Finite Element Algorithm Research Articles

MTAINV3D: A Three-dimensional Adaptive Magnetotelluric Inversion Tool Using Unstructured Grids

Currently, 3D magnetotelluric inversion often uses a fixed inversion grid. Too sparse inversion grids cannot approximate the complex subsurface conductivity distribution, and may also lead to inversion results failing to converge. Too dense inversion grids will increase not only the computational cost, but also the non-uniqueness of the inversion. Aiming at the above problems, we have developed a three-dimensional magnetotelluric adaptive inversion strategy with unstructured finite element and limited memory BFGS (L-BFGS) algorithms. Firstly, based on the unstructured finite element method, the high accuracy forward responses of the 3D geo-electric model with arbitrary complex terrain and conductivity distributions can be obtained. Then, the forward and inversion meshes are decoupled by using the nested forward and inversion tetrahedral meshes. The Thikhonov regularization objective function with smooth constraints is established and minimized by L-BFGS optimization algorithm with inexact line search procedure, where the gradient of the objective function is solved by using the adjoint principle. Most importantly, an inversion grid adjustment strategy based on the dual constraints of sensitivity matrix and model gradient is proposed, which are used to guide the automatic refinement of inversion grid in the optimization process. Finally, a topographic model is used to validate and test the performance of the proposed adaptive inversion algorithm.

Application of Efficient Algorithm in Dynamic Simulation of Viscoelastic Fluid in 3D Animation

With the rapid development of computer technology, 3D animation has become a hot and concerned field. Whether it is movies, TV, games or other digital media, 3D animation is playing an increasingly important role. In the process of 3D animation, computers need to deal with a lot of data and complex calculations, so efficient algorithms are of great significance to improve the efficiency of animation production and the quality of simulation. Efficient algorithm plays a vital role in 3D animation, which can improve the computational efficiency, reduce the computational time and save computational resources, and at the same time improve the accuracy and realism of simulation. In this paper, the application of an efficient algorithm-finite element method in the dynamic simulation of viscoelastic fluid is introduced in detail. At the same time, the article also discusses the future technical trends and development direction, which provides ideas and references for further research.

Equiaxed growth of interacting Al–Cu dendrites in thin samples: a phase-field study at copper concentrations relevant for practical applications

We perform three-dimensional phase-field simulations of equiaxed solidification in Al–Cu thin samples. Purely diffusive conditions are considered in order to describe systems where convection and gravity effects can be neglected. The use of a parallel adaptive finite element algorithm introduced recently [Gong et al., Comput. Mater. Sci. 147 (2018) p. 338-352] allows us to reach the domain of copper concentrations used in practical applications (c≥3 wt% Cu). We compare the present results with those of a previous study which was restricted to lower copper concentrations (c≤2 wt% Cu) [Boukellal et al., Materialia 1 (2018) p. 62-69] due to the use of a finite difference code. In the fast dendritic growth regime, our results confirm that the dimensionless growth length Λ is independent of the copper concentration and the average separation distance between the dendrite nuclei. The new data obtained at higher copper concentrations lead to a more accurate estimate of Λ. Physical arguments are developed to specify the meaning of Λ and the grounds of the scaling law Λ=cst. Comparisons with available experimental results of the literature give additional support to this scaling law.

Generalized viscoelastic flow with thermal radiations and chemical reactions

Background:A generalized model of mathematical nature is considered to address the viscoelastic flow problem using fractional derivatives. Control/freedom of the flow mechanism is achieved with these derivatives. In simulations of industrial interest, more variations are available with fractional derivatives when compared with ordinary derivatives. Relaxation times are incorporated to handle the abrupt changes in the flow domain. Fluid flow is carried out under the influence of thermal radiations and when a heat source or sink is present. Chemical reactions of the first order are observed in the mathematical modeling of the flow. Methods:Flow is induced with the movement of the lower surface while applying force on the x-plane. Simulations of the governing mathematical problem are computed with the combination of finite element and finite difference algorithms. Significant Findings:It is noted that velocity, temperature, and concentration change with the variation of fractional order derivatives which was not possible with the classical derivatives. Moreover, with greater relaxation times, velocity, temperature, and concentration remained at a lower level. The modeled mechanism can be considered to avoid costly trials in chemical and polymer casting industries.

