Preconditioned time-difference methods for advection-diffusion-reaction equations

Conference · Sat Dec 31 04:00:00 EST 1994

OSTI ID:219595

Aro, C; Rodrigue, G ^[1]; Wolitzer, D ^[2]

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1. Lawrence Livermore National Lab., CA (United States)
2. California State Univ., Hayward, CA (United States)

Explicit time differencing methods for solving differential equations are advantageous in that they are easy to implement on a computer and are intrinsically very parallel. The disadvantage of explicit methods is the severe restrictions placed on stepsize due to stability. Stability bounds for explicit time differencing methods on advection-diffusion-reaction problems are generally quite severe and implicit methods are used instead. The linear systems arising from these implicit methods are large and sparse so that iterative methods must be used to solve them. In this paper the authors develop a methodology for increasing the stability bounds of standard explicit finite differencing methods by combining explicit methods, implicit methods, and iterative methods in a novel way to generate new time-difference schemes, called preconditioned time-difference methods.

• Research Organization: Front Range Scientific Computations, Inc., Boulder, CO (United States); USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 219595
• Report Number(s): CONF-9404305--Vol.2; ON: DE96005736
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ADVECTION
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
DIFFUSION
ITERATIVE METHODS
MATRICES
STABILITY