scholarly journals Parallel Algorithms for Forward and Back Substitution in Linear Algebraic Equations of Finite Element Method

2019 ◽  
Vol 4 (2019) ◽  
pp. 20-29
Author(s):  
Sergiy Fialko
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Parallel Algorithms ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Element Method

An Analysis of the Large Deflections of Beams using the Rayleigh-Ritz Finite Element Method

1968 ◽  
Vol 19 (4) ◽  
pp. 357-367 ◽  
Author(s):  
A. C. Walker ◽  
D. G. Hall
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Method ◽  
Large Deflection ◽  
Energy Functional ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Non Linear ◽  
Comparison Of The Results ◽  
Element Method

SummaryThe Rayleigh-Ritz finite element method is used to obtain an approximate solution of the exact non-linear energy functional describing the large deflection bending behaviour of a simply-supported inextensible uniform beam subjected to point loads. The solution of the non-linear algebraic equations resulting from the use of this method is effected, using three different techniques, and comparisons are made regarding the accuracy and computing effort involved in each. A description is given of an experimental investigation of the problem and comparison of the results with those of the numerical method, and of the available exact continuum analyses, indicates that the numerical method provides satisfactory predictions for the non-linear beam behaviour for deflections up to one quarter of the beam’s length.

Stabilized numerical method for solving the Oseen type problem with a singularity

2018 ◽  
Author(s):  
А.В. Рукавишников
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Krylov Subspace ◽  
Stokes Equations ◽  
Domain Decomposition Method ◽  
Algebraic Equations ◽  
Type Problem ◽  
Curvilinear Boundary ◽  
Linear Algebraic Equations ◽  
Element Method

На основе метода декомпозиции области построен стабилизационный неконформный метод конечных элементов для решения задачи типа Озеена. Для конвективно доминирующих течений с разрывным коэффициентом вязкости определена шкала оптимального выбора стабилизирующего параметра. Результаты численных экспериментов согласуются с теоретической оценкой сходимости. Purpose. To construct modified approximation approach using the finite element method and to perform numerical analysis for a two dimensional problem on the flow of a viscous inhomogeneous fluids — the Oseen type problem, that is obtained by sampling in time and linearizing the incompressible Navier—Stokes equations. To consider the convection dominated flow case. Methodology. Based on the domain decomposition method with a smooth curvilinear boundary between subdomains, a stabilization nonconformal finite element method is constructed that satisfies the inf-sup-stability condition. To solve the resulting system of linear algebraic equations, an iterative process is considered that uses the decomposition of the vector in the Krylov subspace with minimal inviscidity, with a block preconditioning of the matrix. Findings. The results of the numerical experiments demonstrate the robustness of the considered method for different (even small) discontinuous values of viscosity. The differences between finite element and exact solutions for the velocity field and pressure in the norms of the grid spaces decrease as

The Combination of Multi-Step Differential Transformation Method and Finite Element Method in Vibration Analysis of Non-Prismatic Beam

2017 ◽  
Vol 09 (01) ◽  
pp. 1750010 ◽  
Author(s):  
Ryszard Hołubowski ◽  
Kamila Jarczewska
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Algebraic Equations ◽  
Differential Transformation ◽  
Prismatic Beam ◽  
Time Histories ◽  
Euler Bernoulli Beam ◽  
Element Method

The paper presents a new algorithm being the combination of multi-step differential transformation method (MsDTM) and finite element method (FEM) as a powerful tool for solving variety dynamic problems. The proposed algorithm, named as differential transformation finite element method (DTFEM), transforms partial differential equation into a set of recursive algebraic equations. The final form of a solution is a piecewise function which in general case may be a symbolic function. High effectiveness and accuracy of DTFEM is demonstrated on the example of forced vibrations of non-prismatic Euler–Bernoulli beam. Computed time histories of displacements, velocities and accelerations are highly consistent with results obtained by Newmark method.

scholarly journals Application of the finite element method to solving the duffing equation of ground motion