Crash Box Impact Energy Absorption

Abstract: Crashworthiness parameters like internal energy absorption and crush force efficiency are the key constants in evaluating the component crashworthiness and its safety in the design of automotive structures for crashworthiness, there is an immense requirement for null strain sub modules that provide a rigid room of survival area for the occupants and deformable sub modules. Which can dematerialize the kinetic energy effectively? The front crash box of an automotive car is one of the most important deformable components which dissipate kinetic energy while frontal crash, which is the most persistent crash situation, affects the entire automotive structural behavior. In this research, quasi-static axial loading response and crashworthiness characteristics of empty hollow tube have been investigated through experimental and numerical simulations. The axial quasi-static loading was executed at a feed rate to evaluate the crashworthiness constants of each sample against quasi-static loading. The supremacy of feed rate empty hallow structures were pursued. The numerical simulation of quasi-static test was performed in accordance with explicit finite element algorithm of LS-DYNA in order to investigate and justify the crashworthiness of each variety of specimens with experimental results.

A decoupled, unconditionally energy-stable and conservative finite element algorithm for a constrained transport model of the incompressible MHD equations

This article mainly considers numerical approximation for a constrained transport magnetohydrodynamic (CT-MHD) model in three dimensions. The superiority of the algorithm is that the magnetic field and current density naturally satisfy divergence-free at the discrete level, the divergence of velocity is improved simultaneously, and the electromagnetic field and the fluid field are decoupled. Finally, we rigorously prove the unconditional energy stability of the proposed algorithm and display five simulations to confirm its accuracy and validity.

Convergent evolving finite element approximations of boundary evolution under shape gradient flow

Abstract As a specific type of shape gradient descent algorithm, shape gradient flow is widely used for shape optimization problems constrained by partial differential equations. In this approach, the constraint partial differential equations could be solved by finite element methods on a domain with a solution-driven evolving boundary. Rigorous analysis for the stability and convergence of such finite element approximations is still missing from the literature due to the complex nonlinear dependence of the boundary evolution on the solution. In this article, rigorous analysis of numerical approximations to the evolution of the boundary in a prototypical shape gradient flow is addressed. First-order convergence in time and $k$th order convergence in space for finite elements of degree $k\geqslant 2$ are proved for a linearly semi-implicit evolving finite element algorithm up to a given time. The theoretical analysis is consistent with the numerical experiments, which also illustrate the effectiveness of the proposed method in simulating two- and three-dimensional boundary evolution under shape gradient flow. The extension of the formulation, algorithm and analysis to more general shape density functions and constraint partial differential equations is also discussed.

Two-grid algorithm of lumped mass finite element approximation for Allen-Cahn equations

In this paper, we present a two-grid lumped mass finite element algorithm for 2D Allen-Cahn equations, where Crank-Nicolson scheme and piecewise linear element are utilized for temporal and spatial discretization, respectively. Both the maximum-norm boundedness and H1-norm error estimates of the proposed two-grid scheme are discussed. Finally, a numerical example is given to verify the theoretical results. By comparing with the finite element scheme and the two-grid finite element scheme, we found that our scheme has a great advantage in calculation time.

Retracted: Sports Injury Modeling of the Anterior Cruciate Ligament Based on the Intelligent Finite Element Algorithm.

[This retracts the article DOI: 10.1155/2021/3606863.].

