KRYSI, an ODE solver combining a semi-implicit Runge-Kutta method and a preconditioned Krylov method

Technical Report · Sun May 01 04:00:00 EDT 1988

OSTI ID:6963749

Hindmarsh, A C; Noersett, S P

This report describes KRYSI, a solve for ODE initial value problems that uses a combination of two powerful techniques in the case of stiff systems. KRYSI is based on the SIMPLE solver, and (like SIMPLE) uses a 3-stage 3rd order SDIRK method. When solving the implicit stage equations in the stiff case, both use some form of Newton iteration. But there, KRYSI (unlike SIMPLE) uses a Krylov subspace iteration method, called SPIGMR : scaled Preconditioned Incomplete Generalized Minimum Residual method. The SPIGMR algorithm is outlined in the SDIRK context. No explicit Jacobian storage is required, except where used in preconditioning. The KRYSI package and its usage are described briefly. One test (demonstration) problem is given, along with a description of two preconditioners that are natural for its solution by KRYSI. The KRYSI solution results are given, and compared with those of LSODPK, a solver that combines a BDF method with the same SPIGMR algorithm. 11 refs., 1 fig.

• Research Organization: Lawrence Livermore National Lab., CA (USA); Trondheim Univ. (Norway). Div. of Mathematical Sciences
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 6963749
• Report Number(s): UCID-21422; ON: DE88012245
• 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)
COMPUTER CODES
DIFFERENTIAL EQUATIONS
EQUATIONS
FORTRAN
ITERATIVE METHODS
K CODES
NUMERICAL SOLUTION
PROGRAMMING LANGUAGES
RUNGE-KUTTA METHOD