A space decomposition method for parabolic equations

✍ Scribed by Xue-Cheng Tai

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 296 KB
• Volume: 14
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/(sici)1098-2426(199801)14:1<27::aid-num2>3.0.co;2-n

✦ Synopsis

A convergence proof is given for an abstract parabolic equation using general space decomposition techniques. The space decomposition technique may be a domain decomposition method, a multilevel method, or a multigrid method. It is shown that if the Euler or Crank-Nicolson scheme is used for the parabolic equation, then by suitably choosing the space decomposition, only O(| log τ |) steps of iteration at each time level are needed, where τ is the time-step size. Applications to overlapping domain decomposition and to a two-level method are given for a second-order parabolic equation. The analysis shows that only a one-element overlap is needed. Discussions about iterative and noniterative methods for parabolic equations are presented. A method that combines the two approaches and utilizes some of the good properties of the two approaches is tested numerically.