Premium
Error analysis of penalty function techniques for constraint definition in linear algebraic systems
Author(s) -
Felippa Carlos A.
Publication year - 1977
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620110408
Subject(s) - penalty method , mathematics , discretization , constraint (computer aided design) , finite element method , algebraic equation , function (biology) , boundary value problem , algebraic number , linear system , solver , system of linear equations , representation (politics) , boundary (topology) , mathematical optimization , mathematical analysis , nonlinear system , geometry , law , physics , quantum mechanics , evolutionary biology , biology , thermodynamics , politics , political science
The penalty function approach has been recently formalized as a general technique for adjoining constraint conditions to algebraic equation systems resulting from variational discretization of boundary value problems by finite difference or finite element techniques. This paper studies the numerical behaviour of the penalty function method for the special case of individual equation constraints imposed on a symmetric system of linear algebraic equations. Constraint representation and computational roundoff error components are distinguished and asymptotically characterized in terms of the penalty function weight coefficients. On the basis of this study, practical rules for the automatic assignment of values to those coefficients within the linear equation solver are proposed. Numerical problems encountered in the case of more general constraints are briefly discussed, and procedures for circumventing such difficulties are suggested.