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Browsing by Author "Mateescu, Gabriel"

Now showing 1 - 4 of 4
  • Derandomized Vector Sorting
    Heath, Lenwood S.; Mateescu, Gabriel (Department of Computer Science, Virginia Polytechnic Institute & State University, 1998-08-01)
    An instance of the vector sorting problem is a sequence of k-dimensional vectors of length n. A solution to the problem is a permutation of the vectors such that in each dimension the length of the longest decreasing subsequence is O(sqrt(n)). A random permutation solves the problem. Here we derandomize the obvious probabilistic algorithm and obtain a deterministic O(kn^3.5) time algorithm that solves the vector sorting problem. We also apply the algorithm to a book embedding problem.
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    A Domain Decomposition Preconditioner for Hermite Collocation Problems
    Mateescu, Gabriel; Ribbens, Calvin J.; Watson, Layne T. (Department of Computer Science, Virginia Polytechnic Institute & State University, 2002)
    We propose a preconditioning method for linear systems of equations arising from piecewise Hermite bicubic collocation applied to two dimensional elliptic PDEs with mixed boundary conditions. We construct an efficient, parallel preconditioner for the GMRES method. The main contribution of the paper is a novel interface preconditioner derived in the framework of substructuring and employing a local Hermite collocation discretization for the interface subproblems based on a hybrid fine-coarse mesh. Interface equations based on this mesh depend only weakly on unknowns associated with subdomains. The effectiveness of the proposed method is highlighted by numerical experiments that cover a variety of problems.
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    Domain Decomposition Preconditioners for Hermite Collocation Problems
    Mateescu, Gabriel (Virginia Tech, 1998-12-14)
    Accelerating the convergence rate of Krylov subspace methods with parallelizable preconditioners is essential for obtaining effective iterative solvers for very large linear systems of equations. Substructuring provides a framework for constructing robust and parallel preconditioners for linear systems arising from the discretization of boundary value problems. Although collocation is a very general and effective discretization technique for many PDE problems, there has been relatively little work on preconditioners for collocation problems. This thesis proposes two preconditioning methods for solving linear systems of equations arising from Hermite bicubic collocation discretization of elliptic partial differential equations on square domains with mixed boundary conditions. The first method, called edge preconditioning, is based on a decomposition of the domain in parallel strips, and the second, called edge-vertex preconditioning, is based on a two-dimensional decomposition. The preconditioners are derived in terms of two special rectangular grids -- a coarse grid with diameter H and a hybrid coarse/fine grid -- which together with the fine grid of diameter h provide the framework for approximating the interface problem induced by substructuring. We show that the proposed methods are effective for nonsymmetric indefinite problems, both from the point of view of the cost per iteration and of the number of iterations. For an appropriate choice of H, the edge preconditioner requires O(N) arithmetic operations per iteration, while the edge-vertex preconditioner requires O(N 4/3 ) operations, where N is the number of unknowns. For the edge-vertex preconditioner, the number of iterations is almost constant when h and H decrease such that H/h is held constant and it increases very slowly with H when h is held constant. For both the edge- and edge-vertex preconditioners the number of iterations depends only weakly on h when H is constant. The edge-vertex preconditioner outperforms the edge-preconditioner for small enough H. Numerical experiments illustrate the parallel efficiency of the preconditioners which is similar or even better than that provided by the well-known PETSc parallel software library for scientific computing.
  • Effect of a Sawtooth Boundary on Couette Flow
    Mateescu, Gabriel; Wang, Chang Y.; Ribbens, Calvin J.; Watson, Layne T. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1998)
    The relative tagential motion of a smooth plate and a corrugated plate separated by a viscous fluid is studied. The full Navier-Stokes equations are solved using Hermite collocation and Newton's method. Detailed streamlines and vorticity distributions are determined. The increased drag due to corrugation is found to be substantial.