PCG methods in transient FE analysis. Part II: Second order problems | Zendy

Wong S. W. | Zendy; Smith I. M. | Zendy; Gladwell I. | Zendy

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PCG methods in transient FE analysis. Part II: Second order problems

Author(s) -

Wong S. W.,

Smith I. M.,

Gladwell I.

Publication year - 1989

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.1620280708

Subject(s) - conjugate gradient method , discretization , finite element method , mathematics , mass matrix , partial differential equation , matrix (chemical analysis) , transient (computer programming) , order (exchange) , mathematical analysis , mathematical optimization , computer science , physics , materials science , finance , nuclear physics , neutrino , economics , composite material , thermodynamics , operating system

In the Part I companion paper, various PCG (preconditioned conjugate gradient) strategies for solving the first order time dependent problem M u̇ + Ku = f were compared. In all cases M was assumed to be the consistent ‘mass’ matrix arising out of conventional finite element semi‐discretization of the partial differential equation, and not its lumped approximation. In the present paper, similar PCG strategies are applied to the second order time dependent problem M ü + C u̇ + Ku = f . Again consistent M and C can be retained. Various global and element level preconditioners are compared and optimized.

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