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1
Content available remote

Arbitrary high-order finite element schemes and high-order mass lumping

100%
Jund S., Salmon S.
International Journal of Applied Mathematics and Computer Science
|
2007
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tom 17
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nr 3
375-393
EN
Computers are becoming sufficiently powerful to permit to numerically solve problems such as the wave equation with high-order methods. In this article we will consider Lagrange finite elementsof order k and show how it is possible to automatically generate the mass and stiffness matrices of any order with the help of symbolic computation software. We compare two high-order time discretizations: an explicit one using a Taylor expansion in time (a Cauchy-Kowalewski procedure) and an implicit Runge-Kutta scheme. We also construct in a systematic way a high-order quadrature which is optimal in terms of the number of points, which enables the use of mass lumping, up to P5 elements. We compare computational time and effort for several codes which are of high order in time and space and study their respective properties.
2
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FEMLab software applied to Active Magnetic Bearing analysis

100%
Piłat A.
International Journal of Applied Mathematics and Computer Science
|
2004
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tom 14
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nr 4
497-501
EN
This paper presents how the FEMLab package can be used to perform the magnetic field analysis in the Active Magnetic Bearing (AMB). The AMB is an integral part of the industrial rotational machine laboratory model. The electromagnetic field distribution and density analysis allow verifying the designed AMB and the influence of the shaft and coil current changes on the bearing parameters.
3
Content available remote

Relative performance of antisymmetric angle-ply laminated stiffened hypar shell roofs with cutout in terms of static behavior

100%
Chowdhury P. B., Mitra A., Sahoo S.
Curved and Layered Structures
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2016
|
tom 3
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nr 1
EN
A review of literature reveals that bending analysis of laminated composite stiffened hypar shells with cutout have not received due attention. Being a doubly ruled surface, a skewed hypar shell fulfils aesthetic as well as ease of casting requirements. Further, this shell allows entry of north light making it suitable as civil engineering roofing units. Hypar shell with cutout subjected to uniformly distributed load exhibits improved performances with stiffeners. Hence relative performances of antisymmetric angle-ply laminated composite stiffened hypar shells in terms of displacements and stress resultants are studied in this paper under static loading. A curved quadratic isoparametric eight noded element and three noded beam elements are used to model the shell surface and the stiffeners respectively. Results obtained from the present study are compared with established ones to check the correctness of the present approach. A number of additional problems of antisymmetric angle-ply laminated composite stiffened hypar shells are solved for various fibre orientations, number of layers and boundary conditions. Results are interpreted from practical application standpoints and findings important for a designer to decide on the shell combination among a number of possible options are highlighted.
4
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Using a graph grammar system in the finite element method

100%
Strug B., Paszyńska A., Paszyński M., Grabska E.
International Journal of Applied Mathematics and Computer Science
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2013
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tom 23
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nr 4
839-853
EN
The paper presents a system of Composite Graph Grammars (CGGs) modelling adaptive two dimensional hp Finite Element Method (hp-FEM) algorithms with rectangular finite elements. A computational mesh is represented by a composite graph. The operations performed over the mesh are defined by the graph grammar rules. The CGG system contains different graph grammars defining different kinds of rules of mesh transformations. These grammars allow one to generate the initial mesh, assign values to element nodes and perform h- and p-adaptations. The CGG system is illustrated with an example from the domain of geophysics.
5
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BEM and FEM results of displacements in a poroelastic column

100%
Albers B., Savidis S., Taşan H., von Estorff O., Gehlken M.
International Journal of Applied Mathematics and Computer Science
|
2012
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tom 22
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nr 4
883-896
EN
The dynamical investigation of two-component poroelastic media is important for practical applications. Analytic solution methods are often not available since they are too complicated for the complex governing sets of equations. For this reason, often some existing numerical methods are used. In this work results obtained with the finite element method are opposed to those obtained by Schanz using the boundary element method. Not only the influence of the number of elements and time steps on the simple example of a poroelastic column but also the impact of different values of the permeability coefficient is investigated.
6
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Numerical Solution of Time Fractional Schrödinger Equation by Using Quadratic B-Spline Finite Elements

100%
Esen A., Tasbozan O.
Annales Mathematicae Silesianae
|
2017
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tom 31
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nr 1
83-98
EN
In this article, quadratic B-spline Galerkin method has been employed to solve the time fractional order Schrödinger equation. Numerical solutions and error norms L2 and L∞ are presented in tables.
7
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A finite element method for extended KdV equations

88%
Karczewska A., Rozmej P., Szczeciński M., Boguniewicz B.
International Journal of Applied Mathematics and Computer Science
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2016
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tom 26
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nr 3
555-567
EN
The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov-Galerkin method are used. It is shown that the FEM gives a reasonable description of the wave dynamics of soliton waves governed by extended KdV equations. Some new results for several cases of bottom shapes are presented. The numerical scheme presented here is suitable for taking into account stochastic effects, which will be discussed in a subsequent paper.
8
Content available remote

SDPBS Web Server for Calculation of Electrostatics of Ionic Solvated Biomolecules

