ODE recursions and iterative solvers for linear equations

Journal Article · Mon Jan 01 04:00:00 EST 1996 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/0917006· OSTI ID:218522

Lorber, A A; Carey, G F ^[1]; Joubert, W D ^[2]

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1. Univ. of Texas, Austin, TX (United States)
2. Los Alamos National Lab., NM (United States)

Timestepping to a steady-state solution is increasingly applied in engineering and scientific applications as a means for solving equilibrium problems. In the present work the authors examine the relation between the recursion in timestepping algorithms for semidiscrete systems of ODEs and certain types of iterative methods for solving discretized systems of equilibrium PDEs. They consider, in particular, the possibility of accelerating the ODE approach using recursions that are not time accurate together with parameter selection based on the theory of iterative methods. As one example, they take the parameters arising from the Chebyshev-type iterative methods and use them in a two-stage Runge-Kutta scheme. A comparison study for a representative steady-state diffusion problem indicates a dramatic improvement in convergence and efficiency. The authors remark that this approach can be trivially incorporated into existing time-integration codes to significant advantage. This yields a hybrid adaptive approach in a single code.

• Sponsoring Organization: USDOE
• DOE Contract Number: FG03-93ER25183; W-7405-ENG-36
• OSTI ID: 218522
• Journal Information: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 1 Vol. 17; ISSN 1064-8275; ISSN SJOCE3
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
DIFFERENTIAL EQUATIONS
HYBRID SYSTEMS
ITERATIVE METHODS
PARTIAL DIFFERENTIAL EQUATIONS
RECURSION RELATIONS
RUNGE-KUTTA METHOD