Reduced-storage techniques in the numerical method of lines
The method of lines replaces a PDE problem by an ODE initial value problem which is typically stiff and often solved by BDF methods. This normally requires the system Jacobian matrix. But Krylov subspace iteration methods solve linear systems without explicit need for the matrix. Within a BDF method and Newton (nonlinear) iteration, a Krylov method such as GMRES (Generalized Minimum Residual) can be used with the matrix involved only in operator form by way of a difference quotient. We present a scaled and preconditioned GMRES algorithm called SPIGMR. For reaction-transport PDE systems, several preconditioners arise in a natural way, using the reaction and transport operators separately, or in succession as in operator splitting. A variant of the general purpose solver LSODE, called LSODPK, contains various preconditioned Krylov methods. Tests on a reaction-diffusion system demonstrate their effectiveness.
- Research Organization:
- Lawrence Livermore National Lab., CA (USA)
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 6574159
- Report Number(s):
- UCRL-96261; CONF-870677-2; ON: DE87007093
- Resource Relation:
- Conference: 6. IMACS international symposium on computer methods for partial differential equations, Bethlehem, PA, USA, 23 Jun 1987; Other Information: Portions of this document are illegible in microfiche products
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
PARTIAL DIFFERENTIAL EQUATIONS
G CODES
NUMERICAL SOLUTION
ALGORITHMS
ITERATIVE METHODS
COMPUTER CODES
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL LOGIC
990220* - Computers
Computerized Models
& Computer Programs- (1987-1989)
990230 - Mathematics & Mathematical Models- (1987-1989)