Models of nonlinear deformation of concrete in a triaxial stress state and their implementation in the PRINS computational complex

Modern construction standards and regulations prescribe to carry out calculations of concrete and reinforced concrete structures in a nonlinear formulation with account of the real properties of concrete and reinforcement. However, the most of finite-element program complexes cannot perform such calculations in a nonlinear formulation with account of plastic deformations of concrete and reinforcement. To solve this problem, a methodology has been developed and a solid finite element adapted to the PRINS computing complex has been created, which made it possible to perform calculations of reinforced concrete structures considering their actual work. The aim of the study - development and implementation of a method for calculating reinforced concrete structures under conditions of a three-dimensional stress state, considering both brittle fracture and elastic-plastic deformation of concrete. A finite-element methodology, algorithm, and program for calculation of massive reinforced concrete structures with account of plastic deformations of concrete have been presented. The methodology is based on the modified Willam and Warnke strength criterion supplemented with the flow criterion. Two models of volumetric deformation of concrete have been regarded: the elastic model at brittle failure and the ideal elastoplastic model. An eight-node finite element with linear approximating functions of displacements implementing the mentioned deformation models is created. Verification calculations of a massive concrete structure in three-axial compression testify to the accuracy and convergence of the developed finite elements. The PRINS can be effectively used by engineers of designing and scientific organizations to solve a wide class of engineering problems related to calculations of building structures.

Numerical simulation and intelligent prediction of thermal transport of a water-based copper oxide nanofluid in a lid-driven trapezoidal cavity

This article investigates the fluid dynamics and heat transfer properties in a trapezoidal enclosure containing a heated cylindrical object. It involves the interaction of multiple physical processes such as the magnetic field, thermal radiation, porous materials, and aqueous copper oxide nanoparticles. The governing partial differential equations are analyzed numerically through the continuous Galerkin finite element algorithm. The analysis takes into account various physical parameter factors, including the Richardson number (0–5), the Hartmann number (5−40), the Darcy number (0.001−0.1), thermal radiation parameter (0.5−2), and nanoparticle volume concentration (0.01−0.1). The physical mechanism of thermal and mass transfer in the enclosure caused by various factors is fully explored. In addition, the multiple expression programming (MEP) technique is implemented to report a comparative analysis of flow profiles and thermal distribution. The findings demonstrated that at low Ri, the primary flow within the cavity is driven by the shear friction generated by the moving walls. The growing importance of radiative heat transfer reduces the effectiveness of convective heat transfer, resulting in a decline in the average Nusselt number with R. The heat transfer rate rises up to 27.7% as ϕ augments; however, its value declines by 9.37% against Ha. The expected results obtained by the MEP approach are very consistent with the numerical ones. There is no doubt that the new MEP concept provides a valuable tool for researchers to predict the heat transfer behavior of any data set in cavities of different shapes. It is expected to provide new idea for the development of efficient cooling systems and the improvement of energy efficiency in various engineering applications.

Finite element algorithm with a second‐order shifted composite numerical integral formula for a nonlinear time fractional wave equation

AbstractIn this article, we propose a second‐order shifted composite numerical integral formula, which is denoted as the SCNIF2. We transform the nonlinear time fractional wave equation into a partial differential equation with a fractional integral term and use the SCNIF2 in time and the finite element algorithm in space to formulate a fully discrete scheme. In order to decrease the initial error of the numerical scheme, we add some starting parts. In addition, we prove the stability and error estimation of the algorithm. Finally, we illustrate the effect of the starting parts and the accuracy of the numerical scheme through some numerical tests.

