Chemical equilibrium systems as numerical test problems

1990 ◽  
Vol 16 (2) ◽  
pp. 143-151 ◽  
Author(s):  
Keith Meintjes ◽  
Alexander P. Morgan
Keyword(s):  
Chemical Equilibrium ◽  
Numerical Test ◽  
Test Problems

scholarly journals A Collocation Approach for Solving Time-Fractional Stochastic Heat Equation Driven by an Additive Noise

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 904 ◽  
Author(s):  
Afshin Babaei ◽  
Hossein Jafari ◽  
S. Banihashemi
Keyword(s):  
Order Of Convergence ◽  
Additive Noise ◽  
Numerical Solutions ◽  
Numerical Test ◽  
Test Problems ◽  
Heat Equations ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Stochastic Heat Equations ◽  
Collocation Approach

A spectral collocation approach is constructed to solve a class of time-fractional stochastic heat equations (TFSHEs) driven by Brownian motion. Stochastic differential equations with additive noise have an important role in explaining some symmetry phenomena such as symmetry breaking in molecular vibrations. Finding the exact solution of such equations is difficult in many cases. Thus, a collocation method based on sixth-kind Chebyshev polynomials (SKCPs) is introduced to assess their numerical solutions. This collocation approach reduces the considered problem to a system of linear algebraic equations. The convergence and error analysis of the suggested scheme are investigated. In the end, numerical results and the order of convergence are evaluated for some numerical test problems to illustrate the efficiency and robustness of the presented method.

Comprehensive Study of Typical Metamodel Methods Applied in Aircraft Multidisciplinary Design Optimization

2011 ◽  
Vol 110-116 ◽  
pp. 3031-3039 ◽  
Author(s):  
Teng Long ◽  
Li Liu
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Least Squares Method ◽  
Numerical Test ◽  
Kriging Model ◽  
Multidisciplinary Design ◽  
Test Problems ◽  
Comparison Results ◽  
Moving Least Squares Method ◽  
Comprehensive Study

—Metamodels have been widely applied in aircraft multidisciplinary design optimization (MDO) to alleviate the computation burden and improve the optimization efficiency. At present, there are various metamodel methods available, such as response surface method, Kriging model, moving least squares method, radial basis function, neural networks and so on. However, it is difficult to confirm which metamodel method is more promising, which is also an interesting question puzzled most designers. In this article, by using a series of numerical test problems with different inherent features, a comprehensive study is employed to compare five typical metamodel methods commonly applied in aircraft MDO under multiple metrics. In term of the comparison results, the conclusions are drawn and recommendations for selecting suitable metamodels in aircraft MDO practice are also summarized.

Design and Simulation of an Improved Particle Swarm Optimization

2010 ◽  
Vol 20-23 ◽  
pp. 1280-1285
Author(s):  
Jian Xiang Wei ◽  
Yue Hong Sun
Keyword(s):  
Particle Swarm Optimization ◽  
Dimensional Space ◽  
Numerical Test ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Population Diversity ◽  
Test Problems ◽  
Local Optimum ◽  
Swarm Optimization ◽  
Improved Pso

The particle swarm optimization (PSO) algorithm is a new population search strategy, which has exhibited good performance through well-known numerical test problems. However, it is easy to trap into local optimum because the population diversity becomes worse during the evolution. In order to overcome the shortcoming of the PSO, this paper proposes an improved PSO based on the symmetry distribution of the particle space position. From the research of particle movement in high dimensional space, we can see: the more symmetric of the particle distribution, the bigger probability can the algorithm be during converging to the global optimization solution. A novel population diversity function is put forward and an adjustment algorithm is put into the basic PSO. The steps of the proposed algorithm are given in detail. With two typical benchmark functions, the experimental results show the improved PSO has better convergence precision than the basic PSO.

P3GA: An Algorithm for Technology Characterization

2015 ◽  
Vol 137 (1) ◽  
Author(s):  
Edgar Galvan ◽  
Richard J. Malak
Keyword(s):  
Design Automation ◽  
Design Space Exploration ◽  
Design Space ◽  
Space Exploration ◽  
Numerical Test ◽  
Pareto Frontier ◽  
Test Problems ◽  
Genetic Optimization ◽  
Technology Evaluation ◽  
Mathematical Basis

