TWO-GRID WEAK GALERKIN METHOD FOR SEMILINEAR ELLIPTIC DIFFERENTIAL EQUATIONS

In this paper, we investigate a two-grid weak Galerkin method for semilinear elliptic differential equations. The method mainly contains two steps. First, we solve the semi-linear elliptic equation on the coarse mesh with mesh size H, then, we use the coarse mesh solution as a initial guess to linearize the semilinear equation on the fine mesh, i.e., on the fine mesh (with mesh size $h$), we only need to solve a linearized system. Theoretical analysis shows that when the exact solution u has sufficient regularity and $h=H^2$, the two-grid weak Galerkin method achieves the same convergence accuracy as weak Galerkin method. Several examples are given to verify the theoretical results.

Residue Regulating Homotopy Method for Strongly Nonlinear Oscillator

It is highly desired yet challenging to obtain analytical approximate solutions to strongly nonlinear oscillators accurately and efficiently. Here we propose a new approach, which combines the homtopy concept with a “residue-regulating” technique to construct a continuous homotopy from an initial guess solution to a high-accuracy analytical approximation of the nonlinear problems, namely the residue regulating homotopy method (RRHM). In our method, the analytical expression of each order homotopy-series solution is associated with a set of base functions which are pre-selected or generated during the previous order of approximations, while the corresponding coefficients are solved from deformation equations specified by the nonlinear equation itself and auxiliary residue functions. The convergence region, rate and final accuracy of the homotopy are controlled by a residue-regulating vector and an expansion threshold. General procedures of implementing RRHM are demonstrated using the Duffing and Van der Pol-Duffing oscillators, where approximate solutions containing abundant frequency components are successfully obtained, yielding significantly better convergence rate and performance stability compared to the other conventional homotopy-based methods.

Robust dynamic experiments for the precise estimation of respiration and fermentation parameters of fruit and vegetables

Dynamic models based on non-linear differential equations are increasingly being used in many biological applications. Highly informative dynamic experiments are valuable for the identification of these dynamic models. The storage of fresh fruit and vegetables is one such application where dynamic experimentation is gaining momentum. In this paper, we construct optimal O2 and CO2 gas input profiles to estimate the respiration and fermentation kinetics of pear fruit. The optimal input profiles, however, depend on the true values of the respiration and fermentation parameters. Locally optimal design of input profiles, which uses a single initial guess for the parameters, is the traditional method to deal with this issue. This method, however, is very sensitive to the initial values selected for the model parameters. Therefore, we present a robust experimental design approach that can handle uncertainty on the model parameters.

Dealing with artefacts In JET iterative bolometric tomography using masks

Bolometric tomography is a widely applied technique to infer important indirect quantities in magnetically confined plasmas, such as the total radiated power. However, being an inverse and ill-posed problem, the tomographic algorithms have to be carefully steered to converge on the most approriate solutions and often specialists have to balance the quality of the obtained reconstructions between the core and the edge of the plasma. Given the topology of the emission and the layout of the diagnostics in practically all devices, the tomographic inversions of bolometry are often affected by artefacts, which can influence derived quantities and specific studies based on the reproduced tomograms, such as power balance studies and benchmarching of gyrokinetic simulations. This article deals with the introduction of a simple, but very efficient methodology. It is based on constraining the solution of the tomographic inversions by using a specific estimate of the initial solution, built with the data from specific combinations of detectors (called ‘masks’). It has been tested with phantoms and with real data, using the Maximum Likelihood approach at JET. Results show how the obtained tomograms improve sensibly both in the core and at the edge of the device when compared with those obtained without the use of masks as initial guess. The correction for the main artefacts can have a significant impact on the interpretation of both the core (electron transport, alpha heating) and the edge physics (detachment , SOL). The method is completely general and can be applied by any iterative algorithm starting from an initial guess for the emission profile to be reconstructed.

Temperature sounding of the atmosphere over the Indian region using satellite data

Capability has been developed at the INSAT Meteorological Data Utilisation Centre (MDUC). New Delhi for making sounding retrievals using data from the U.S. Polar Orbiting Satellites; The International TOYS Processing Package (ITPP) developed by the University of Wisconsin, USA, was used for asking temperature soundings software for front-end processing and input of 1000 hPa analysis data Into the retrieval algorithm was developed at MDUC. In the physical retrieval method regression estimates generated listing stratospheric level HIRS channels and MSU channels were used as Initial guess. For the surface, two options were used, (i) climatological guess, and (ii) 1000 hPa analysis. The paper discusses temperature retrievals over the Indian region made on 13 selected dates from different seasons in 1989-91. Results of comparison of satellite retrievals with colocated radiosonde data are presented. There is good agreement between the two from 700 hPa to 150 hPa levels, with RMSE with 3 C. The error is higher at 850 hPa and near the surface, when climatologic IS used as surface guess, but IS within 3°-4° C when the 1000 hPa analysis is used.

