This paper is devoted to numerical analysis of an inverse source problem in a degenerate parabolic equation. The aims of this work are to show the well-posedness of the discrete inverse problem and its convergence to the continuous one. For this, we reformulate first the encountered inverse problem to a regularized optimal control one. Then, we approximate our optimal control problem by finite element

Different types of effective neural network structures have been developed, including the recurrent neural networks (RNNs), concurrent neural networks (CNNs), among others. The TrumpetNet was recently proposed by the leading author for creating two-way deepnets using physics-law-based models, such as finite element method (FEM) and smoothed FEM or S-FEM. The unique feature of the TrumpetNet is the

In this paper, the semi-inverse method is applied to derive the Lagrangian of the 5αth Korteweg de Vries equation (KdV). Then the time and space differential operators of the Lagrangian are replaced by corresponding fractional derivatives. The variation of the functional of this Lagrangian is devoted to lead the fractional Euler Lagrangian via Agrawal’s method, which gives the space-time fractional

The current work aspires to design and study the construction of an efficient preconditioner for linear symmetric systems in a Hilbert space setting. Compliantly to Josef Málek and Zdeněk Strakoš’s work [Preconditioning and the Conjugate Gradient Method in the Context of Solving, PDEs, Vol. 1 (SIAM, USA).], we shed new light on the dependence of algebraic preconditioners with the resolution steps of

In this paper, numerical solutions of the extended Fisher–Kolmogorov equation are obtained using finite pointset method. Finite pointset method is a meshless method which is a local iterative method based on the weighted least square approximation. By employing splitting technique, the extended Fisher–Kolmogorov equation is split into a two coupled system of differential equations by introducing an

Slope limiters have been widely used to eliminate nonphysical oscillations near discontinuities generated by finite volume methods for hyperbolic systems of conservation laws. In this study, we investigate the performance of these limiters as applied to three-dimensional modified method of characteristics on unstructured tetrahedral meshes. The focus is on the construction of monotonicity-preserving

This paper presents a hybrid snapshot simulation methodology to accelerate the generation of high-quality data for proper orthogonal decomposition (POD) and reduced-order model (ROM) development. The entire span of the snapshot simulation is divided into multiple intervals, each simulated by either high-fidelity full-order model (FOM) or fast local ROM. The simulation then alternates between FOM and

This paper presents the state-of-the-art on different moving least square (MLS)-based dimension decomposition schemes for reliability analysis and demonstrates a modified version for high fidelity applications. The aim is to improve the performance of MLS-based dimension decomposition in terms of accuracy, number of function evaluations and computational time for large-dimensional problems. With this

Reliability-based design optimization (RBDO) under epistemic uncertainty (i.e., imprecise probabilistic information), especially in the presence of dependency of input variables, is a challenging problem. In this paper, we propose a dimension reduction-based RBDO framework considering dependent interval variables, which is pursued in a purely probabilistic manner. Most probable point (MPP) based dimension

A multiple variational iteration method (VIM) is proposed to effectively solve the second-order nonlinear two-point boundary value problems. For problems where convergence speed of the original VIM is slow or the original method is divergent, the multiple VIM method (MVIM) presented in this paper can readily improve the rate of convergence.

In this paper, the meshless method is extended to simulate the interaction between soil and structure through 2D finite element (FE) model. The background mesh line shared by each surface of interface is introduced for Gauss points’ generation and interpolation. Thus, instead of a series of interface elements, the whole soil–structure interface can be presented by an arbitrary number of nodes with

Identifying centers of vortices of fluid flow accurately is one of the accuracy measures for computational methods. After verifying the accuracy of the 2D adaptive mesh refinement (AMR) method in the benchmarks of 2D lid-driven cavity flow, this paper shows the accuracy verification by the benchmarks of 2D backward-facing step flow. The AMR method refines a mesh using the numerical solution of the

Methods of artificial neural networks (ANNs) have been applied to solve various science and engineering problems. TrumpetNets and TubeNets were recently proposed by the author for creating two-way deepnets using the standard finite element method (FEM) and smoothed FEM (S-FEM) as trainers. The significance of these specially configured ANNs is that the solutions to inverse problems have been, for the

In order to identify the upper and lower bounds of distributed force exciting on an uncertain structure, a comprehensive approach combining genetic algorithm based on Latin hypercube sampling (LHS-GA) and improved L-curve method is built up in this paper. For uncertain parameter expressed by interval form, LHS-GA is presented to seeking the maximum and minimum amplitudes of distributed load in the

A radial basis function (RBF)-based ghost cell method is presented to simulate flows around a rigid or flexible moving hydrofoil on a Cartesian grid. A compactly supported radial basis function (CSRBF) is introduced to the ghost cell immersed boundary method to treat the complex flexible boundaries in the fluid. The results indicate that this RBF representation method can accurately track tempo-spatially