2020 ◽  
Vol 26 (1) ◽  
pp. 65-71
Author(s):  
Godwin C.E. Mbah ◽  
Kingsley Kelechi Ibeh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Duffing Equation ◽  
Weight Functions ◽  
Algebraic Equations ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Minimization Technique ◽  
The Galerkin Method ◽  
Element Method

In this paper, we applied the Galerkin Finite Element Method to solve a damped, externally forced, second order ordinary differential equation with cubic nonlinearity known as the Duffing Equation. The Galerkin method uses the functional minimization technique which sets the equation in systems of algebraic equations to be solved. Various simulation on the effect of change on some parametric values of the Duffing equation are shown. Keywords: Galerkin Finite Element Method, stiffness matrix, Duffing Equation, shape functions, basis functions, weight functions.

Calculation of the Blade-to-Blade Compressible Flow Field in Turbo Impellers Using the Finite-Element Method

1977 ◽  
Vol 19 (3) ◽  
pp. 108-112 ◽  
Author(s):  
D. Adler ◽  
Y. Krimerman
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Variational Approach ◽  
Iterative Procedure ◽  
Coefficient Matrix ◽  
Algebraic Equations ◽  
The Finite Element Method ◽  
Variational Functional ◽  
Linear Algebraic Equations ◽  
Computer Storage

No variational principle can be found for Wu's blade-to-blade equation and therefore no appropriate variational functional associated with the problem can be derived. This difficulty is overcome by using a Poisson equation as the basis for an iterative procedure. Thus the method retains the advantage of the variational approach in which the coefficient matrix of the linear algebraic equations is always symmetric. The symmetry of the coefficient matrix allows reduction of computer storage.

scholarly journals Application Of The Interlaced Sweep Method For The Solution Of Problems In Field Theory

2015 ◽  
Vol 3 ◽  
pp. 170
Author(s):  
Aloizs Ratnieks ◽  
Marina Uhanova
Keyword(s):  
Field Theory ◽  
Finite Element Method ◽  
Finite Element ◽  
Direct Methods ◽  
System Of Equations ◽  
Algebraic Equations ◽  
The Finite Element Method ◽  
Sweep Method ◽  
Linear Algebraic Equations ◽  
Separate Block

<p class="R-AbstractKeywords"><span lang="EN-US">For solution of problems in field theory the method of sweep is very popular. The authors suggest a very effective method of interlaced sweep. The essence of the interlaced sweep method lies in the fact that matrix of the linear algebraic equations system is broken into parts and the solution of separate blocks is sought by direct methods. Usually for each line of the grid a separate block is created. The system of block equations has a tridiagonal matrix where only elements of the main diagonal and two neighboring diagonals are different from zero. The system of equations with such a matrix is easily solved by the method of elimination of unknowns.</span></p><p class="R-AbstractKeywords"><span lang="EN-US">By solving the problems by the finite element method, the nodes of touching of neighboring elements can be placed on curved lines, and the sweep on these lines can be performed observing the principle of interlaced sweep. By following this method, the neighboring lines should not belong to the same half-step.</span></p>

scholarly journals Solution of Nonlinear Coupled Heat and Moisture Transport Using Finite Element Method

10.14311/622 ◽  
2004 ◽  
Vol 44 (5-6) ◽  
Author(s):  
T. Krejčí
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Moisture Transfer ◽  
Coupled Problems ◽  
Algebraic Equations ◽  
Capillary Pressures ◽  
Coupled Heat And Moisture ◽  
Attention Systems ◽  
Heat And Moisture ◽  
Element Method

This paper deals with a numerical solution of coupled of heat and moisture transfer using the finite element method. The mathematical model consists of balance equations of mass, energy and linear momentum and of the appropriate constitutive equations. The chosen macroscopic field variables are temperature, capillary pressures, gas pressure and displacement. In contrast with pure mechanical problems, there are several difficulties which require special attention. Systems of algebraic equations arising from coupled problems are generally nonlinear, and the matrices of such systems are nonsymmetric and indefinite. The first experiences of solving complicated coupled problems are mentioned in this paper. 

Sign in / Sign up

Export Citation Format

Share Document