OpenMp solvers for parallel finite element and meshless analyses

2014 ◽  
Vol 31 (1) ◽  
pp. 2-17 ◽  
Author(s):  
S.H. Ju
Keyword(s):  
Finite Element ◽  
Stiffness Matrix ◽  
Preconditioned Conjugate Gradient ◽  
Content Type ◽  
Minimum Requirement ◽  
Source Codes ◽  
Parallel Solution ◽  
Parallel Finite Element ◽  
Fortran 90 ◽  
Global Stiffness Matrix

Purpose – This paper develops C++ and Fortran-90 solvers to establish parallel solution procedures in a finite element or meshless analysis program using shared memory computers. The paper aims to discuss these issues. Design/methodology/approach – The stiffness matrix can be symmetrical or unsymmetrical, and the solution schemes include sky-line Cholesky and parallel preconditioned conjugate gradient-like methods. Findings – By using the features of C++ or Fortran-90, the stiffness matrix and its auxiliary arrays can be encapsulated into a class or module as private arrays. This class or module will handle how to allocate, renumber, assemble, parallelize and solve these complicated arrays automatically. Practical implications – The source codes can be obtained online at http//myweb.ncku.edu.tw/∼juju. The major advantage of the scheme is that it is simple and systematic, so an efficient parallel finite element or meshless program can be established easily. Originality/value – With the minimum requirement of computer memory, an object-oriented C++ class and a Fortran-90 module were established to allocate, renumber, assemble, parallel, and solve the global stiffness matrix, so that the programmer does not need to handle them directly.

Large-Scale Parallel Finite Element Analysis of the Stress Singular Problems

2002 ◽  
Author(s):  
Noriyuki Kushida ◽  
Hiroshi Okuda ◽  
Genki Yagawa
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Preconditioned Conjugate Gradient Method ◽  
Preconditioned Conjugate Gradient ◽  
Singular Problems ◽  
Parallel Finite Element

In this paper, the convergence behavior of large-scale parallel finite element method for the stress singular problems was investigated. The convergence behavior of iterative solvers depends on the efficiency of the preconditioners. However, efficiency of preconditioners may be influenced by the domain decomposition that is necessary for parallel FEM. In this study the following results were obtained: Conjugate gradient method without preconditioning and the diagonal scaling preconditioned conjugate gradient method were not influenced by the domain decomposition as expected. symmetric successive over relaxation method preconditioned conjugate gradient method converged 6% faster as maximum if the stress singular area was contained in one sub-domain.

Scalability Study on Large-Scale Parallel Finite Element Computing in PANDA Frame

2011 ◽  
Vol 117-119 ◽  
pp. 489-492
Author(s):  
Xuan Hua Fan ◽  
Rui An Wu ◽  
Pu Chen
Keyword(s):  
Finite Element ◽  
Parallel Computing ◽  
Large Scale ◽  
Gradient Methods ◽  
Preconditioned Conjugate Gradient ◽  
Implementation Processes ◽  
Parallel Performance ◽  
Linear Speedup ◽  
Parallel Finite Element ◽  
Preconditioned Conjugate Gradient Methods

A Finite-element parallel computing frame—PANDA and its implementation processes are introduced. To validate the parallel performance of the PANDA frame, a series of tests were carried out to obtain the computing scale and the speedup ratios. First, three different large-scale freedom degree models (i.e. 1.83 million, 7 million and 10 million) of a typical engineering clamp were created in MSC.Patran and were translated into geometric-grid files that can be identified in PANDA frame. Second, Linear static parallel computations of the three cases were successfully carried out on large parallel computers with preconditioned conjugate gradient methods in PANDA frame. The speedup ratios of the three cases were obtained with a maximum process number of 64. The results show that the PANDA frame is competent for carrying out large-scale parallel computing of 10 million freedom degrees. In each scale，the parallel computing is nearly linearly accelerated along with the increase of process numbers, moreover, a super-linear speedup appears in some cases. The speedup curves show that the linear degree increases when the computing scale enlarges. The influence of different communication bandwidths on computing efficiency was also discussed. All the testing results indicate that the PANDA frame has excellent parallel performance and favorable computing scalability.

Finite Element Method for Solving Bucking Load of Semi-Rigid Steel Frame

2013 ◽  
Vol 834-836 ◽  
pp. 1337-1342
Author(s):  
Hua Hu Cheng ◽  
Ai Min Li ◽  
Ming Wen Guan ◽  
Xian Wei Yang ◽  
Jing Luo
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Internal Force ◽  
Steel Frame ◽  
Buckling Load ◽  
Stability Characteristic ◽  
The Stability ◽  
Global Stiffness Matrix ◽  
Element Method

Took two layers of single span lateral sway semi-rigid connecting steel frame to bear vertical load function as the research object, adopting finite element method for solving the bucking load of the whole losing the stability of the semi-rigid connecting steel frame. Using based on the energy method and the three parabolic interpolation deflection curve function to obtain the relationship between the both element ends of internal force and displacement and introducing semi-rigid beam element stiffness matrix and geometric stiffness matrix of element integrate the global stiffness matrix which contains the flexibility of the connections and the component geometry nonlinear, thus deducing the stability characteristic equation of semi-rigid steel frame. And the MATLAB language composition program is applied to calculate the buckling load of overall losing stability of the semi-rigid steel frame, thus obtaining the buckling load of semi-rigid steel frame. The method is a very effective numerical calculating method which can solve the stability problems of relatively complicated stress conditions or relatively complicated structure composition conditions and it can also satisfy the requirement of higher calculation accuracy, easy for programming and calculation and of great practicability.