88%
Jiang Y., Xie Y., Ying J., Xie D., Yu Z.
Molecular Based Mathematical Biology
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2015
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tom 3
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nr 1
EN
The Poisson-Boltzmann equation (PBE) is one important implicit solvent continuum model for calculating electrostatics of protein in ionic solvent. We recently developed a PBE solver library, called SDPBS, that incorporates the finite element, finite difference, solution decomposition, domain decomposition, and multigrid methods. To make SDPBS more accessible to the scientific community, we present an SDPBS web server in this paper that allows clients to visualize and manipulate the molecular structure of a biomolecule, and to calculate PBE solutions in a remote and user friendly fashion. The web server is available on the website https://lsextrnprod.uwm.edu/electrostatics/.
9
Content available remote

A Poisson-Boltzmann Equation Test Model for Protein in Spherical Solute Region and its Applications

88%
Jiang Y., Ying J., Xie D.
Molecular Based Mathematical Biology
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2014
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tom 2
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nr 1
EN
The Poisson-Boltzmann equation (PBE) is one important implicit solvent continuum model for calculating electrostatics of protein in ionic solvent. Several numerical algorithms and program packages have been developed but verification and comparison between them remains an interesting topic. In this paper, a PBE test model is presented for a protein in a spherical solute region, along with its analytical solution. It is then used to verify a PBE finite element solver and applied to a numerical comparison study between a finite element solver and a finite difference solver. Such a study demonstrates the importance of retaining the interface conditions in the development of PBE solvers.
10
Content available remote

Modeling and Simulating Asymmetrical Conductance Changes in Gramicidin Pores

88%
Xu S., Chen M., Majd S., Yue X., Liu C.
Molecular Based Mathematical Biology
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2014
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tom 2
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nr 1
EN
Gramicidin A is a small and well characterized peptide that forms an ion channel in lipid membranes. An important feature of gramicidin A (gA) pore is that its conductance is affected by the electric charges near the its entrance. This property has led to the application of gramicidin A as a biochemical sensor for monitoring and quantifying a number of chemical and enzymatic reactions. Here, a mathematical model of conductance changes of gramicidin A pores in response to the presence of electrical charges near its entrance, either on membrane surface or attached to gramicidin A itself, is presented. In this numerical simulation, a two dimensional computational domain is set to mimic the structure of a gramicidin A channel in the bilayer surrounded by electrolyte. The transport of ions through the channel is modeled by the Poisson-Nernst-Planck (PNP) equations that are solved by Finite Element Method (FEM). Preliminary numerical simulations of this mathematical model are in qualitative agreement with the experimental results in the literature. In addition to the model and simulations, we also present the analysis of the stability of the solution to the boundary conditions and the convergence of FEM method for the two dimensional PNP equations in our model.
11
Content available remote

Probabilistic fracture investigation of symmetric angle ply laminated composite plates using displacement correlation method

75%
Lal A., Palekar Shailesh P.
Curved and Layered Structures
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2016
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tom 3
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nr 1
EN
The second order statistics of mixed mode stress intensity factors (MSIF) of single edge V-notched angle ply laminated composite plate subjected to uniaxial tensile load with uncertinity in the system properties using displacement correlation method (DCM) is evaluated. The random system properties such as material properties, crack opening and crack length are modelled as combined uncorrelated and correlated random system variables. A C0 finite element method (FEM) based on higher order shear deformation plate theory (HSDT) is used for basic formulation. The Taylor series based first order perturbation technique (FOPT), second order perturbation technique (SOPT) are used and direct Monte Carlo simulation (MCS) is performed to evaluate the statistics (mean and coefficient of variance) of the mixed mode SIFs. The present work signifies the accurate analysis of frature behaviour by influence of different random variables and fibre orientations on the fracture behaviour in angle ply laminates.
12
Content available remote

Exact 3D solutions and finite element 2D models for free vibration analysis of plates and cylinders

75%
Brischetto S., Torre R.
Curved and Layered Structures
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2014
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tom 1
|
nr 1
EN
The paper proposes a comparison between classical two-dimensional (2D) finite elements (FEs) and an exact three-dimensional (3D) solution for the free vibration analysis of one-layered and multilayered isotropic, composite and sandwich plates and cylinders. Low and high order frequencies are analyzed for thick and thin simply supported structures. Vibration modes are investigated to make a comparison between results obtained via the finite element method and those obtained by means of the exact three-dimensional solution. The 3D exact solution is based on the differential equations of equilibrium written in general orthogonal curvilinear coordinates. This exact method is based on a layer-wise approach, the continuity of displacements and transverse shear/normal stresses is imposed at the interfaces between the layers of the structure. The geometry for shells is considered without any simplifications. The 2D finite element results are obtained by means of a well-known commercial FE code. The differences between 2D FE solutions and 3D exact solutions depend on the considered mode, the order of frequency, the thickness ratio of the structure, the geometry, the embedded material and the lamination sequence.
13
Content available remote

An analytical and numerical approach to a bilateral contact problem with nonmonotone friction

63%
Barboteu M., Bartosz K., Kalita P.
International Journal of Applied Mathematics and Computer Science
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2013
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tom 23
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nr 2
263-276
EN
We consider a mathematical model which describes the contact between a linearly elastic body and an obstacle, the so-called foundation. The process is static and the contact is bilateral, i.e., there is no loss of contact. The friction is modeled with a nonmotonone law. The purpose of this work is to provide an error estimate for the Galerkin method as well as to present and compare two numerical methods for solving the resulting nonsmooth and nonconvex frictional contact problem. The first approach is based on the nonconvex proximal bundle method, whereas the second one deals with the approximation of a nonconvex problem by a sequence of nonsmooth convex programming problems. Some numerical experiments are realized to compare the two numerical approaches.
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