It is important for engineers to understand the capabilities and limitations of the technologies they consider for use in their systems. However, communicating this information can be a challenge. Mathematical characterizations of technical capabilities are of interest as a means to reduce ambiguity in communication and to increase opportunities to utilize design automation methods. The parameterized Pareto frontier (PPF) was introduced in prior work as a mathematical basis for modeling technical capabilities. One advantage of PPFs is that, in many cases, engineers can model a system by composing frontiers of its components. This allows for rapid technology evaluation and design space exploration. However, finding the PPF can be difficult. The contribution of this article is a new algorithm for approximating the PPF, called predictive parameterized Pareto genetic algorithm (P3GA). The proposed algorithm uses concepts and methods from multi-objective genetic optimization and machine learning to generate a discrete approximation of the PPF. If needed, designers can generate a continuous approximation of the frontier by generalizing beyond these data. The algorithm is explained, its performance is analyzed on numerical test problems, and its use is demonstrated on an engineering example. The results of the investigation indicate that P3GA may be effective in practice.

Rectangular hybrid elements for the analysis of sandwich plate structures

1987 ◽  
Vol 14 (4) ◽  
pp. 455-460 ◽  
Author(s):  
P. Fazio ◽  
K. Gowri ◽  
K. H. Ha
Keyword(s):  
Finite Element ◽  
Sandwich Panel ◽  
Sandwich Plate ◽  
Hybrid Approach ◽  
Numerical Test ◽  
Computation Time ◽  
Test Problems ◽  
Plate Bending ◽  
Structural Behaviour ◽  
Plate Structures

The structural behaviour of sandwich plate structures are characterized by transverse shear deformations in the core. The assumed stress hybrid finite element technique is particularly suitable for developing sandwich plate bending elements. In the present study, rectangular three-layer sandwich plate elements have been formulated using simple assumed stress functions. Numerical test problems have been solved to examine the convergence property and suitability of these elements. The results are compared with that of a complete quadratic stress mode element and with analytical solutions. Six degrees of freedom per node shell elements are formulated by combining the plate bending elements with membrane elements. A folded plate sandwich panel roof has been analyzed using these elements and the results are compared with the experimental values. The use of simple stress function gives satisfactory results and reduces the size of the matrices to be used, the length of the program, and the computation time for the formulation of element stiffness matrices. Key words: sandwich panel, structural analysis, finite element method, stress hybrid approach, folded plates.

scholarly journals On the Approximated Solution of a Special Type of Nonlinear Third-Order Matrix Ordinary Differential Problem

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2262
Author(s):  
Emilio Defez ◽  
Javier Ibáñez ◽  
José M. Alonso ◽  
Michael M. Tung ◽  
Teresa Real-Herráiz
Keyword(s):  
Differential Equations ◽  
Numerical Test ◽  
Test Problems ◽  
Science And Engineering ◽  
Third Order ◽  
Differential Problem ◽  
Order Matrix ◽  
Engineering Problems ◽  
Matrix Differential Equations ◽  
Matrix Differential

Matrix differential equations are at the heart of many science and engineering problems. In this paper, a procedure based on higher-order matrix splines is proposed to provide the approximated numerical solution of special nonlinear third-order matrix differential equations, having the form Y(3)(x)=f(x,Y(x)). Some numerical test problems are also included, whose solutions are computed by our method.

scholarly journals Computer-Based Fuzzy Numerical Method for Solving Engineering and Real-World Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Naila Rafiq ◽  
Naveed Yaqoob ◽  
Nasreen Kausar ◽  
Mudassir Shams ◽  
Nazir Ahmad Mir ◽  
...  
Keyword(s):  
Fuzzy Sets ◽  
Numerical Method ◽  
Nonlinear Equations ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Numerical Solutions ◽  
Numerical Test ◽  
Real Life ◽  
Triangular Fuzzy Number ◽  
Test Problems

The nonlinear equation is a fundamentally important area of study in mathematics, and the numerical solutions of the nonlinear equations are also an important part of it. Fuzzy sets introduced by Zedeh are an extension of classical sets, which have several applications in engineering, medicine, economics, finance, artificial intelligence, decision-making, and so on. The most special types of fuzzy sets are fuzzy numbers. The important fuzzy numbers are trapezoidal fuzzy and triangular fuzzy numbers, which have several applications. In this research article, we propose an efficient numerical iterative method for estimating roots of fuzzy nonlinear equations, which are based on the special type of fuzzy number called triangular fuzzy number. Convergence analysis proves that the order of convergence of the numerical method is three. Some real-life applications are considered as numerical test problems from engineering, which contain fuzzy quantities in the parametric form. Engineering models include fractional conversion of nitrogen-hydrogen feed into ammonia and Van der Waal’s equation for calculating the volume and pressure of a gas and motion of the object under constant force of gravity. Numerical illustrations are given to show the dominance efficiency of the newly constructed iterative schemes as compared to existing methods in the literature.

