The extended unsymmetric frontal solution for multiple-point constraints

Purpose – The purpose of this paper is to discuss the linear solution of equality constrained problems by using the Frontal solution method without explicit assembling. Design/methodology/approach – Re-written frontal solution method with a priori pivot and front sequence. OpenMP parallelization, ne...

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Bibliographic Details
Published in:Engineering computations 2014-01, Vol.31 (7), p.1582-1607
Main Authors: Miguel de Almeida Areias, Pedro, Rabczuk, Timon, Infante Barbosa, Joaquim
Format: Article
Language:English
Subjects:
Algorithms
Assembling
Boundary conditions
Computation
Decomposition
FORTRAN
Lagrange multiplier
Linear algebra
Mathematical models
Methods
Newton methods
Nonlinearity
Order disorder
Partial differential equations
Pivots
Solvers
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Summary:Purpose – The purpose of this paper is to discuss the linear solution of equality constrained problems by using the Frontal solution method without explicit assembling. Design/methodology/approach – Re-written frontal solution method with a priori pivot and front sequence. OpenMP parallelization, nearly linear (in elimination and substitution) up to 40 threads. Constraints enforced at the local assembling stage. Findings – When compared with both standard sparse solvers and classical frontal implementations, memory requirements and code size are significantly reduced. Research limitations/implications – Large, non-linear problems with constraints typically make use of the Newton method with Lagrange multipliers. In the context of the solution of problems with large number of constraints, the matrix transformation methods (MTM) are often more cost-effective. The paper presents a complete solution, with topological ordering, for this problem. Practical implications – A complete software package in Fortran 2003 is described. Examples of clique-based problems are shown with large systems solved in core. Social implications – More realistic non-linear problems can be solved with this Frontal code at the core of the Newton method. Originality/value – Use of topological ordering of constraints. A-priori pivot and front sequences. No need for symbolic assembling. Constraints treated at the core of the Frontal solver. Use of OpenMP in the main Frontal loop, now quantified. Availability of Software.
ISSN:0264-4401
1758-7077
DOI:10.1108/EC-10-2013-0263