XFEM analysis for effectively modeling the singularity of the capacitor edge

Fluorescence diffuse optical tomography is a powerful tool for the investigation of molecular events in studies for new therapeutic developments. Here, the emphasis is put on the mathematical problem of tomography, which can be formulated in terms of an estimation of physical parameters appearing as a set of Partial Differential Equations (PDEs). The standard polynomial Finite Element Method (FEM) is a method of choice to solve the diffusion equation because it has no restriction in terms of neither the geometry nor the homogeneity of the system, but it is time consuming. In order to speed up computation time, this paper proposes an alternative numerical model, describing the diffusion operator in orthonormal basis of compactly supported wavelets. The discretization of the PDEs yields to matrices which are easily computed from derivative wavelet product integrals. Due to the shape of the wavelet basis, the studied domain is included in a regular fictitious domain. A validation study and a comparison with the standard FEM are conducted on synthetic data.

Energy-preserving finite element methods for a class of nonlinear wave equations

An edge-based smoothed tetrahedron finite element method (ES-T-FEM) for thermomechanical problems

It has been well known that exact closed-form solutions are not available for non-Levy-type plates. Thus, more accurate and efficient computational methods have been required for the plates subjected to arbitrary boundary conditions. This paper presents a frequency-domain spectral element model for the rectangular finite plate element. The spectral element model is developed by using two methods in combination: (1) the boundary splitting and (2) the super spectral element method in which the Kantorovich method-based finite strip element method and the frequency-domain waveguide method are utilized. The present spectral element model has nodes on four edges of the finite plate element, but no nodes inside. This can reduce the total number of degrees of freedom a lot to improve the computational efficiency significantly, when compared with the standard finite element method (FEM). The high solution accuracy and computational efficiency of the present spectral element model are evaluated by the comparison with exact solutions and the solutions by the standard FEM.

An enriched finite element method with interpolation cover functions for acoustic analysis in high frequencies

Directional drilling technique can provide flexibility in rig location selection as well as increase drilling and production efficiencies through extended reach to isolated reservoirs. However, as well complexity increases, analyzing the mechanical performance of the associated drillstring and its components becomes more difficult. A standard Finite element method (FEM) can accurately analyze directional drilling statics and dynamics by discretizing the structure into a series of straight beam elements. However, this method has a drawback of high computational cost. To increase the computational efficiency, this paper introduces the application of curved beam FEM to model directional drillstring. The minimum curvature method is applied to obtain directional well profiles in which the adjacent survey points are connected by circular arcs. Based upon this assumption, the curved beam is used to model the curved drillstring to minimize the discretization error and to increase the computational efficiency. Static and dynamic analyses are carried out to verify the proposed method. As compared to the straight beam approximation method, fewer elements are needed to obtain a given accuracy, leading to more efficient simulations. The utility of the proposed model is also demonstrated through analyzing realistic drilling scenarios.

We propose the nonconforming Finite Element (FE) method based on Nitsche-type mortaring for efficiently solving the inhomogeneous wave equation, where due to the change of material properties the wavelength in the subdomains strongly differs. Therewith, we gain the flexibility to choose for each subdomain an optimal grid. The proposed method fulfills the physical conditions along the nonconforming interfaces, namely the continuity of the acoustic pressure and the normal component of the acoustic particle velocity. We apply the nonconforming grid method to the computation of transmission loss (TL) of an expansion chamber utilizing micro-perforated panels (MPPs), which are modeled by a homogenization approach via a complex fluid. The results clearly demonstrate the superiority of the nonconforming FE method over the standard FE method concerning pre-processing, mesh generation flexibility and computational time.

Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: convection—diffusion type

Coupling multiscale finite element method for consolidation analysis of heterogeneous saturated porous media

Weak boundary penalization for Dirichlet boundary control problems governed by elliptic equations

A topology optimization, based on a coupling method of finite element and meshless method, is proposed for continuum structure. A reasonable arrangement of the meshless domain can guarantee the accuracy of the meshless methods and meanwhile keep the computational efficiency of the finite element method. Besides, as the coupling method is adopted, the displacement boundary conditions are applied to finite elements nodes by standard finite element method. A dual-level density approximant is carried out to approximate and interpolate a unified and continuous density field. An unstable nodes phenomenon is observed in the interface domain, leading to nonconvergence of the equilibrium iterations. A smooth blending function and an energy convergence criterion are used to circumvent the convergent difficulty. Three benchmark problems of topology optimization are given to demonstrate the effectiveness of the proposed approach. Neither “islanding” phenomenon nor other common numerical instabilities of the SIMP method occur in this approach.

A weakly singular symmetric Galerkin boundary element method (SGBEM) is coupled with the standard finite element method (FEM) in order to establish an accurate and efficient numerical technique for analysis of fractures in three‐dimensional, anisotropic, linearly elastic media. In the strategy, the weakly singular SGBEM developed by Rungamornrat and Mear (textitInt. J. Solids Struct. 2008; 45:1283–1301; Comput. Methods Appl. Mech. Engrg 2008; 197:4319–4332) is utilized to model a small‐scale region containing the crack while the (possibly large and complex) compliment region is treated by the FEM. The coupled technique exploits the positive features of both methods; the SGBEM proves to be a convenient and highly accurate method for obtaining mixed‐mode stress intensity factors along the crack front, whereas the FEM is very efficient for modeling large‐scale problems in the absence of cracks. An important aspect of the formulation and implementation of the technique is that continuity of displacement and traction across the interface between the SGBEM and FEM regions is enforced in a weak sense. This allows the two regions (one modeled by the SGBEM and the other by the FEM) to be discretized independently without the need for the resulting meshes to conform on the interface separating the regions, and this flexibility in the discretization process leads to a significant reduction in the modeling effort. To demonstrate the utility and accuracy of the technique, several boundary value problems involving both embedded and surface breaking cracks are treated, and it is shown that the coupled technique yields highly accurate stress intensity factors that exhibit only a slight dependence upon mesh refinement. Copyright © 2010 John Wiley & Sons, Ltd.

Extended multiscale finite element method based on polyhedral coarse grid elements for heterogeneous materials and structures

Free and forced vibration analysis over meshes with tangled (non-convex) elements

A numerical method for analyzing eddy current magnetic field in high-speed moving conductors using local discontinuous Galerkin (LDG) method is presented. A typical numerical example is chosen to illustrate the accuracy and nonoscillatory nature of the method for a convection dominated case. The simulation results using the proposed algorithm are validated using standard finite element method (FEM). As an application of LDG method in engineering problems, the TEAM workshop problem 9 is studied and solved by the proposed method with second order rectangular discontinuous elements. Numerical results show that the method can solve eddy current problems with high speed moving conductors accurately.