In this paper we give a convergence analysis of a two-level additive Schwarz method in which the coarse mesh basis is constructed with aggregation, a method common in algebraic multigrid. This coarse mesh does not need geometric information about the subdomains and can readily be used on unstructured spatial meshes. We illustrate the performance with several computational examples.

We consider numerical methods for the computation of the eigenvalues of the tridiagonal hyperbolic quadratic eigenvalue problem. The eigenvalues are computed as zeros of the characteristic polynomial using the bisection, Laguerre’s method, the Ehrlich–Aberth method, and the Durand–Kerner method. Initial approximations are provided by a divide-and-conquer approach using rank two modifications. T...

In this paper, we propose a method to solve the Nonlinear Multicommodity Network Flow (NMNF) Problem. We have combined this method with a projected-Jacobi (PJ) method and a duality based method possessing decomposition effects. With the decomposition, our method can be parallel processed and is computationally efficient. We have tested our method on several examples of NMNF problem and obtained...

in this paper, we apply the laplace decomposition method to obtain a series solutions of the burgers-huxley and burgers-fisher equations. the technique is based on the application of laplace transform to nonlinear partial differential equations. the method does not need linearization, weak nonlinearity assumptions or perturbation theory and the nonlinear terms can be easily handled by using the...

This paper describes the parallel finite element analysis of large scale problem for a nonsteady heat conductive problem using domain decomposition method. In order to solve the issue of scalability of a domain decomposition method, the developed system employs the balancing domain decomposition method and hierarchical data management technique among the parallel processors. The present system ...

In this paper, Adomian Decomposition Method (ADM) is used to study the linear time-invariant transistor circuit. The results obtained using Adomian Decomposition Method and the methods taken from the literature [5] were compared with the exact solutions of the linear time-invariant transistor circuit. It is found that the solution obtained using the Adomian Decomposition Method is closer to the...

\Tree-codes" and \Multigrid" methods are both hierarchical, recursive algorithms for solving vector eld equations, faster than traditional methods. If the methods are non-adaptive, then both Tree-codes and Multigrid methods require identical parallel communication strategies since they share the same internal structure. This paper contains a description of Tree-codes followed by an overview of ...

The balancing domain decomposition method for mixed finite elements by Cowsar, Mandel, and Wheeler is extended to the case of mortar mixed finite elements on non-matching multiblock grids. The algorithm involves an iterative solution of a mortar interface problem with one local Dirichlet solve and one local Neumann solve per subdomain on each iteration. A coarse solve is used to guarantee that ...

the main purpose of this paper is to consider adomian's decomposition method in non-linear volterra integro-differential equations. the advantages of this method, compared with the recent numerical techniques (in particular the implicitly linear collocation methods) , and the convergence of adomian's method applied to such nonlinear integro-differential equations are discussed. finall...