MIXED EXPLICIT-IMPLICIT ITERATIVE FINITE ELEMENT SCHEME FOR DIFFUSION-TYPE PROBLEMS: I. THEORY.

Shlomo P Neuman, T. N. Narasimhan, A. L. Edwards

Research output: Contribution to journalArticle

30 Citations (Scopus)

Abstract

A Galerkin finite element formulation of diffusion processes based on a diagonal capacity matrix is analysed from the standpoint of local stability and convergence. The theoretical analysis assumes that the conductance matrix is locally diagonally dominant, and it is shown that one can always construct a finite element network of linear triangles satisfying this condition. Time derivatives are replaced by finite differences, leading to a mixed explicit-implicit system of algebraic equations which can be efficiently solved by a point iterative technique. In this work the accelerated point iterative method is adopted and is shown to converge when the conductance matrix is locally diagonally dominant. Several examples are included in Part II of this paper to demonstrate the efficiency of the new approach.

Original languageEnglish (US)
Pages (from-to)309-323, 325
JournalInternational Journal for Numerical Methods in Engineering
Volume11
Issue number2
StatePublished - 1977
Externally publishedYes

Fingerprint

Finite Element
Conductance
Local Convergence
Local Stability
Stability and Convergence
Iterative methods
Algebraic Equation
Galerkin
Diffusion Process
Triangle
Theoretical Analysis
Finite Difference
Derivatives
Converge
Iteration
Derivative
Formulation
Demonstrate

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Computational Mechanics
  • Applied Mathematics

Cite this

MIXED EXPLICIT-IMPLICIT ITERATIVE FINITE ELEMENT SCHEME FOR DIFFUSION-TYPE PROBLEMS : I. THEORY. / Neuman, Shlomo P; Narasimhan, T. N.; Edwards, A. L.

In: International Journal for Numerical Methods in Engineering, Vol. 11, No. 2, 1977, p. 309-323, 325.

Research output: Contribution to journalArticle

@article{0eb87c92981143bbaf9abf47d2e314ad,
title = "MIXED EXPLICIT-IMPLICIT ITERATIVE FINITE ELEMENT SCHEME FOR DIFFUSION-TYPE PROBLEMS: I. THEORY.",
abstract = "A Galerkin finite element formulation of diffusion processes based on a diagonal capacity matrix is analysed from the standpoint of local stability and convergence. The theoretical analysis assumes that the conductance matrix is locally diagonally dominant, and it is shown that one can always construct a finite element network of linear triangles satisfying this condition. Time derivatives are replaced by finite differences, leading to a mixed explicit-implicit system of algebraic equations which can be efficiently solved by a point iterative technique. In this work the accelerated point iterative method is adopted and is shown to converge when the conductance matrix is locally diagonally dominant. Several examples are included in Part II of this paper to demonstrate the efficiency of the new approach.",
author = "Neuman, {Shlomo P} and Narasimhan, {T. N.} and Edwards, {A. L.}",
year = "1977",
language = "English (US)",
volume = "11",
pages = "309--323, 325",
journal = "International Journal for Numerical Methods in Engineering",
issn = "0029-5981",
publisher = "John Wiley and Sons Ltd",
number = "2",

}

TY - JOUR

T1 - MIXED EXPLICIT-IMPLICIT ITERATIVE FINITE ELEMENT SCHEME FOR DIFFUSION-TYPE PROBLEMS

T2 - I. THEORY.

AU - Neuman, Shlomo P

AU - Narasimhan, T. N.

AU - Edwards, A. L.

PY - 1977

Y1 - 1977

N2 - A Galerkin finite element formulation of diffusion processes based on a diagonal capacity matrix is analysed from the standpoint of local stability and convergence. The theoretical analysis assumes that the conductance matrix is locally diagonally dominant, and it is shown that one can always construct a finite element network of linear triangles satisfying this condition. Time derivatives are replaced by finite differences, leading to a mixed explicit-implicit system of algebraic equations which can be efficiently solved by a point iterative technique. In this work the accelerated point iterative method is adopted and is shown to converge when the conductance matrix is locally diagonally dominant. Several examples are included in Part II of this paper to demonstrate the efficiency of the new approach.

AB - A Galerkin finite element formulation of diffusion processes based on a diagonal capacity matrix is analysed from the standpoint of local stability and convergence. The theoretical analysis assumes that the conductance matrix is locally diagonally dominant, and it is shown that one can always construct a finite element network of linear triangles satisfying this condition. Time derivatives are replaced by finite differences, leading to a mixed explicit-implicit system of algebraic equations which can be efficiently solved by a point iterative technique. In this work the accelerated point iterative method is adopted and is shown to converge when the conductance matrix is locally diagonally dominant. Several examples are included in Part II of this paper to demonstrate the efficiency of the new approach.

UR - http://www.scopus.com/inward/record.url?scp=0017427169&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0017427169&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0017427169

VL - 11

SP - 309-323, 325

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

SN - 0029-5981

IS - 2

ER -