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Frontal Solver (frontal + solver)

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Engineering100%

Selected Abstracts

A frontal solver for the 21st century

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2006
Jennifer A. Scott
Abstract In recent years there have been a number of important developments in frontal algorithms for solving the large sparse linear systems of equations that arise from finite-element problems. We report on the design of a new fully portable and efficient frontal solver for large-scale real and complex unsymmetric linear systems from finite-element problems that incorporates these developments. The new package offers both a flexible reverse communication interface and a simple to use all-in-one interface, which is designed to make the package more accessible to new users. Other key features include automatic element ordering using a state-of-the-art hybrid multilevel spectral algorithm, minimal main memory requirements, the use of high-level BLAS, and facilities to allow the solver to be used as part of a parallel multiple front solver. The performance of the new solver, which is written in Fortran 95, is illustrated using a range of problems from practical applications. The solver is available as package HSL_MA42_ELEMENT within the HSL mathematical software library and, for element problems, supersedes the well-known MA42 package. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Multilevel hybrid spectral element ordering algorithms

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2005
Jennifer A. Scott
Abstract For frontal solvers to perform well on finite-element problems it is essential that the elements are ordered for a small wavefront. Multilevel element ordering algorithms have their origins in the profile reduction algorithm of Sloan but for large problems often give significantly smaller wavefronts. We examine a number of multilevel variants with the aim of finding the best methods to include within a new state-of-the-art frontal solver for finite-element applications that we are currently developing. Numerical experiments are performed using a range of problems arising from real applications and comparisons are made with existing element ordering algorithms. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Accelerating strategies to the numerical simulation of large-scale models for sequential excavation

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2007
M. Noronha
Abstract In this paper, a novel combination of well-established numerical procedures is explored in order to accelerate the simulation of sequential excavation. Usually, large-scale models are used to represent these problems. Due to the high number of equations involved, the solver algorithm represents the critical aspect which makes the simulation very time consuming. The mutable nature of the excavation models makes this problem even more pronounced. To accomplish the representation of geometrical and mechanical aspects in an efficient and simple manner, the proposed solution employs the boundary element method with a multiple-region strategy. Together with this representational system, a segmented storage scheme and a time-ordered tracking of the changes form an adequate basis for the usage of fast updating methods instead of frontal solvers. The present development employs the Sherman,Morrison,Woodbury method to speed up the calculation due to sequential changes. The efficiency of the proposed framework is illustrated through the simulation of test examples of 2D and 3D models. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Multilevel hybrid spectral element ordering algorithms

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2005
Jennifer A. Scott
Abstract For frontal solvers to perform well on finite-element problems it is essential that the elements are ordered for a small wavefront. Multilevel element ordering algorithms have their origins in the profile reduction algorithm of Sloan but for large problems often give significantly smaller wavefronts. We examine a number of multilevel variants with the aim of finding the best methods to include within a new state-of-the-art frontal solver for finite-element applications that we are currently developing. Numerical experiments are performed using a range of problems arising from real applications and comparisons are made with existing element ordering algorithms. Copyright © 2005 John Wiley & Sons, Ltd. [source]