Decomposition and Fictitious Domains Methodsfor
نویسنده
چکیده
Boundary value problems for elliptic second order equations in three-dimensional domains with piecewise smooth boundaries are considered. Discretization of the problem is performed using a conventional version of the nite element method with piecewise linear basis functions. The main purpose of the paper is the construction of a preconditioning operator for the resulting system of grid equations. The method is based on two approaches: decomposition of the domain into subdomains and using a new version of the method of ctitious domains. The rate of convergence of the corresponding conjugate gradient method is independent of both the grid size and the number of subdomains.
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