The extended unsymmetric frontal solution for multiple-point constraints

Pedro Miguel De Almeida Areias, Timon Rabczuk, Joaquim Infante Barbosa

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1582-1607
Number of pages26
JournalEngineering Computations (Swansea, Wales)
Volume31
Issue number7
DOIs
Publication statusPublished - 2014 Sep 30
Externally publishedYes

Fingerprint

Newton-Raphson method
Lagrange multipliers
Software packages
Substitution reactions
Availability
Data storage equipment
Costs

Keywords

  • Frontal solution method
  • Multiple point constraints
  • OpenMP

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Software
  • Engineering(all)

Cite this

The extended unsymmetric frontal solution for multiple-point constraints. / De Almeida Areias, Pedro Miguel; Rabczuk, Timon; Barbosa, Joaquim Infante.

In: Engineering Computations (Swansea, Wales), Vol. 31, No. 7, 30.09.2014, p. 1582-1607.

Research output: Contribution to journalArticle

De Almeida Areias, Pedro Miguel ; Rabczuk, Timon ; Barbosa, Joaquim Infante. / The extended unsymmetric frontal solution for multiple-point constraints. In: Engineering Computations (Swansea, Wales). 2014 ; Vol. 31, No. 7. pp. 1582-1607.
@article{0a5694d957444748a160330fd7f7935f,
title = "The extended unsymmetric frontal solution for multiple-point constraints",
abstract = "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.",
keywords = "Frontal solution method, Multiple point constraints, OpenMP",
author = "{De Almeida Areias}, {Pedro Miguel} and Timon Rabczuk and Barbosa, {Joaquim Infante}",
year = "2014",
month = "9",
day = "30",
doi = "10.1108/EC-10-2013-0263",
language = "English",
volume = "31",
pages = "1582--1607",
journal = "Engineering Computations",
issn = "0264-4401",
publisher = "Emerald Group Publishing Ltd.",
number = "7",

}

TY - JOUR

T1 - The extended unsymmetric frontal solution for multiple-point constraints

AU - De Almeida Areias, Pedro Miguel

AU - Rabczuk, Timon

AU - Barbosa, Joaquim Infante

PY - 2014/9/30

Y1 - 2014/9/30

N2 - 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.

AB - 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.

KW - Frontal solution method

KW - Multiple point constraints

KW - OpenMP

UR - http://www.scopus.com/inward/record.url?scp=84923372525&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84923372525&partnerID=8YFLogxK

U2 - 10.1108/EC-10-2013-0263

DO - 10.1108/EC-10-2013-0263

M3 - Article

VL - 31

SP - 1582

EP - 1607

JO - Engineering Computations

JF - Engineering Computations

SN - 0264-4401

IS - 7

ER -