3 edition of Finite elements and the method of conjugate gradients on a concurrent processor found in the catalog.
Finite elements and the method of conjugate gradients on a concurrent processor
by National Aeronautics and Space Administration, Jet Propulsion Laboratory, California Institute of Technology? in [Pasadena, Calif.?
Written in English
|Statement||Gregory A. Lyzenga, Arthur Raefsky, Bradford H. Hager.|
|Series||NASA contractor report -- NASA CR-175812.|
|Contributions||Raefsky, Arthur., Hager, Bradford H., Jet Propulsion Laboratory (U.S.)|
|The Physical Object|
Parallel finite element method using domain decomposition technique is adapted to a distributed parallel environment of workstation cluster. The algorithm is presented for parallelization of the preconditioned conjugate gradient method based on domain decomposition. Using the developed code, a dam structural analysis problem is solved on workstation cluster and results are given. The parallel. • The assumptions on which the shape functions are based require no element loading! • The choice of a cubic polynomial is related to the homogenous form of the problem EIv’’ = 0 • The exact solution therefore exists only on elements without element loads (i.e. element 2) Element 1: Element 2.
• So what is the conjugate gradient method computing? Acceleration of Conjugate Gradient • Rescaling of the problem •Consequences: •Note: finite termination in n steps. How to find a preconditioner? • Idea (from Theorem ). Compute a C such that the eigenvalues are “clustered”, then convergence is fast. For example. The method I tested are: CG = Conjugate Gradient as implemented in scipy. conjugate_gradient_damping (float) – Damping factor used in the conjugate gradient method. 1 The resulting algorithm 3. 2 Octo 1 Assignment: conjugate gradient Conjugate Gradient (CG) method is an iterative solver of linear systems.
() 6 What is the FEM? Description-FEM cuts a structure into several elements (pieces of the structure).-Then reconnects elements at “nodes” as if nodes were pins or drops of glue that hold elements together.-This process results in a set of simultaneous algebraic : Method for numerical solution of field problems. Number of degrees-of-freedom (DOF). Purchase Elliptic Problem Solvers - 1st Edition. Print Book & E-Book. ISBN ,
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The extended finite element method (XFEM) is a numerical technique based on the generalized finite element method (GFEM) and the partition of unity method (PUM).
It extends the classical finite element method by enriching the solution space for solutions. The aim of this book is to present both methods in the context of complicated problems modeled by linear and nonlinear partial differential equations, to provide an in-depth discussion on their implementation aspects.
The authors show that conjugate gradient methods and finite element methods apply to the solution of real-life problems. Get this from a library. Finite elements and the method of conjugate gradients on a concurrent processor. [Gregory A Lyzenga; Arthur Raefsky; Bradford H Hager; Jet Propulsion Laboratory (U.S.)].
An algorithm for the iterative solution of finite element problems on a concurrent processor is presented. The method of conjugate gradients is used to solve the system of.
the advantages of the iterative methods count again. The aim of the present paper is to show that the method of conjugate gradients is well suited for the solution of the sparse symmetric equations arising from the finite element method for elliptic and biharmonic problems if appropriate measures are taken.
By use of "conjugate gradients" technique, concurrent efficiency greater than 90 percent. Algorithm applies method of conjugate gradients to iterative solution of finite-element problems on concurrent processor. With algorithm, iteration rates nearly proportional to number of processors.
The second big group of linear algebra methods for solving algebraic equations is Iterative methods of algebraic equations solving such as Conjugate gradient method. Processor of AutoFEM Analysis uses both of these groups methods for solvinglinear and non-linear algebraic equations which are considered in finite element modeling.
The results shown in figure 1 give the performance of two key sections of code in the conjugate gradient solver. This is for the dot product and saxpy operation. The results are all in bit precision. The cache size of the Pentium processor is 16kB which is equivalent to elements (as indicated by the dotted line in figure 1).
Some of the. The Finite Element Method: Theory, Implementation, and Practice November 9, Springer. Preface This is a set of lecture notes on ﬁnite elements for the solution of partial differential equations. The approach taken is mathematical in nature with a strong focus on the. We investigate topology optimization based on the solid isotropic material with penalization approach on compute unified device architecture enabled graphics cards in three dimensions.
Linear elasticity is solved entirely on the GPU by a matrix-free conjugate gradient method using finite elements. Due to the unique requirements of the single instruction, multiple data stream processors.
Recent papers  and conferences  have pointed out the advantages of utilizing iterative methods in finite element systems. In particular, the conjugate gradient method [42,43], with various forms of preconditioning [44,45], has been recently proven to be very effective in the solution of linear, nonlinear and eigenvalue prob- lems [ T1 - Parallel finite element analysis using Jacobi-conditioned conjugate gradient algorithm.
AU - Khan, A. AU - Topping, B. H V. PY - /3. Y1 - /3. N2 - In this paper a modified parallel Jacobi-conditioned conjugate gradient (CG) method is proposed for solving linear elastic finite element system of equations.
Paralleled Time-Domain Finite-Element Method (TDFEM) is developed based on OpenMP for 2-D electromagnetic scattering analysis in this paper. The matrix-vector multiplication in conjugate gradient (CG) solver is parallelized with OpenMP.
As a result, the efficiency of TDFEM algorithm is accelerated dramatically with multi-processor PC. The bistatic radar cross sections (RCSs) of some typical 2.
Finite Element Analysis in Concurrent Processing: Computational Issues Article in Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and.
Home Conferences C3P Proceedings C 3 P Implementation of the conjugate gradient algorithm on a vector hypercube multiprocessor. ARTICLE. Implementation of the conjugate gradient algorithm on a vector hypercube multiprocessor.
Share on. Authors: C. Aykanat. Department of Electrical Engineering, The Ohio State University, Columbus, Ohio. The finite element method (FEM), or finite element analysis (FEA), is a computational technique used to obtain approximate solutions of boundary value problems in engineering.
Boundary value problems are also called field problems. The field is the domain of interest. () A block preconditioned conjugate gradient method for solving high-order finite element matrix equations.
Computer Physics Communications() Two-dimensional simulation of laser diodes in the steady state. It introduces PDEs and their classification, covers (briefly) finite-difference methods, and then offers a thorough treatment of finite-element methods, both conforming and nonconforming.
After discussing the conjugate gradient method and multigrid methods, Braess concludes with a chapter on finite elements in solid s: 7. MFEM is a free, lightweight, scalable C++ library for finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of discretizations, and emphasis on usability, generality, and high-performance computing efficiency.
MFEM team BSD: Free Linux, Unix, Mac OS X, Windows. Download Finite Element Method (Analysis) Books – We have compiled a list of Best & Standard Reference Books on Finite Element Method (Analysis) books are used by students of top universities, institutes and colleges.
The finite element method (FEM) is a numerical method for solving problems of engineering and mathematical physics. Keyword; Citation; DOI/ISSN; Advanced Search.In this paper, an integrated, three-dimensional, finite element package for the analysis and design of power transformers is developed, requiring no prior user experience in numerical methods and magnetic field simulation.
The package consists of an automated pre-processor, magnetostatic solver and post-processor.It allows you to easily implement your own physics modules using the provided FreeFEM language.
FreeFEM offers a large list of finite elements, like the Lagrange, Taylor-Hood, etc., usable in the continuous and discontinuous Galerkin method framework.
Pre-built physics. Incompressible Navier-Stokes (using the P1-P2 Taylor Hood element).