An iterative process similar to the Schwartz method for non-overlapping adjacent domains is constructed for solving the monoenergetic transport equation in a domain decomposed into a finite number of disjoint subdomains. Under the boundary conditions, most important for applications, the sufficient conditions are determined for the convergence of the process constructed. The paper is mainly aimed at proving the convergence of the iterative method.Brought to you by | New York University Bobst Library Technical Services Authenticated Download Date | 6/16/15 1:40 PM L J Wi X <^ J and €{^λί f σ(χ)(/ί(χ,Ω)) 2 αχαΩ] 1/2 <Α 1 ||/ΐ||^ι
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An iterative process is formulated on subdomains for odd P 2N +i-approximation in a bounded domain K c jR 3 conditionally decomposed into a finite set of subdomains. The convergence of the iterative algorithm is proved. This paper is a logical sequel to [2] where a similar problem was solved for a large class of boundary value problems with a monoenergetic integro-differential transport operator.Let V c £ 3 be a bounded domain in which we seek for the solution to a boundary value problem in P 2 N+i approximation [3], conditionally decomposed into a finite number of subdomains K v , v = 1,2,..., v 0 . The iterative algorithm suggested although somewhat similar to the Schwartz subdomain alternating method differs from the latter first of all in the fact that the domains V v are adjacent without overlapping. In our algorithm (in the Schwartz algorithm as well) it is possible in principle to reduce the problem in a geometrically complex domain V to the subsequent solution of problems in geometrically simplified subdomains V v .The paper is generally aimed at proving the convergence of the iterative process on the basis of the generalized solution concept.
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