Propagation of diffusing pollutant by kinetic flux-vector splitting method

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Saqib Zia ◽  
Omar Rabbani ◽  
Asad Rehman ◽  
Munshoor Ahmed
Keyword(s):  
Numerical Test ◽  
Splitting Method ◽  
Test Problems ◽  
Flux Vector ◽  
Order Accuracy ◽  
Time Stepping ◽  
Flux Vector Splitting ◽  
And Performance ◽  
The One ◽  
Central Scheme

Abstract In this article, the transport of a passive pollutant by a flow modeled by shallow water equations is numerically investigated. The kinetic flux-vector splitting (KFVS) scheme is extended to solve the one and two-dimensional equations. The first two equations of the considered model are mass and momentum equations and the third equation is the transport equation. The suggested scheme focuses on the direct splitting of the macroscopic flux functions at the cell interfaces. It achieves second-order accuracy by using MUSCL-type initial reconstruction and the Runge–Kutta time stepping technique. Several numerical test problems from literature are considered to check the efficiency and performance of the scheme. The results of the proposed scheme are compared to the central scheme for validation. It is found that the results of both the schemes are in close agreement with each other. However, our suggested KFVS scheme resolves the sharp discontinuous profiles precisely.

scholarly journals Well-balanced finite volume multi-resolution schemes for solving the Ripa models

2021 ◽  
Vol 13 (3) ◽  
pp. 168781402110034
Author(s):  
Asad Rehman ◽  
Ishtiaq Ali ◽  
Saqib Zia ◽  
Shamsul Qamar
Keyword(s):  
Steady State ◽  
Finite Volume ◽  
Numerical Test ◽  
Temperature Gradients ◽  
Water Model ◽  
Test Problems ◽  
Numerical Schemes ◽  
Weno Schemes ◽  
Horizontal Temperature Gradients ◽  
Fifth Order

In this article, fifth order well-balanced finite volume multi-resolution weighted essentially non-oscillatory (FV MR-WENO) schemes are constructed for solving one-dimensional and two-dimensional Ripa models. The Ripa system generalizes the shallow water model by incorporating horizontal temperature gradients. The presence of temperature gradients and source terms in the Ripa models introduce difficulties in developing high order accurate numerical schemes which can preserve exactly the steady-state conditions. The proposed numerical methods are capable to exactly preserve the steady-state solutions and maintain non-oscillatory property near the shock transitions. Moreover, in the procedure of derivation of the FV MR-WENO schemes unequal central spatial stencils are used and linear weights can be chosen any positive numbers with only restriction that their total sum is one. Various numerical test problems are considered to check the validity and accuracy of the derived numerical schemes. Further, the results obtained from considered numerical schemes are compared with those of a high resolution central upwind scheme and available exact solutions of the Ripa model.

A locking-free coupled polynomial Timoshenko piezoelectric beam finite element

2015 ◽  
Vol 32 (5) ◽  
pp. 1251-1274 ◽  
Author(s):  
Litesh N Sulbhewar ◽  
P. Raveendranath
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Electromechanical Coupling ◽  
Numerical Test ◽  
Shear Deformation Theory ◽  
Test Problems ◽  
Field Representation ◽  
Content Type ◽  
Piezoelectric Beam ◽  
Consistent Manner

Purpose – Piezoelectric extension mode smart beams are vital part of modern control technology and their numerical analysis is an important step in the design process. Finite elements based on First-order Shear Deformation Theory (FSDT) are widely used for their structural analysis. The performance of the conventional FSDT-based two-noded piezoelectric beam formulations with assumed independent linear field interpolations is not impressive due to shear and material locking phenomena. The purpose of this paper is to develop an efficient locking-free FSDT piezoelectric beam element, while maintaining the same number of nodal degrees of freedom. Design/methodology/approach – The governing equations are derived using a variational formulation to establish coupled polynomial field representation for the field variables. Shape functions based on these coupled polynomials are employed here. The proposed formulation eliminates all locking effects by accommodating strain and material couplings into the field interpolation, in a variationally consistent manner. Findings – The present formulation shows improved convergence characteristics over the conventional formulations and proves to be the most efficient way to model extension mode piezoelectric smart beams, as demonstrated by the results obtained for numerical test problems. Originality/value – To the best of the authors’ knowledge, no such FSDT-based finite element with coupled polynomial shape function exists in the literature, which incorporates electromechanical coupling along with bending-extension and bending-shear couplings at the field interpolation level itself. The proposed formulation proves to be the fastest converging FSDT-based extension mode smart beam formulation.

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