Many industrial thermal processes belong to distributed parameter systems (DPSs), which have two coupled nonlinear blocks. Dual least square support vector machines (LS-SVM) has been proposed to model such systems. However, due to the use of two LS-SVM, this method often leads to heavy computation and long learning time, which does not suit for online application. In this study, a dual extreme learning

Computer aided design (CAD) models are widely employed in the current computer aided engineering or finite element analysis (FEA) systems that necessitate an optimal meshing as a function of their geometry. To this effect, the sub-mapping method is advantageous, as it segments the CAD model into different sub-parts, with the aim mesh them independently. Many of the existing 3D shape segmentation methods

The forced responses of bladed disks are highly sensitive to inevitable random mistuning. Considerable computational efforts are required for the sampling process to assess the statistical vibration properties of mistuned bladed disks. Therefore, efficient surrogate models are preferred to accelerate the process for probabilistic analysis. In this paper, four surrogate models are utilized to construct

In this study, a method for numerically solving Riccatti type differential equations with functional arguments under the mixed condition is presented. For the method, Legendre polynomials, the solution forms and the required expressions are written in the matrix form and the collocation points are defined. Then, by using the obtained matrix relations and the collocation points, the Riccati problem

In this paper, an adaptive phase-field scaled boundary finite element method for fracture in functionally graded material (FGM) is presented. The model accounts for spatial variation in the material and fracture properties. The quadtree decomposition is adopted for refinement, and the refinement is based on an error indicator evaluated directly from the solutions of the scaled boundary finite element

Unbonded fiber-reinforced elastomeric isolator (U-FREI) is an improved device for seismic mitigation of low-rise buildings. The horizontal force — displacement behavior of U-FREI is nonlinear due to rollover deformation and the horizontal stiffness is a function of both vertical load and horizontal displacement. In this paper, stability of a prototype U-FREI is studied based on the dynamic response

A numerical framework is proposed to couple the finite element (FE) and lattice Boltzmann methods (LBM) for simulating fluid–structure interaction (FSI) problems. The LBM is used as an efficient method for solving the weakly-compressible fluid flows. The corotational FE method for beam elements is used to solve the thin plate deformation. The two methods are coupled via a direct-forcing immersed boundary

The friction of two bodies in relative motion is accompanied by several phenomena such as elevation of temperature. The aim of this work is to calculate the braking temperature of the brake disc of an aircraft during the landing phase, using a calculation code based on Finite Element Method (FEM) and the analytical method of Newcomb. This investigation uses two kinds of disc — full and real disc (original

Setting friction pendulum bearings (FPB) at the top of central columns may be a good strategy to reduce the stations’ seismic responses. In this paper, the FPB is simulated in a detailed manner. The seismic reduction effectiveness of the FPB is studied with the three-dimensional dynamic time history analysis method. It is found that FPB can effectively reduce the maximum shearing force of the central

Matched interface and boundary (MIB) method is introduced for free vibration analysis of irregular membranes. Two distinct schemes-on-interface and off-interface schemes are used to deal with the topological relations between edges of irregular domains and the Cartesian mesh lines. Different geometric shapes such as triangle and quadrilateral are dealt with by using MIB procedures. A number of examples

Numerical modeling of whole blood still faces great challenges although significant progress has been achieved in recent decades, because of the large differences of physical and geometric properties among blood components, including red blood cells (RBCs), platelets (PLTs) and white blood cells (WBCs). In this work, we develop a three-dimensional (3D) smoothed particle hydrodynamics (SPH) model to

This paper concerns development and illustration of a hydrodynamic optimization tool, OPTShip-SJTU, which contains four main components, i.e., hull form modifier, performance evaluator, surrogate model building, and optimizer module. It has been further developed by integrating a new method into the performance evaluator module, which combines the Neumann–Michell (NM) theory with computational fluid

We present a complex field general variational statement to study the waves propagating in the circumferential directions of cylindrical curved waveguides. A semi-analytical technique that has been applied on straight waveguides in the literature is reformulated to adapt to the circumferential directions and used for constructing the trial wavefunction in complex field. The method requires the waveguide

In this study, element-free Galerkin method (EFGM), a meshless method, is proposed for wrinkling analysis of pre-stressed rectangular membranes. The mathematical model for studying wrinkling of pre-stressed membranes is derived by considering the bending stiffness, though it is negligible. Moving least-square approximation for deflection is constructed by considering three degrees of freedom per node

Use of artificial networks to signify the onset of dynamic catastrophes in engineering systems is a simple and efficient strategy. Here an ordinal partition network and its construction from time series are introduced. The selection of mapping parameter is discussed in detail, which may significantly enhance the performance of the proposed method. Topological properties of the resulting network can

