Reduced-storage techniques in the numerical method of lines

Conference · Sun Feb 01 04:00:00 EST 1987

OSTI ID:6574159

Hindmarsh, A C; Brown, P N

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
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990220* -- Computers
Computerized Models
& Computer Programs-- (1987-1989)
990230 -- Mathematics & Mathematical Models-- (1987-1989)
ALGORITHMS
COMPUTER CODES
DIFFERENTIAL EQUATIONS
EQUATIONS
G CODES
ITERATIVE METHODS
MATHEMATICAL LOGIC
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS