A domain decomposition algorithm for elliptic problems in three dimensions

Technical Report · Thu Sep 01 04:00:00 EDT 1994

OSTI ID:10184113

Smith, B F

Most domain decomposition algorithms have been developed for problems in two dimensions. One reason for this is the difficulty in devising a satisfactory, easy-to-implement, robust method of providing global communication of information for problems in three dimensions. Several methods that work well in two dimensions do not perform satisfactorily in three dimensions. A new iteractive substructuring algorithm for three dimensions is proposed. It is shown that the condition number of the resulting preconditioned problem is bounded independently of the number of subdomains and that the growth is quadratic in the logarithm of the number of degrees of freedom associated with a subdomain. The condition number is also bounded independently of the jumps in the coefficients of the differential equation between subdomains. The new algorithm also has more potential parallelism than the iterative substructuring methods previously proposed for problems in three dimensions.

• Research Organization: Argonne National Lab., IL (United States)
• Sponsoring Organization: USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
• DOE Contract Number: W-31109-ENG-38
• OSTI ID: 10184113
• Report Number(s): ANL/MCS/PP--71520; ON: DE94019265
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200
ALGORITHMS
DIFFERENTIAL EQUATIONS
FINITE ELEMENT METHOD
MATHEMATICS
MATHEMATICS AND COMPUTERS
THREE-DIMENSIONAL CALCULATIONS