This work presents a data-driven approach for the automated risk estimation of the voyage of a vessel or ship. While the industry is moving from a compliance-based framework with existing rules to a risk-based one, there is also a need to monitor the risk of a vessel from the perspective of the navigation. This is of even higher importance for the case of autonomous ships. Built based on the state-of-the-art

This paper outlines a new approach to identify a source term of a 2D elliptic equation for anisotropic nonhomogenous media. The proposed methodology is based on the minimization of an objective function representing differences between the measured potential and those calculated by using the discontinuous dual reciprocity boundary element method, the measurements are required to render a unique solution

The paper presents examples of approximate calculations of force values in members of selected types of trusses, which are at the same time an internal and external statically indeterminate systems. The two-stage method makes possible the approximate calculation of such trusses by help of, for example, the Cremona’s method. In each stage, a statically determinate truss is considered, pattern of which

Usually, within stochastic framework, a testing dataset is used to evaluate the approximation error between a surrogate model (e.g., a polynomial chaos expansion) and the exact model. We propose here another method to estimate the quality of an approximated solution of a stochastic process, within the context of structural dynamics. We demonstrate that the approximation error is governed by an equation

In this paper, a canonical transformation is proposed to solve the eigenvalue problem related to the dynamics of rotor-bearing systems. In this problem, all matrices are real, but they may not be symmetric, which leads to the appearance of complex eigenvalues and eigenvectors. The bi-iteration method is selected to solve the original eigenproblem whereas the QR algorithm is adopted to solve the reduced

To solve the rerouting problem resulted from uncertain adverse weather and multiple flight-confined areas, absolute robust, deviation robust, and relative robust optimization models for flight rerouting were proposed. Maximum flow method was applied for determining the value of maximum flow for the en-route network affected by adverse weather. A numerical test based on the simulated data of a civil

To improve the accuracy of the standard finite element (FE) solutions for acoustic radiation computation, this work presents the coupling of a radial point interpolation method (RPIM) with the standard FEM based on triangular (T3) mesh to give a coupled “FE-Meshfree” Trig3-RPIM element for two-dimensional acoustic radiation problems. In this coupled Trig3-RPIM element, the local approximation (LA)

In this paper, the solution domain is divided into multi-patches on which B-spline basis functions are used for approximation. The different B-spline patches are connected by a transition region which is described by several elements. The basis functions in different B-spline patches are modified in the transition region to ensure the basic polynomial reconstruction condition and the compatibility

In this paper, a new interval multi-objective optimization (MOO) method integrating with the multidimensional parallelepiped (MP) interval model has been proposed to handle the uncertain problems with dependent interval variables. The MP interval model is integrated to depict the uncertain domain of the problem, where the uncertainties are described by marginal intervals and the degree of the dependencies

Geotechnical systems often examine interactions that occur between continuum bodies and granular soils. The systems and interactions can be accurately simulated by using multiscale coupling approaches. The model for the continuum bodies is often constructed into a mesh. The meshing, however, is time consuming for a huge spatial system and if distorted is subject to adjustments. A mesh-free approach

Rackwitz–Fiessler (RF) method is well accepted as an efficient way to solve the uncorrelated non-Normal reliability problems by transforming original non-Normal variables into equivalent Normal variables based on the equivalent Normal conditions. However, this traditional RF method is often abandoned when correlated reliability problems are involved, because the point-by-point implementation property

The Chinese remainder theorem (CRT), which appeared in ancient China, is widely used in many modern computer applications. This paper presents the CRT implementation by using the interval-index characteristic and minimum redundancy residue code. The proposed algorithm does not use large modulo addition operations and provides low computational complexity compared to conventional non-redundant RNS.

Hyperelastic models are of particular interest in modeling biomaterials. In order to implement them, one must derive the stress and elasticity tensors from the given potential energy function explicitly. However, it is often cumbersome to do so because researchers in biomechanics may not be well-exposed to systematic approaches to derive the stress and elasticity tensors as it is vaguely addressed

In the robust design, correlations of uncertain parameters exist widely and have an influence on the results in most cases. It is essential to develop a robust design optimization method considering parametric correlation to future improve the analysis accuracy and engineering applicability. In this paper, a robust design optimization method based on multidimensional parallelepiped convex model is

A two-dimensional (2D) elliptic problem with nonlocal boundary conditions on both regular and irregular domains is solved numerically by Pascal polynomial basis unified with multiple-scale technique. Very accurate numerical solutions and quite reasonable condition numbers are obtained with the proposed method which is also a truly meshfree method since difficult meshing processes or numerical integrations

