Capacitance matrix methods for the Helmholtz equation on general three-dimensional regions. [DPOLE, driver program for HELM3D, which solves Dirichlet problem of bounded 3D region imbedded in unit cube, in CDC ANSI FORTRAN for CDC 6600, CDC 7600, Amdahl 470V/6]

Technical Report · Sun Oct 01 04:00:00 EDT 1978

DOI:https://doi.org/10.2172/6424896· OSTI ID:6424896

O'Leary, D. P.; Widlund, O.

The highly structured systems of linear algebraic equations that arise when Helmholtz's equation, -..delta..u + cu = f, is discretized by finite difference or finite element methods can be solved by capacitance matrix, or imbedding, methods. This paper extends the method to three-dimensional problems. After a review of classical potential theory, the capacitance matrix methods are derived. Then the algorithmic aspects of importance for developing fast, reliable computer codes are examined; conjugate gradient methods and the use of spectral information and approximate inverses of the capacitance matrices are considered. Next, the fast Poisson solver used is described. Finally, the computer code developed is discussed and a listing is given. 3 tables. (RWR)

• Research Organization: Michigan Univ., Ann Arbor (USA). Dept. of Mathematics; New York Univ., NY (USA). Courant Inst. of Mathematical Sciences
• DOE Contract Number: EY-76-C-02-3077
• OSTI ID: 6424896
• Report Number(s): COO-3077-155
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
AMDAHL COMPUTERS
CDC COMPUTERS
COMPUTER CALCULATIONS
COMPUTER CODES
COMPUTERS
D CODES
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE DIFFERENCE METHOD
FINITE ELEMENT METHOD
FORTRAN
H CODES
ITERATIVE METHODS
NUMERICAL SOLUTION
PROGRAMMING LANGUAGES
THREE-DIMENSIONAL CALCULATIONS