TUHH Open Research (TORE)https://tore.tuhh.deTORE captures, stores, indexes, preserves, and distributes digital research material.Mon, 30 Jan 2023 11:39:35 GMT2023-01-30T11:39:35Z5041- Rapid error reduction for block Gauss-Seidel based on p-hierarchical basishttp://hdl.handle.net/11420/4951Title: Rapid error reduction for block Gauss-Seidel based on p-hierarchical basis
Authors: Le Borne, Sabine; Ovall, Jeffrey S.
Abstract: We consider a two-level block Gauss-Seidel iteration for solving systems arising from finite element discretizations employing higher-order elements. A p-hierarchical basis is used to induce this block structure. Using superconvergence results normally employed in the analysis of gradient recovery schemes, we argue that a massive reduction of the H1-error occurs in the first iterate, so that the discrete solution is adequately resolved in very few iterates-sometimes a single iteration is sufficient. Numerical experiments on uniform and adapted meshes support these claims.
Tue, 08 May 2012 00:00:00 GMThttp://hdl.handle.net/11420/49512012-05-08T00:00:00Z
- ℋ-matrix preconditioners for symmetric saddle-point systems from meshfree discretizationhttp://hdl.handle.net/11420/10619Title: ℋ-matrix preconditioners for symmetric saddle-point systems from meshfree discretization
Authors: Le Borne, Sabine; Oliveira, Suely; Yang, Fang
Abstract: Meshfree methods are suitable for solving problems on irregular domains, avoiding the use of a mesh. To deal with the boundary conditions, we can use Lagrange multipliers and obtain a sparse, symmetric and indefinite system of saddle-point type. Many methods have been developed to solve the indefinite system. Previously, we presented an algebraic method to construct an LU-based preconditioner for the saddle-point system obtained by meshfree methods, which combines the multilevel clustering method with the ℋ-matrix arithmetic. The corresponding preconditioner has both ℋ-matrix and sparse matrix subblocks. In this paper we refine the above method and propose a way to construct a pure ℋ-matrix preconditioner. We compare the new method with the old method, JOR and smoothed algebraic multigrid methods. The numerical results show that the new preconditioner outperforms the preconditioners based on the other methods. Copyright © 2008 John Wiley & Sons, Ltd.
Mon, 28 Apr 2008 00:00:00 GMThttp://hdl.handle.net/11420/106192008-04-28T00:00:00Z
- On the distribution of real eigenvalues in linear viscoelastic oscillatorshttp://hdl.handle.net/11420/2138Title: On the distribution of real eigenvalues in linear viscoelastic oscillators
Authors: Mohammadi, Seyyed Abbas; Voß, Heinrich
Abstract: © 2019 John Wiley & Sons, Ltd. In this paper, a linear viscoelastic system is considered where the viscoelastic force depends on the past history of motion via a convolution integral over an exponentially decaying kernel function. The free-motion equation of this nonviscous system yields a nonlinear eigenvalue problem that has a certain number of real eigenvalues corresponding to the nonoscillatory nature. The quality of the current numerical methods for deriving those eigenvalues is directly related to damping properties of the viscoelastic system. The main contribution of this paper is to explore the structure of the set of nonviscous eigenvalues of the system while the damping coefficient matrices are rank deficient and the damping level is changing. This problem will be investigated in the cases of low and high levels of damping, and a theorem that summarizes the possible distribution of real eigenvalues will be proved. Moreover, upper and lower bounds are provided for some of the eigenvalues regarding the damping properties of the system. Some physically realistic examples are provided, which give us insight into the behavior of the real eigenvalues while the damping level is changing.
Fri, 01 Mar 2019 00:00:00 GMThttp://hdl.handle.net/11420/21382019-03-01T00:00:00Z
- A Jacobi-Davidson method for two-real-parameter nonlinear eigenvalue problems arising from delay-differential equationshttp://hdl.handle.net/11420/6302Title: A Jacobi-Davidson method for two-real-parameter nonlinear eigenvalue problems arising from delay-differential equations
Authors: Meerbergen, Karl; Schröder, Christian; Voß, Heinrich
Abstract: The critical delays of a delay-differential equation can be computed by solving a nonlinear two-parameter eigenvalue problem. The solution of this two-parameter problem can be translated to solving a quadratic eigenvalue problem of squared dimension. We present a structure preserving QR-type method for solving such quadratic eigenvalue problem that only computes real-valued critical delays; that is, complex critical delays, which have no physical meaning, are discarded. For large-scale problems, we propose new correction equations for a Newton-type or Jacobi-Davidson style method, which also forces real-valued critical delays. We present three different equations: one real-valued equation using a direct linear system solver, one complex valued equation using a direct linear system solver, and one Jacobi-Davidson style correction equation that is suitable for an iterative linear system solver. We show numerical examples for large-scale problems arising from PDEs. © 2012 John Wiley & Sons, Ltd.
Mon, 09 Jul 2012 00:00:00 GMThttp://hdl.handle.net/11420/63022012-07-09T00:00:00Z