OpenMP based parallel normalized direct methods for sparse finite element linear systems

2008 ◽  
Vol 47 (1) ◽  
pp. 44-52 ◽  
Author(s):  
George A. Gravvanis
Keyword(s):  
Finite Element ◽  
Linear Systems ◽  
Direct Methods

scholarly journals Variational Methods for Glacier Mechanics Problems

1981 ◽  
Vol 27 (95) ◽  
pp. 19-24 ◽  
Author(s):  
Robert G. Oakberg
Keyword(s):  
Finite Element ◽  
Melting Point ◽  
Variational Principle ◽  
Finite Element Model ◽  
Related Problem ◽  
Cylindrical Channel ◽  
Direct Methods ◽  
Approximate Solutions ◽  
Element Model ◽  
Coordinate Functions

AbstractThe object of the research is to determine whether direct methods from the calculus of variations can provide convenient approximate solutions of complex problems in glacier mechanics. The Ritz technique is used to minimize an appropriate functional. Coordinate functions obtained from a finite-element model are combined with a coordinate function that is the solution of a related problem. The finite-element coordinate functions make localized adjustments to the related solution. Solutions of two sample problems are presented. An analysis of the closure of an intergranular vein in ice at the melting point is based upon a variational principle for velocities. An analysis of the flow of ice in a cylindrical channel is based upon a variational principle for stresses.

scholarly journals Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems

2012 ◽  
Vol 20 (3) ◽  
pp. 241-255 ◽  
Author(s):  
Eric Bavier ◽  
Mark Hoemmen ◽  
Sivasankaran Rajamanickam ◽  
Heidi Thornquist
Keyword(s):  
Linear Systems ◽  
Iterative Methods ◽  
Sparse Matrix ◽  
Sparse Matrices ◽  
Direct Methods ◽  
Iterative Solvers ◽  
Software Project ◽  
Sparse Linear Systems ◽  
Scalar Type ◽  
Mixed Precision

Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples the algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.

scholarly journals A Fully Implicit, Lower Bound, Multi-Axial Solution Strategy for Direct Ratchet Boundary Evaluation: Implementation and Comparison

2012 ◽  
Author(s):  
Alan Jappy ◽  
Donald Mackenzie ◽  
Haofeng Chen
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Hybrid Method ◽  
Direct Methods ◽  
Benchmark Problems ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Boundary Evaluation ◽  
Fully Implicit ◽  
Tangent Moduli

Ensuring sufficient safety against ratcheting is a fundamental requirement of pressure vessel design. However, determining the ratchet boundary using a full elastic plastic finite element analysis can be problematic and a number of direct methods have been proposed to overcome difficulties associated with ratchet boundary evaluation. This paper proposes a new approach, similar to the previously proposed Hybrid method but based on fully implicit elastic-plastic solution strategies. This method utilizes superimposed elastic stresses and modified radial return integration to converge on the residual state throughout, resulting in one Finite Element model suitable for solving the cyclic stresses (stage 1) and performing the augmented limit analysis to determine the ratchet boundary (stage 2). The modified radial return methods for both stages of the analysis are presented, with the corresponding stress update algorithm and resulting consistent tangent moduli. Comparisons with other direct methods for selected benchmark problems are presented. It is shown that the proposed method consistently evaluates a lower bound estimate of the ratchet boundary, which has not been demonstrated for the Hybrid method and is yet to be clearly shown for the UMY and LDYM methods. Limitations in the description of plastic strains and compatibility during the ratchet analysis are identified as being a cause for the differences between the proposed methods and other current upper bound methods.

scholarly journals Variational Methods for Glacier Mechanics Problems

1981 ◽  
Vol 27 (95) ◽  
pp. 19-24
Author(s):  
Robert G. Oakberg
Keyword(s):  
Finite Element ◽  
Melting Point ◽  
Variational Principle ◽  
Finite Element Model ◽  
Related Problem ◽  
Cylindrical Channel ◽  
Direct Methods ◽  
Approximate Solutions ◽  
Element Model ◽  
Coordinate Functions

AbstractThe object of the research is to determine whether direct methods from the calculus of variations can provide convenient approximate solutions of complex problems in glacier mechanics. The Ritz technique is used to minimize an appropriate functional. Coordinate functions obtained from a finite-element model are combined with a coordinate function that is the solution of a related problem. The finite-element coordinate functions make localized adjustments to the related solution. Solutions of two sample problems are presented. An analysis of the closure of an intergranular vein in ice at the melting point is based upon a variational principle for velocities. An analysis of the flow of ice in a cylindrical channel is based upon a variational principle for stresses.

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