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This paper aims to present a computational framework to generate numeric enrichment functions for two-dimensional problems dealing with single/multiple local phenomenon/phenomena. The two-scale generalized/extended finite element method (G/XFEM) approach used here is based on the solution decomposition, having global- and local-scale components. This strategy allows the use of a coarse mesh even when the problem produces complex local phenomena. For this purpose, local problems can be defined where these local phenomena are observed and are solved separately by using fine meshes. The results of the local problems are used to enrich the global one improving the approximate solution.

The implementation of the two-scale G/XFEM formulation follows the object-oriented approach presented by the authors in a previous work, where it is possible to combine different kinds of elements and analyses models with the partition of unity enrichment scheme. Beside the extension of the G/XFEM implementation to enclose the global–local strategy, the imposition of different boundary conditions is also generalized.

The generalization done for boundary conditions is very important, as the global–local approach relies on the boundary information transferring process between the two scales of the analysis. The flexibility for the numerical analysis of the proposed framework is illustrated by several examples. Different analysis models, element formulations and enrichment functions are used, and the accuracy, robustness and computational efficiency are demonstrated.

This work shows a generalize imposition of different boundary conditions for global–local G/XFEM analysis through an object-oriented implementation. This generalization is very important, as the global–local approach relies on the boundary information transferring process between the two scales of the analysis. Also, solving multiple local problems simultaneously and solving plate problems using global–local G/XFEM are other contributions of this work.

Presents a review on implementing finite element methods on supercomputers, workstations and PCs and gives main trends in hardware and software developments. An appendix included at the end of the paper presents a bibliography on the subjects retrospectively to 1985 and approximately 1,100 references are listed.

The purpose of this study is to (1) improve the spectral features of the second-order uniformly non-oscillatory (UNO) slope limiters, and (2) numerical simulation of the unified-form of generalized fully-coupled saturated thermo-poro-elastic systems in the axisymmetric cylindrical coordinate via cell-adaptive Kurganov-Tadmor (KT) central high-resolution scheme using the UNO limiters.

(1) The spectral features of the UNO limiter are improved by compression-adaptive MINMOD (MM) limiters, achieved by blending different types of MM limiters to achieve less numerical dissipation and dispersion. These blended MM limiters preserve the total variation diminishing (TVD) feature over non-uniform non-centered cells. Also, the spectral features of the central schemes using the UNO limiters are investigated. (2) For the thermo-poro-elastic problem, corresponding first-order hyperbolic system is provided, including flux, source, diffusion and nonlinear terms. Where, there are different interacting components in the source and flux terms. The nonlinear terms are also considered by the Picard-like linearization concept.

Compression-adaptive UNO limiters would be stable over adapted cells with centered and non-centered cells. The benchmarks confirm that both spectral features and numerical accuracy are improved. For the generalized thermo-poro-elastic problem, corresponding responses including the shock waves can properly be captured.

Studying heat effects (e.g. hot fluid or freezing) and explosions on tunnels. Also, the UNO limiters could be used for simulations of various systems of conservation laws.

The purpose of this paper is to describe an extension of the boundary element method (BEM) and the dual reciprocity boundary element method (DRBEM) formulations developed for one- and two-dimensional steady-state problems, to analyse transient convection–diffusion problems associated with first-order chemical reaction.

The mathematical modelling has used a dual reciprocity approximation to transform the domain integrals arising in the transient equation into equivalent boundary integrals. The integral representation formula for the corresponding problem is obtained from the Green’s second identity, using the fundamental solution of the corresponding steady-state equation with constant coefficients. The finite difference method is used to simulate the time evolution procedure for solving the resulting system of equations. Three different radial basis functions have been successfully implemented to increase the accuracy of the solution and improving the rate of convergence.

The numerical results obtained demonstrate the excellent agreement with the analytical solutions to establish the validity of the proposed approach and to confirm its efficiency.

Finally, the proposed BEM and DRBEM numerical solutions have not displayed any artificial diffusion, oscillatory behaviour or damping of the wave front, as appears in other different numerical methods.

The purpose of this paper is to propose a new scheme for obtaining acceptable solutions for problems of continuum topology optimization of structures, regarding the distribution and limitation of discretization errors by considering h-adaptivity.

The new scheme encompasses, simultaneously, the solution of the optimization problem considering a solid isotropic microstructure with penalization (SIMP) and the application of the h-adaptive finite element method. An analysis of discretization errors is carried out using an a posteriori error estimator based on both the recovery and the abrupt variation of material properties. The estimate of new element sizes is computed by a new h-adaptive technique named “Isotropic Error Density Recovery”, which is based on the construction of the strain energy error density function together with the analytical solution of an optimization problem at the element level.

Two-dimensional numerical examples, regarding minimization of the structure compliance and constraint over the material volume, demonstrate the capacity of the methodology in controlling and equidistributing discretization errors, as well as obtaining a great definition of the void–material interface, thanks to the h-adaptivity, when compared with results obtained by other methods based on microstructure.

