Domain Decomposition Method Of Elongated Domain

In this thesis, through the idea of domain decomposition method and the theory ofnatural boundary reduction, and using the alternate iteration, we study non-overlappingdomain decomposition method and overlapping domain decomposition method for theDirichlet exterior boundary value problems in outer circle and elongated domains. Manyscientific and engineering computing can be attributed to the partial differential equation onunbounded domain boundary value problem, and partial differential equation numericalsolution of problems in unbounded domain has a very important significance. The boundaryelement method is used to solve problems in unbounded domain is quite effective method,and the finite element coupling method has become the treatment of unbounded domainproblems frequently used method; on the other hand, in recent years the development ofemerging domain decomposition algorithm for solving problems on unbounded domainsprovides a new way. Domain decomposition algorithms in unbounded domains based onthe area of the theory of natural boundary reduction theory also have the advantage of theboundary element method with domain decomposition algorithm; this method divides theunbounded regions into two parts by introducing artificial boundary, bounded and typicalunbounded domain; the bounded region can use finite element method combined with theartificial boundary method to solve; in external unbounded domain, we can use the naturalreduction theory and alternate solution in the bounded and unbounded domains. For theelongated outer regions of domain decomposition algorithm, and based on the analysis ofbi-harmonic equation, the author select the ellipse as artificial boundary and structureoverlap region of domain decomposition method; so, the scale of the problem will changefrom big to small, and greatly reduce the calculation region and process.