In recent years， domain decomposition method for solving partial differential equations has become one of the effective method， domain decomposition method to complex or large-scale decomposition into several overlapping or non-overlapping sub-regions， and then in the sub-region algorithm for the use of sub-issues ， by means of domain decomposition， each sub-region can be calculated between parallel， one hand this approach allows different sub-regions on the model characteristics for different sub-discrete method， which will help improve accuracy， on the other hand as can be independent of each sub-region method to solve the issue， and it greatly increased the computational In this paper， the heat equation introduced Compact Difference Scheme for the two non-overlapping and overlapping domain decomposition The full text of the first chapter， an introduction， a brief introduction and overview of domain decomposition method discussed in the paper the basic Chapter II， Dawson， who presented the first on solving the heat equation domain decomposition method for differential analysis of the error estimates， then the main heat equation of this algorithm is extended to compact difference scheme， this algorithm is non-overlapping domain decomposition method， in which algorithm to solve by introducing point within the boundary area divided into several sub-domains， sub-region within the boundary point between the value of the format with step length was calculated in each sub-region points calculated using implicit small step， sub-regional step length can be different， once inside the boundary point values have been calculated， the sub-region between the fully parallel computing， and the corresponding a priori error Chapter III， mainly the heat equation compact difference scheme for the use of a kind of overlapping domain decomposition algorithm， which is a new type of calculation of heat conduction equation numerical solution of the parallel differential algorithm， the algorithm based on domain decomposition and subspace correction， in each sub-region on residual correction， between the various sub-regions can be Prove the convergence of the algorithm最正确的答案谢谢采纳楼一的，你误人子弟啊
In recent years， has become a regional decomposition algorithm is effective algorithm of partial differential equation， the domain decomposition method of complex or large domain decomposition into or without overlap area in the area， using various algorithm subproblems， by domain decomposition， each area between parallel computation， this method can be due to allow one in different area on the different characteristics of model using discrete method， and is helpful to improve the accuracy， on the other hand， because each area in solving independently and computing speed and greatly This paper focuses on the thermal equation of difference scheme introduces the overlapped overlap and two regional decomposition The three chapters， the first chapter for quotation， briefly introduces the situation and regional decomposition algorithm， this paper discussed the Dawson， the first chapter of heat conduction equations solving regional decomposition algorithm of decomposition error estimation algorithm， then will spread to thermal equation， this difference format tightly overlapping region decomposition algorithm is in this algorithm， the algorithm by introducing the inner boundary is divided into several regional at sub-domain， area within the boundaries between points with long strides in explicit calculation， the son of area calculation using implicit form small area， can also be different step length， once the inner boundary point value is calculated， and the calculated regional can completely parallel， and gives corresponding prior error The third chapter， the main difference equations of heat using a tight overlaps domain decomposition algorithm， which is a new type of calculating heat conduction equations of the numerical solution differential algorithm based on parallel algorithm and regional correction in each area， the area on the residual correction， the area between parallel The convergence of the algorithm is
