Sharif Digital Repository

The algebraic multigrid (AMG) algorithm as a preconditioner to the Krylov subspace methods has drawn the attention of many researchers in solving fluid flow and heat transfer problems. However, the efficient employment of this solver needs experience, because users have to quantify several important parameters. In this work, we choose a hybrid finite-volume element method and quantify the optimum magnitudes for those parameters. To generalize our results, two sets of fluid flow governing equations, the thermobuoyant flow and confined diffusion flame, are studied and the optimum values are determined. The results indicate that the AMG can be very effective if a proper storage method is chosen... 

In papers [Jafarizadehn and Salimi, Ann. Phys. 322, 1005 (2007) and J. Phys. A: Math. Gen. 39, 13295 (2006)], the amplitudes of continuous-time quantum walk (CTQW) on graphs possessing quantum decomposition (QD graphs) have been calculated by a new method based on spectral distribution associated with their adjacency matrix. Here in this paper, it is shown that the CTQW on any arbitrary graph can be investigated by spectral analysis method, simply by using Krylov subspace-Lanczos algorithm to generate orthonormal bases of Hilbert space of quantum walk isomorphic to orthogonal polynomials. Also new type of graphs possessing generalized quantum decomposition (GQD) have been introduced, where... 

The main purpose of the present work is to study the performance of an algebraic multigrid (AMG) algorithm as a preconditioner to the Krylov subspace methods, mainly GMRES methods. The method is used to solve the set of linear algebraic equations resulted from treating simultaneous simulation of fluid dynamics and heat transfer problems. The extended algorithm is fully implicit which results in a huge system of linear algebraic equations. Different parameters affecting the performance of the AMG are taken into account to enhance the performance of our extended algorithm. Because of high level of sparsity of the matrix of coefficients, the current results indicate that the AMG can be very...