boundary element (BE) solution of wave propagation, infinite absorbing elements are introduced to minimize diffractions from truncated edges of models. This leads to a significant simplification and reduction of computational effort, especially for 3-D problems. The infinite BE absorbing boundary condition has a general form for both 2-D and 3-D problems and for both acoustic and elastic cases. Its implementation is facilitated by the introduction of the corresponding shape functions. Numerical experiments illustrate a nearly perfect absorption of unwanted diffractions. The approach overcomes some of the difficulties encountered in conventional absorbing techniques and takes less memory space and less computing time.

scholarly journals An Opposition-Based Group Search Optimizer with Diversity Guidance

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Dan Wang ◽  
Congcong Xiong ◽  
Xiankun Zhang
Keyword(s):  
Convergence Rate ◽  
Evolutionary Algorithm ◽  
Numerical Experiments ◽  
Computing Time ◽  
Premature Convergence ◽  
Selection Mechanism ◽  
Opposition Based Learning ◽  
Experiment Verification ◽  
Group Search ◽  
Solution Accuracy

Group search optimizer (GSO) which is an effective evolutionary algorithm has been successfully applied in many applications. However, the purely stochastic resampling or selection mechanism in GSO leads to long computing time and premature convergence. In this paper, we propose a diversity-guided group search optimizer (DGSO) with opposition-based learning (OBL) to overcome these limitations. Opposition-based learning is utilized to accelerate the convergence rate of GSO, while the diversity guidance (DG) is used to increase the diversity of population. When compared with the standard GSO, a novel operator using OBL and DG is developed for the population initialization as well as the generation jumping. A comprehensive set of 19 complex benchmark functions is used for experiment verification and is compared to the original GSO algorithm. Numerical experiments show that the proposed DGSO leads to better performance in comparison with the standard GSO in the convergence rate and the solution accuracy.

Calculation of structure images of crystalline defects

1978 ◽  
Vol 36 (1) ◽  
pp. 282-283
Author(s):  
M.A. O'Keefe ◽  
Sumio Iijima
Keyword(s):  
Diffuse Scattering ◽  
Computing Time ◽  
Continuous Distribution ◽  
Sampling Interval ◽  
Reciprocal Space ◽  
Objective Lens ◽  
Lattice Images ◽  
Slice Method ◽  
Space Cell ◽  
Beam Lattice

We have extended the multi-slice method of computating many-beam lattice images of perfect crystals to calculations for imperfect crystals using the artificial superlattice approach. Electron waves scattered from faulted regions of crystals are distributed continuously in reciprocal space, and all these waves interact dynamically with each other to give diffuse scattering patterns.In the computation, this continuous distribution can be sampled only at a finite number of regularly spaced points in reciprocal space, and thus finer sampling gives an improved approximation. The larger cell also allows us to defocus the objective lens further before adjacent defect images overlap, producing spurious computational Fourier images. However, smaller cells allow us to sample the direct space cell more finely; since the two-dimensional arrays in our program are limited to 128X128 and the sampling interval shoud be less than 1/2Å (and preferably only 1/4Å), superlattice sizes are limited to 40 to 60Å. Apart from finding a compromis superlattice cell size, computing time must be conserved.

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