A comparison of conjugate gradient, SIP, and other iterative methods for the solution of Poisson's equation with irregular boundary conditions

Technical Report · Fri Jun 01 00:00:00 EDT 1990

DOI:https://doi.org/10.2172/6686014· OSTI ID:6686014

Bergmann, D J

Several well known iterative methods for solving Poisson's equation, including Strongly Implicit Procedure and several preconditioned conjugate gradient methods are first applied to a problem with simple boundary conditions and a known solution. Then a problem with more complicated boundary conditions, similar to those encountered when modeling AVLIS plasmas, is solved. Differences in the solutions of the various methods are examined through the use of Fourier analysis. It was found that combinations of different iterative schemes will in some cases be the most efficient method of solution. 22 refs., 29 figs.

• Research Organization: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
• Sponsoring Organization: DOE/DP
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 6686014
• Report Number(s): UCRL-LR-103745; ON: DE90015603
• Resource Relation: Other Information: Thesis (M.S.)
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
POISSON EQUATION
NUMERICAL SOLUTION
ALGORITHMS
BOUNDARY CONDITIONS
COMPARATIVE EVALUATIONS
FOURIER ANALYSIS
ITERATIVE METHODS
MATRICES
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL LOGIC
PARTIAL DIFFERENTIAL EQUATIONS
990200* - Mathematics & Computers