โ Scribed by M. Dryya
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An efficient algorithm is described for solving the sets of algebraic equations that arise in the finite element method for the Dirichlet problem, in a domain composed of rectangles with sides parallel to the axes. The algorithm is based on the method with capacitance matrix and reduces the problem to the solution of problems in rectangles and a system with capacitance matrix C. A problem in rectangles is solved by means of a fast F.ourier transformation involving -li'1og"V. N=I/h operations, and the system with matrix C, by an iterative method involving -Nlog,Nlne-' operations.
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We describe below an algorithm for solving the sets of variational-difference equations approximating a Dirichlet boundary value problem. This problem is considered in a domain Q composed of a finite number of rectangles with sides parallel to the axes. For brevity, the trea~ent is given for Poisson's equation, considered in an L-shaped domain Q. The solution of such sets of equations has often been considered. We may mention the block-relaxation methods in subspaces /1/, the methods based on bordering of matrices /2/, the methods of ficititious domains (unknown) (see /3,4, etc./), and the methods with capacitance matrix (see /5-8, etc./); pee also the references in /9, 10/.
The algorithm below is based on the capacitance matrix method, and is better from the point of view of the amount of work involved than the familiar methods (see Theorem 2).
The present paper is a direct continuation of /8/, where the same problem was considered, but we have used a different approach to constructing the algorithm with capacitance matrix.
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