scholarly journals 3‐D non‐uniform time step locally one‐dimensional FDTD method

2016 ◽  
Vol 52 (12) ◽  
pp. 993-994 ◽  
Author(s):  
Zaifeng Yang ◽  
Eng Leong Tan
Keyword(s):  
Fdtd Method ◽  
Time Step ◽  
One Dimensional

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

scholarly journals Comparison of numerical schemes of river flood routing with an inertial approximation of the Saint Venant equations

RBRH ◽  
2018 ◽  
Vol 23 (0) ◽  
Author(s):  
Alice César Fassoni-Andrade ◽  
Fernando Mainardi Fan ◽  
Walter Collischonn ◽  
Artur César Fassoni ◽  
Rodrigo Cauduro Dias de Paiva
Keyword(s):  
Numerical Stability ◽  
Flood Routing ◽  
Computational Time ◽  
Numerical Schemes ◽  
Time Step ◽  
Simple Formulation ◽  
One Dimensional ◽  
Saint Venant Equations ◽  
Original Scheme ◽  
The One

ABSTRACT The one-dimensional flow routing inertial model, formulated as an explicit solution, has advantages over other explicit models used in hydrological models that simplify the Saint-Venant equations. The main advantage is a simple formulation with good results. However, the inertial model is restricted to a small time step to avoid numerical instability. This paper proposes six numerical schemes that modify the one-dimensional inertial model in order to increase the numerical stability of the solution. The proposed numerical schemes were compared to the original scheme in four situations of river’s slope (normal, low, high and very high) and in two situations where the river is subject to downstream effects (dam backwater and tides). The results are discussed in terms of stability, peak flow, processing time, volume conservation error and RMSE (Root Mean Square Error). In general, the schemes showed improvement relative to each type of application. In particular, the numerical scheme here called Prog Q(k+1)xQ(k+1) stood out presenting advantages with greater numerical stability in relation to the original scheme. However, this scheme was not successful in the tide simulation situation. In addition, it was observed that the inclusion of the hydraulic radius calculation without simplification in the numerical schemes improved the results without increasing the computational time.

Enhanced Explicit Scheme to Solve Transient Heat Conduction Problem

2007 ◽  
Vol 2 (1) ◽  
Author(s):  
Ganesh Hegde ◽  
Madhu Gattumane
Keyword(s):  
Heat Conduction ◽  
Correction Factor ◽  
Truncation Error ◽  
Transient Heat Conduction ◽  
Explicit Scheme ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
Time Step ◽  
One Dimensional ◽  
Partial Derivatives

Improvement in accuracy without sacrificing stability and convergence of the solution to unsteady diffusion heat transfer problems by computational method of enhanced explicit scheme (EES), has been achieved and demonstrated, through transient one dimensional and two dimensional heat conduction. The truncation error induced in the explicit scheme using finite difference technique is eliminated by optimization of partial derivatives in the Taylor series expansion, by application of interface theory developed by the authors. This theory, in its simple terms gives the optimum values to the decision vectors in a redundant linear equation. The time derivatives and the spatial partial derivatives in the transient heat conduction, take the values depending on the time step chosen and grid size assumed. The time correction factor and the space correction factor defined by step sizes govern the accuracy, stability and convergence of EES. The comparison of the results of EES with analytical results, show decreased error as compared to the result of explicit scheme. The paper has an objective of reducing error in the explicit scheme by elimination of truncation error introduced by neglecting the higher order terms in the expansion of the governing function. As the pilot examples of the exercise, the implementation is aimed at solving one-dimensional and two-dimensional problems of transient heat conduction and compared with the results cited in the referred literature.

scholarly journals From Time-Collocated to Leapfrog Fundamental Schemes for ADI and CDI FDTD Methods

Axioms ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 23
Author(s):  
Eng Leong Tan
Keyword(s):  
Finite Difference ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Fdtd Method ◽  
Unconditionally Stable ◽  
Alternating Direction Implicit ◽  
One Dimensional ◽  
Alternating Direction ◽  
Fdtd Methods ◽  
Difference Time