Smoothed particle hydrodynamics (SPH) has its unique advantages in simulating large deformation. However, in its calculation, it is easy for some regional particles to break off. This paper puts forward the concept of virtual crack boundary to solve crack propagating problems in the framework of SPH. The parameters of virtual crack boundary are determined by the projection method of descending dimension

Abrasive waterjet is widely used for mass-cutting during coal mining or other mining process. Such a cutting process involves complex fluid–solid coupling, which require an effective method capable of simulating the large deformation and spalling of materials. This paper uses method of smoothed particle hydrodynamics (SPH) to establish a model to simulate the cutting process of coal seams by abrasive

A robust discontinuous Galerkin (DG) finite element method is proposed for elasticity problems with interfaces, where the continuity across the interfaces is weakly enforced by using Nitsche’s method. We employ a weighting for the interfacial consistency terms arising in the Nitsche variational form and present a detailed finite element formulation of this DG method. The stabilization parameter is

We propose an efficient Eulerian approach to compute the Lagrangian-averaged vorticity deviation (LAVD) of given flow fields. Traditional approaches need to solve d+1 ordinary differential equations (ODEs) for a d-dimensional flow. Furthermore, if the velocity data are discrete, interpolation is required to obtain the velocity and vorticity data along the particle trace of any sampling point, which

Integration algorithm is a key to ensure the better application of the dynamic constitutive model. As for the bounding surface model based on swell–shrink rules in this paper, an explicit integration algorithm based on sub-stepping and error control scheme has be described in detail. For being adaptable to the constitutive model, several modifications have been made. The modified explicit algorithm

Enlightened by the Caputo fractional derivative, this study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of magnetic field and moving heat source in a rod in the context of dual-phase lag (DPL) theory of thermoelasticity based on Eringen’s nonlocal elasticity. Both ends of the rod are fixed and heat insulated. Employing

As is known to all, there always exists the numerical dispersive effects of the standard finite element (FE) for the wave propagation problems and the corresponding FE solutions are usually unreliable in relatively high frequency range. In this work, a coupled “FE-Meshfree” element based on triangular mesh is introduced to reduce the dispersion effects for wave propagation problems. In this coupled

An inverse analysis technique based on the conjugate gradient method (CGM) and the discrepancy principle is employed to estimate the time-wise variation of the unknown cooling heat flux in the spray cooling of a hot surface. In contrast to previous studies, the heat conduction equation of the cooled surface is formulated using a dual-phase-lag (DPL) model. In addition, no assumptions are made regarding

The main purpose of this work is to provide a numerical approach for linear second-order differential and integro-differential equations with constant delay. An algorithm based on the use of Taylor polynomials is developed to construct a collocation solution u∈Sm(1)(ΠN) for approximating the solution of second-order linear DDEs and DIDEs. It is shown that this algorithm is convergent. Some numerical

The pure boundary element method (BEM) is effective for the solution of a large class of problems. The main appeal of this BEM (reduction of the problem dimension by one) is tarnished to some extent when a fundamental solution to the governing equations does not exist as in the case of nonlinear problems. The easy to implement local point interpolation method applied to the strong form of differential

In the past, contact model in the combined finite-discrete element method (FDEM) does not include the influence of the tangential contact interaction, and the deficient model associated with the contact force can seriously degrade the computing accuracy. In order to overcome this defect, an improved FDEM is developed in this work. The potential contact mechanism is implemented to calculate the normal

Consider the class of four point nonlinear BVPs −w″(x)=f(x,w,w′),x∈I,w′(0)=0,w(1)=δ1w(η1)+δ2w(η2), where f∈(I×ℝ×ℝ,ℝ) is continuous, I=[0,1], η1,η2∈(0,1) such that η1≤η2 and δ1,δ2≥0. In this paper, we demonstrate an iterative technique. The iterative scheme is deduced by using quasilinearization. Then we consider upper-lower solutions in well ordered and reverse ordered cases and prove existence of

To investigate crack initiation and propagation of rock mass under coupled thermo-mechanical (TM) condition, a two-dimensional coupled TM model based on the numerical manifold method (NMM) is proposed, considering the effect of thermal damage on the rock physical properties and stress on the heat conductivity. Then, the NMM, using empirical strength criteria as the crack propagation critical criterion

Lightweight of wheel hubs is the linchpin for reducing the unsprung mass and improving the vehicle dynamic and braking performance of vehicles, thus, sustaining stability and comfortability. Current experience-based lightweight designs of wheel hubs have been argued to render uneven distribution of materials. This work develops a novel method to combine the reverse modeling technique with the topological

Modeling and simulation of the acoustic response in enclosed cavities of a diesel engine are of great significance for optimal design of an engine to achieve a better acoustic performance. Nevertheless, the use of the traditional finite element method (FEM) for the mid to high frequency acoustic prediction is limited by the well-known numerical dispersion errors and the tedious preprocessing of the