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A fractional splitting algorithm for nonoverlapping domain decomposition for parabolic problem
Author(s) -
Daoud Daoud S.,
Subasi D.
Publication year - 2002
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.10019
Subject(s) - mathematics , domain decomposition methods , discretization , boundary value problem , decomposition method (queueing theory) , backward euler method , variable (mathematics) , convergence (economics) , initial value problem , domain (mathematical analysis) , polygon mesh , extrapolation , euler's formula , method of lines , partial differential equation , mathematical analysis , algorithm , finite element method , differential equation , ordinary differential equation , geometry , physics , discrete mathematics , economics , thermodynamics , economic growth , differential algebraic equation
Abstract In this article we study the convergence of the nonoverlapping domain decomposition for solving large linear system arising from semi‐discretization of two‐dimensional initial value problem with homogeneous boundary conditions and solved by implicit time stepping using first and two alternatives of second‐order FS‐methods. The interface values along the artificial boundary condition line are found using explicit forward Euler's method for the first‐order FS‐method, and for the second‐order FS‐method to use extrapolation procedure for each spatial variable individually. The solution by the nonoverlapping domain decomposition with FS‐method is applicable to problems that requires the solution on nonuniform meshes for each spatial variable, which will enable us to use different time‐stepping over different subdomains and with the possibility of extension to three‐dimensional problem. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 609–624, 2002