A Dimension-Reduced Line Element Method for 3D Transient Free Surface Flow in Porous Media

In order to reduce the numerical difficulty of the 3D transient free surface flow problems in porous media, a line element method is proposed by dimension reduction. Different from the classical continuum-based methods, homogeneous permeable pores in the control volume are conceptualized by a 3D orthogonal network of tubes. To obtain the same hydraulic solution with the continuum model, the equivalent formulas of flow velocity, continuity equation and transient free surface boundary are derivable from the principle of flow balance. In the solution space of transient free surface flow, the 3D problem is transformed into 1D condition, and then a finite element algorithm is simply deduced. The greatest advantage of the line element method is line integration instead of volume/surface integration, which has dramatically decreased the integration difficulty across the jump free surface. Through the analysis of transient free surface flow in the unconfined aquifer, trapezoidal dam, sand flume and wells, the transient free surface locations predicted from the proposed line element method generally agree well with the analytical, experimental and other numerical data in the available literatures, the numerical efficiency can also be well guaranteed. Furthermore, the hydraulic anisotropy has significant effect on the evolution of free surface locations and the shape of depression cones in spatial. The line element method can be expanded to model the 3D unsaturated seepage flow, two-phase flow and thermos problems in porous media because of the similarity between the similarity of Darcy’s law, Buckingham Law and Fourier’s law.

A convergent finite element algorithm for mean curvature flow in arbitrary codimension

Optimal-order uniform-in-time H^1 -norm error estimates are given for semi- and full discretizations of mean curvature flow of surfaces in arbitrarily high codimension. The proposed and studied numerical method is based on a parabolic system coupling the surface flow to evolution equations for the mean curvature vector and for the orthogonal projection onto the tangent space. The algorithm uses evolving surface finite elements and linearly implicit backward difference formulas. This numerical method admits a convergence analysis in the case of finite elements of polynomial degree at least 2 and backward difference formulas of orders 2 to 5. Numerical experiments in codimension 2 illustrate and complement our theoretical results.

Analysis of Vibration Characteristics and Noise Reduction for 10kV Oil-Immersed Transformer

Distribution transformers are usually located near residential buildings, which cause serious noise pollution. This paper focuses on reducing the vibration noise of 10[Formula: see text]kV oil-immersed transformer by optimization of transformer case structure. Based on the analysis of the vibration characteristics for the transformer case surface, the noise reduction measures were put forward for the 10[Formula: see text]kV oil-immersed transformer. An optimization method combining finite element and genetic algorithm was proposed, and the surface vibration velocity was reduced by optimizing the size of the heat sink. At the same time, a noise reduction strategy based on modal vibration amplitude optimization was proposed by increasing additional mass blocks. The structure of oil-immersed transformer was designed rationally according to the proposed optimization measures. The measurement result showed that the average A-weighted sound pressure level of the optimized transformer was reduced by 8.41[Formula: see text]dB(A).

Design and adaptive finite element simulation of conformal transformation optics devices with isotropic materials

Traditional transform optical devices are designed from anisotropic magnetic materials which are difficult to fabricate. In this paper, we design and simulate a conformal carpet invisible cloak and bending waveguide device with isotropic material. According to the existing conformal coordinate transformation, we deduce the perfect parameters required by the conformal device. And the finite element method and error analysis of the model equation and the basic process of adaptive algorithm are given. We first simulated a carpet cloak and bending waveguide device with perfect parameters; then we used the idea of parameter segmentation to design a carpet cloak that requires 35 isotropic materials and use the idea of layering to design the conformal bending waveguide device, and relevant numerical results are presented; finally, we designed the adaptive finite element algorithm to realize the numerical simulation of Maxwell's equations in isotropic material.

Influence of Concrete Creep on the Bending of a Prestressed Bridge Beam

By present time significant experimental and theoretical material on concrete creep has been accumulated. At the same time, the known approaches to calculation of concrete and reinforced concrete structures with regard to creep are oriented mainly to solving problems with relatively simple geometry of the product. Moreover, there are no mechanic-mathematical models of hereditary type oriented to the finite-element method.The concept of modelling of long-term deformation of reinforced concrete structures in a three-dimensional statement, based on the use of the integral deformation modulus of concrete, does not allow one to carry out designing considering the technological prehistory. Therefore, the problem of developing a finite-element algorithm and corresponding software allowing the modelling of the volumetric stress-strain state of large-span prestressed reinforced concrete structures within the framework of the theory of hereditary aging is relevant.