The leapfrog schemes have been developed for unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method, and recently the complying-divergence implicit (CDI) FDTD method. In this paper, the formulations from time-collocated to leapfrog fundamental schemes are presented for ADI and CDI FDTD methods. For the ADI FDTD method, the time-collocated fundamental schemes are implemented using implicit E-E and E-H update procedures, which comprise simple and concise right-hand sides (RHS) in their update equations. From the fundamental implicit E-H scheme, the leapfrog ADI FDTD method is formulated in conventional form, whose RHS are simplified into the leapfrog fundamental scheme with reduced operations and improved efficiency. For the CDI FDTD method, the time-collocated fundamental scheme is presented based on locally one-dimensional (LOD) FDTD method with complying divergence. The formulations from time-collocated to leapfrog schemes are provided, which result in the leapfrog fundamental scheme for CDI FDTD method. Based on their fundamental forms, further insights are given into the relations of leapfrog fundamental schemes for ADI and CDI FDTD methods. The time-collocated fundamental schemes require considerably fewer operations than all conventional ADI, LOD and leapfrog ADI FDTD methods, while the leapfrog fundamental schemes for ADI and CDI FDTD methods constitute the most efficient implicit FDTD schemes to date.

scholarly journals Calculating the turbulent fluxes in the atmospheric surface layer with neural networks

2018 ◽  
Author(s):  
Lukas Hubert Leufen ◽  
Gerd Schädler
Keyword(s):  
Land Surface ◽  
Field Experiments ◽  
Climate Models ◽  
Similarity Theory ◽  
Turbulent Fluxes ◽  
Global Climate Models ◽  
Surface Model ◽  
Time Step ◽  
One Dimensional ◽  
Stability Functions

Abstract. The turbulent fluxes of momentum, heat and water vapour link the Earth's surface with the atmosphere. The correct modelling of the flux interactions between these two systems with very different time scales is therefore vital for climate (resp. Earth system) models. Conventionally, these fluxes are modelled using Monin–Obukhov similarity theory (MOST) with stability functions derived from a small number of field experiments; this results in a range of formulations of these functions and thus also in the flux calculations; furthermore, the underlying equations are non-linear and have to be solved iteratively at each time step of the model. For these reasons, we tried here a different approach, namely using an artificial neural network (ANN) to calculate the fluxes resp. the scaling quantities u* and θ*, thus avoiding explicit formulas for the stability functions. The network was trained and validated with multi-year datasets from seven grassland, forest and wetland sites worldwide using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton backpropagation algorithm and six-fold cross validation. Extensive sensitivity tests showed that an ANN with six input variables and one hidden layer gave results comparable to (and in some cases even slightly better than) the standard method. Similar satisfying results were obtained when the ANN routine was implemented in a one-dimensional stand alone land surface model (LSM), opening the way to implementation in three-dimensional climate models. In case of the one-dimensional LSM, no CPU time was saved when using the ANN version, since the small time step of the standard version required only one iteration in most cases. This could be different in models with longer time steps, e.g. global climate models.

Effect of Metal Intercalating on Transmission Characteristics of One-Dimensional Photonic Crystal

2011 ◽  
Vol 418-420 ◽  
pp. 679-683
Author(s):  
Bei Jia He ◽  
Xin Yi Chen ◽  
Jian Bo Wang ◽  
Jun Lu ◽  
Jian Chang ◽  
...  
Keyword(s):  
Photonic Crystal ◽  
Plasma Frequency ◽  
Fdtd Method ◽  
Transmission Characteristics ◽  
Material Characteristic ◽  
One Dimensional ◽  
Dimensional Photonic Crystal ◽  
Simulation Results ◽  
The One ◽  
Difference Time

To expand the bandgap's width of the one-dimensional photonic crystal, a crystal named SiO2/Metal/MgF2 is formed by joining some metals into the crystal SiO2/MgF2. Furthermore the Finite Difference Time Domain (FDTD) method is used to explore the metals' influence on the crystal's transmission characteristics. The simulation results show that the metals joined could expand the width of the one-dimensional photonic crystal's bandgap effectively and the bandgap's width increases when the metals' thickness increases. Meanwhile the bandgap's characteristic is affected by the metals' material-characteristic. The higher the plasma frequency is, the wider the bandgap's width will be and the more the number of the bandgaps will be. On the other hand, the metals' damping frequency has no significant effect on the bandgap, but would make the bandgap-edge's transmittance decrease slightly.

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