Abstract
The Bitsadze-Samarskii nonlocal boundary value problem is considered. Variational formulation is done. The domain decomposition and Schwarz-type iterative methods are used. The parallel algorithm as well as sequential ones is investigated.
Highlights
In applied sciences different problems with nonlocal boundary conditions arise very often
Modern investigation of nonlocal elliptic boundary value problems originates from Bitsadze and Samarskii work [1], in which by means of the method of integral equations the theorems are proved on the existence and uniqueness of a solution for the second order multidimensional elliptic equations in rectangular domains
In [7, 11,12,13, 15] using Schwarz alternating method and domain decomposition algorithms BitsadzeSamarskii nonlocal problem is studied for Laplace equation
Summary
In applied sciences different problems with nonlocal boundary conditions arise very often. Modern investigation of nonlocal elliptic boundary value problems originates from Bitsadze and Samarskii work [1], in which by means of the method of integral equations the theorems are proved on the existence and uniqueness of a solution for the second order multidimensional elliptic equations in rectangular domains. In the work [6] the iterative method of proving the existence of a solution of Bitsadze-Samarskii problem for Laplace equation was proposed. In [7, 11,12,13, 15] using Schwarz alternating method and domain decomposition algorithms BitsadzeSamarskii nonlocal problem is studied for Laplace equation. The present work is devoted to the variational formulation and domain decomposition and Schwarz-type iterative methods for Bitsadze-Samarskii nonlocal boundary value problem for Poisson’s two-dimensional equation.
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