Stability of Unsaturated Soil Slope Considering Stratigraphic Uncertainty

Stratigraphic uncertainty is widely present in nature, but it has not been well considered in the stability analysis of unsaturated soil slopes in the past. In this study, the stability of the unsaturated soil slope is evaluated based on borehole data considering stratigraphic uncertainty. Firstly, an enhanced coupled Markov chain model is used to simulate stratigraphic uncertainty. Then, a finite element algorithm for automatically calculating the safety factor (FS) and the average groundwater table (AGT) of the unsaturated soil slope is developed. At last, a hypothetical slope located in the stratum from Perth, West Australia is analyzed using the proposed algorithm under different borehole schemes. The results show that with the increase in the borehole number, the statistics of FS and AGT will not monotonically increase or decrease. But the trend is that the mean values of FS and AGT gradually approach and eventually converge to the real values, and the standard deviations of FS and AGT decrease. There is a linear relationship between the standard deviation of FS (or AGT) and the average information entropy. The FS and AGT are negatively correlated considering stratigraphic uncertainty.

Simulation of Seismoelectric Waves Using Time-Domain Finite-Element Method in 2D PSVTM Mode

The study of the numerical simulation of seismoelectric effects is very helpful for understanding the theory and mechanism of seismoelectric activities. Quasi-static approximation is widely used in the numerical simulation of seismoelectric fields. However, numerical errors occur when the model domain is not within the near-field area of EM waves or the medium is of high salinity. To solve this problem, we propose a time-domain finite-element algorithm (FETD) based on the full-wave electromagnetic (EM) equation to simulate seismoelectric waves in 2D PSVTM mode. By decomposing the electrokinetic coupling equations into two independent ones, we can solve the seismoelectric waves separately. In our implementation, we focus our attention on the solution of EM waves based on vector–scalar potentials, while using the open-source code SPECFEM2D to explicitly solve Biot’s equations and obtain the relative fluid–solid displacement, which is taken as the source for the complete Maxwell’s equations. In the solution of EM wave fields, we use an unconditionally stable implicit method for time discretization. Computation efficiency can be improved by combining explicit and implicit recursions. After conducting the mathematical formulation, we first validate our method by comparing its results with the analytic solutions for a half-space and a two-layer model, as well as with a quasi-static approximation method. Moreover, we run numerical simulations and wavefield analyses on an elliptical hydrocarbon reservoir, and reveal that the interface responses are promising for the identification of underground interfaces and hydrocarbon reservoir exploration.

Research on Channel Characteristics and Electrode Electrical Performance of Earth Current Field Information Transmission Technology.

Starting from the need for emergency rescue information transmission in tunnel engineering accidents, this article focuses on researching and solving the technical problems of information transmission between rescue personnel and trapped personnel after tunnel engineering collapse accidents, before and during the rescue process. The research objects are the information transmission channel and grounding electrode in the earth current field information transmission technology, and the electromagnetic characteristics of the earth medium and the electrical performance of the grounding electrode are studied and analyzed using the electromagnetic simulation software Maxwell based on finite element algorithm, establish a three-dimensional model based on the transmission of current field information of the ground electrode, analyze the effects of the electrode array, electrode depth, and radius on impedance. Research has shown that the impedance of the earth is related to the resistivity of the medium and is not a human-controllable factor. To reduce the contact impedance of an electric dipole antenna, one should start with the contact impedance of the earth electrode. The impedance of the transmitting end is an important factor affecting the efficiency of information transmission; parallel connection of multiple grounding electrodes, increasing the depth of grounding electrode penetration into the soil layer, and increasing the radius between grounding electrode pairs are all effective methods to reduce the contact impedance of electric dipole antennas, thereby improving information transmission capacity. To achieve wireless information transmission through the stratum, by appropriately selecting the operating frequency of electromagnetic waves, a certain distance of signal transmission can be achieved.