A parallel finite element algorithm for nonstationary incompressible magnetohydrodynamics equations

2018 ◽  
Vol 28 (7) ◽  
pp. 1579-1595
Author(s):  
Qili Tang
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Unconditional Convergence ◽  
Content Type ◽  
Fully Discrete ◽  
Parallel Finite Element ◽  
Overlapping Domain Decomposition ◽  
Mhd System ◽  
Element Algorithm ◽  
Incompressible Magnetohydrodynamics

Purpose The purpose of this paper is to design a parallel finite element (FE) algorithm based on fully overlapping domain decomposition for solving the nonstationary incompressible magnetohydrodynamics (MHD). Design/methodology/approach The fully discrete Euler implicit/explicit FE subproblems, which are defined in the whole domain with vast majority of the degrees of freedom associated with the particular subdomain, are solved in parallel. In each subproblem, the linear term is treated by implicit scheme and the nonlinear term is solved by explicit one. Findings For the algorithm, the almost unconditional convergence with optimal orders is validated by numerical tests. Some interesting phenomena are presented. Originality/value The proposed algorithm is effective, easy to realize with low communication costs and preferred for solving the strong nonlinear MHD system.

An analogy between analytical, approximate and numerical methods in nonlinear buckling of functionally graded columns

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Kaveh Salmalian ◽  
Ali Alijani ◽  
Habib Ramezannejad Azarboni
Keyword(s):  
Differential Equation ◽  
Finite Element ◽  
Finite Difference ◽  
Stiffness Matrix ◽  
Functionally Graded ◽  
The Finite Element Method ◽  
Content Type ◽  
Tangent Stiffness Matrix ◽  
Initial Assumption ◽  
Post Buckling

Purpose The purpose of this study is to investigate the post-buckling analysis of functionally graded columns by using three analytical, approximate and numerical methods. A pre-defined function as an initial assumption for the post-buckling path is introduced to solve the differential equation. The finite difference method is used to approximate the lateral deflection of the column based on the differential equation. Moreover, the finite element method is used to derive the tangent stiffness matrix of the column. Design/methodology/approach The non-linear buckling analysis of functionally graded materials is carried out by using three analytical, finite difference and finite element methods. The elastic deformation and Euler-Bernoulli beam theory are considered to establish the constitutive and kinematics relations, respectively. The governing differential equation of the post-buckling problem is derived through the energy method and the calculus variation. Findings An incremental iterative solution and the perturbation of the displacement vector at the critical buckling point are performed to determine the post-buckling path. The convergence of the finite element results and the effects of geometric and material characteristics on the post-buckling path are investigated. Originality/value The key point of the research is to compare three methods and to detect error sources by considering the derivation process of relations. This comparison shows that a non-incremental solution in the analytical and finite difference methods and an initial assumption in the analytical method lead to an error in results. However, the post-buckling path in the finite element method is traced by the updated tangent stiffness matrix in each load step without any initial limitation.

Some modifications for ES-FEM and its application for vehicle design

2015 ◽  
Vol 32 (5) ◽  
pp. 1432-1459 ◽  
Author(s):  
Guanxin Huang ◽  
Hu Wang ◽  
Guangyao Li
Keyword(s):  
Coordinate System ◽  
Stiffness Matrix ◽  
Large Scale ◽  
Local Coordinate System ◽  
Global Coordinate System ◽  
Content Type ◽  
Large Scale Problems ◽  
Edge Based ◽  
Global Stiffness Matrix ◽  
Made In

Purpose – The purpose of this paper is to enhance the feasibility of the edge-based smoothed triangular (EST) element, some modifications are made in this study. Design/methodology/approach – First, an efficient strategy based on graph theory is proposed to construct the edge system. Second, the stress is smoothed in global coordinate system based on edge instead of strain, which makes the theory of EST more rigorous and can be easily extended to the situation of multi elements sharing the same edge. Third, the singular degree of freedoms (DOFs) of the nodes linked by edges are restrained in edge local coordinate system, which makes the global stiffness matrix non-singular and can be decomposed successfully. Findings – First, an efficient edge constructing strategy can make EST element more standout. Second, some modifications should be made to EST element to extend it to the situation with multi elements sharing the same edge, so that EST element can deal with the geometrical models with this kind of features. Third, the way to restrain the singular DOFs of EST element must be different from normal isoparametric triangle element, because the stiffness matrix of the smoothing domain is not computed in local coordinate system. Originality/value – The modified EST element performs stably in engineering analysis including large scale problems and the situation with multi elements sharing the same edge, and the efficiency of edge system constructing is no longer the bottleneck.

Parallel two-step finite element algorithm for the stationary incompressible magnetohydrodynamic equations

2019 ◽  
Vol 29 (8) ◽  
pp. 2709-2727 ◽  
Author(s):  
Yuan Ping ◽  
Haiyan Su ◽  
Xinlong Feng
Keyword(s):  
Finite Element ◽  
Initial Approximation ◽  
Computational Time ◽  
Magnetohydrodynamic Equations ◽  
Content Type ◽  
Parallel Finite Element ◽  
Incompressible Magnetohydrodynamic Equations ◽  
Element Algorithm ◽  
Element Pair ◽  
Order Element

Purpose The purpose of this paper is to propose a local parallel finite element algorithm based on fully overlapping domain decomposition technique to solve the incompressible magnetohydrodynamic equations. Design/methodology/approach The algorithm uses a lower-order element pair to compute an initial approximation by the Oseen-type iteration and uses a higher-order element pair to solve a linear system in each processor. Findings Besides, the convergence analysis of local parallel finite element algorithm is given. Finally, numerical experiments are presented to verify the efficiency of the proposed algorithm. Originality/value Compared with the numerical solution of the common two-step method, this method is easy to realize and can produce a more accurate solution. And, this approach is executed in parallel, so it saves a lot of computational time.

Sign in / Sign up

Export Citation Format

Share Document