Parallel iterative method for solving 3-D elliptic partial differential equations.

摘要

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.