ISSN:
0945-3245
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary This paper describes a fast and numerically stable method for solving the discrete Dirichlet problem for Poisson's equation in case of a rectangle (and mainly, a square). By using a special calculus for difference operators, the system of linear equations is reduced to a block-triangular system such that the diagonal blocks are heavily diagonally dominant. For a standard version of the algorithm, the number of operations and the computing time are proportional toh −2 (h=mesh width). The method is one oftotal reduction compared with the method ofblock-cyclic reduction (odd-even reduction) [2], which we describe as a method ofpartial reduction.—Due to the developed calculus, many generalizations are possible.—In a following part II of the paper, the algorithm and numerical results will be described in detail.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01436620
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