This paper presents a new technique to design a mesh made with isotropic triangular finite elements. Furthermore, this technique is applied to continuum topology optimization problems using a new iterative scheme to obtain solutions with controlled discretization errors, measured in terms of the energy norm, and a great resolution of the material boundary. Regarding the computational cost in terms of degrees of freedom, the present scheme provides approximations with considerable less error if compared to the optimization process on fixed meshes.

The subprime crisis (SPC) (2007–2008) has severely affected the economies across the globe. The Indian economy was also troubled because the SPC led to a sharp reduction in foreign trade and investment, a rise in the exchange rate volatility and disproportionate foreign-currency reserves. The present paper analyzes the financing pattern of Indian listed companies during the SPC. This study aims to ascertain the impacts of the SPC-2008 on the long-term and short-term financing decisions of Indian listed companies using novel data set and appropriate robust methodology.

The study uses fixed effect model autoregressive of order 1 (FEM AR (1)) and system generalised method of moments (GMM) methodology on a sample data of 1,032 Indian non-financial listed companies on the Bombay Stock Exchange (BSE) for the period 1999 to 2019 to analyze the financing pattern during the crisis.

The study finds that the Indian firms opted for de-leveraging, shortening the maturity of debt and short-term borrowing. This significant decline in the leverage and maturity of debt indicates that the companies in India generally followed the “rat race” model of the financing mix in the crisis. After the crisis, the firms have re-leveraged and expanded the maturity of debt up to 90%. This considerable expansion in leverage and maturity implies that the Indian firms are exposed to the “rollover risk.” This re-leverage risk is asymmetrically distributed for manufacturing and services firms. Manufacturing firms are found to be more exposed to this risk. Furthermore, tangibility, free cash flows and the liquidity available within the firms are the compelling elements of the financing decision during the crisis.

The study has not included the private firms and unorganized sectors in India. Moreover, the study has not analyzed disasters such as the Asian liquidity crisis, the information technology (IT) bubble crisis, the euro bond crisis and coronavirus disease 2019 (COVID-19) pandemic.

The study finds that Indian firms are exposed to higher risk during the financial crisis and this risk is further aggravated by the rollover risk. Therefore, investors and creditors should consider these additional risks in the financial decisions and take more precautions. The study suggests that the regulators should make necessary adjustments in lending policy, corporate restructuring and tax policy to deal with the menace of a financial crisis.

Indian firms should avoid following the rate race financing model.

This study aims to ascertain the impacts of the SPC-2008 on the long-term and short-term financing decisions of Indian listed companies using novel data set and appropriate robust methodology.

The purpose of this study is to show the procedure, application and main features of the hybrid numerical-analytical approach known as generalized integral transform technique by using it to study magnetohydrodynamic flow of electrically conductive Newtonian fluids inside flat parallel-plate channels subjected to a uniform and constant external magnetic field.

The mathematical formulation of the analyzed problem is given in terms of a streamfunction, obtained from the Navier–Stokes and energy equations, by considering steady state laminar and incompressible flow and constant physical properties.

Convergence analyses are performed and presented to illustrate the consistency of the integral transformation technique. The results for the velocity and temperature fields are generated and compared with those in the literature as a function of the main governing parameters.

A detailed analysis of the parametric sensibility of the main dimensionless parameters, such as the Reynolds number, Hartmann number, Eckert number, Prandtl number and electrical parameter, for some typical situations is performed.

To describe water absorption by the rice grains over time, diffusion and empirical models were used. Also, an optimization software was developed in this study to determine parameters and their uncertainties for the diffusion models (LS Optimizer, for partial differential equations). Parameters (and their uncertainties) for empirical models were determined by LAB Fit Curve Fitting Software.

Heat and mass diffusion phenomena are found in various processes of technological interest, including pasteurization, drying and water immersion of agricultural products, among others. The objective of this work was to study the process of water absorption by rice grains with and without husk, using diffusion and empirical models to describe the absorption kinetics. Rice grains were immersed (approximately 10 g for each experiment) in drinking water maintained at constant temperatures of 28, 40 and 50 C. In the experiments, the water contents absorbed by rice grains over time were obtained by the gravimetric method.

Among empirical models, Peleg was the most satisfactory to describe the kinetics of water absorption by rice without husk, while the Silva et alii model had the best statistical indicators for rice with husk. It was also verified that a diffusion model with boundary condition of the first kind showed the best (or equivalent) results in the description of all processes of kinetics of water absorption by rice grains, with and without husk. For grains without husk, the effective mass diffusivities were (1.186 ± 0.045) × 10⁻⁹, (1.312 ± 0.024) × 10⁻⁹ and (2.133 ± 0.028) × 10⁻⁹ m² min⁻¹, for the immersion temperatures of 28, 40 and 50C, respectively. For grains with husk, diffusivities were (0.675 ± 0.011) × 10⁻⁹ and (1.269 ± 0.017) × 10⁻⁹ m² min⁻¹, for temperatures of 28 and 50 C, respectively.

This work developed a solver for the diffusion equation in cylindrical geometry and presented the LS Optimizer software developed to determine differential equation parameters through experimental data sets.