Estimation of divergent wind from OLR data for use in objective analysis over the Indian region

A scheme is formulated for the use of OLR data in the estimation of vertical velocity; divergence and then the divergent part of the wind over Indian region. In this scheme, ascending motion over cloudy region is estimated from an empirical relation between the cloud top temperature and descending motion over cloud-free region is estimated from the thermodynamic energy equation and both are blended. From this blended vertical velocity field, aivergence, velocity potential and divergent winds at all standard levels from 4 to 8 July 1979 at 00 UTC are computed. These fields are compared with satellite cloud pictures, rainfall etc and they are found to be realistic in depicting the synoptic conditions. Total wind is computed as the sum of the estimated divergent component and rotational component computed from observed wind field. For assessment of the scheme, this total wind field at 850 hPa is used as initial. guess field in univariate optimum interpolation scheme and analyses were made for the period 4 to 8 July 1979. Results show that scheme is able to produce realistic analyses which included divergent part of the wind.

On the use of outgoing longwave radiation data in incorporating divergent part of the wind in analysis

In the present study, kinematic divergence computed using ECMWF grid point data at 850 hPa is enhanced by using the relationship between OLR and divergence. This new enhanced divergence is used to compute the velocity potential and then, the divergence part of the wind is obtained from velocity potetial. To obtain the rotational part of wind, we computed the vorticity from wind data, and subsequently stream function and obtained and the rotational part of the wind from the stream function. The total wind is the combination of divergent part obtained from modified velocity potential (using OLR data) and rotational part from unmodified stream function. This total wind field is used as initial guess for univariate objective analysis by optimum interpolation scheme so that Initial Guess field contained the more realistic divergent part of the wind. Consequently, the analysed field also will contain the divergent part of the wind.

Assessment of regularization techniques in GNSS tropospheric tomography based on single- and dual-frequency observations

Water vapor is one of the most variable components in the earth's atmosphere and has a significant role in forming clouds, rain and snow, air pollution, and acid rain. Therefore, increasing the accuracy of estimated water vapor can lead to more accurate predictions of severe weather, upcoming storms, and natural hazards. In recent years, GNSS has turned out to be a valuable tool for remotely sensing the atmosphere. In this context, GNSS tomography evolved to an extremely promising technique to reconstruct the spatiotemporal structure of the troposphere. However, locating dual-frequency (DF) receivers with a spatial resolution of a few tens of kilometers sufficient for GNSS tomography is not economically feasible. Therefore, in this research, the feasibility of using single-frequency (SF) observations in GNSS tomography as an alternative approach has been investigated. The algebraic reconstruction technique (ART) and the total variation (TV) method are examined to reconstruct a regularized solution. The accuracy of the reconstructed water vapor distribution model using low-cost receivers is verified by radiosonde measurements in the area of the EPOSA (Echtzeit Positionierung Austria) GNSS network, which is mostly located in the east part of Austria for the period DoY 232–245, 2019. The results indicate that irrespective of the investigated ART and TV techniques, the quality of the reconstructed wet refractivity field is comparable for both SF and DF schemes. However, in the SF scheme the MAE with respect to the radiosonde measurements for ART + NWM and ART + TV can reach up to 10 ppm during noontime. Despite that, all statistical results demonstrate the degradation of the retrieved wet refractivity field of only 10–40% when applying the SF scheme in the presence of the initial guess.

Single-stage to orbit ascent trajectory optimisation with reliable evolutionary initial guess

In this paper, the ascent trajectory optimization of a lifting body Single-Stage To Orbit (SSTO) reusable launch vehicle is investigated. The work is carried out using a Direct Multiple Shooting method to solve the Optimal Control problem. The crucial initialisation of the optimisation process is performed by using a combination of two evolutionary algorithms, namely a Multi-Objective Parzen-based Estimation of Distribution (MOPED) algorithm and a Multi-Population Adaptive Inflationary Differential Evolution Algorithm (MP-AIDEA). Multi-Objective Parzen-based Estimation of Distribution (MOPED) belongs to the class of Estimation of Distribution Algorithms (EDAs) and it is used in the first phase of the initial guess research to explore the search space, then Multi-Population Adaptive Inflationary Differential Evolution Algorithm (MP-AIDEA) is used to refine the obtained results, and better fulfill the imposed constraints. The initial guesses obtained with this evolutionary framework were tested on different multiple shooting configurations. The importance of the continuity properties of the employed mathematical models was also quantitatively addressed.