A parallel iterative method for solving 3-D elliptic partial differential equations

Conference · Sun Jan 01 04:00:00 EST 1989

DOI:https://doi.org/10.1007/978-3-642-75771-6_18· OSTI ID:5216107

Greenbaum, A ^[1]; Reiter, E ^[2]; Rodrigue, G ^[3]

---

1. New York Univ., NY (USA). Courant Inst. of Mathematical Sciences
2. California State Univ., Hayward, CA (USA). Dept. of Mathematics and Computer Science
3. California Univ., Davis, CA (USA). Dept. of Applied Science

In this paper, we will consider the parallel solution of the Dirichlet problem for a second-order uniformly elliptic equation in two and three dimensions. Specifically, we shall consider the problem, L(u) = f in {Omega}, u = g on {Gamma}, where L(u) = {minus} summation ({partial derivative}/{partial derivative}x{sub i}(a{sub i}({partial derivative}u/{partial derivative}x{sub i}))) from i = 1 to 3 with a{sub i} positive, bounded, and piecewise smooth on bounded {Omega} with boundary {Gamma}. For sake of exposition, we will assume the equation is 2-dimensional, however, the extension to 3-dimensions of the numerical methods to be described will be obvious.

• Research Organization: Lawrence Livermore National Lab., CA (USA); New York Univ., NY (USA). Courant Inst. of Mathematical Sciences
• Sponsoring Organization: DOE/DP
• DOE Contract Number: W-7405-ENG-48; AC02-76ER03077
• OSTI ID: 5216107
• Report Number(s): UCRL-102220; CONF-8906268--1; ON: DE90005187
• Country of Publication: United States
• Language: English

Related Subjects

657000* -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ALGORITHMS
CONFIGURATION
CONVERGENCE
DIFFERENTIAL EQUATIONS
DIRICHLET PROBLEM
ELLIPTICAL CONFIGURATION
EQUATIONS
ITERATIVE METHODS
MATHEMATICAL LOGIC
PARALLEL PROCESSING
PARTIAL DIFFERENTIAL EQUATIONS
PROGRAMMING