Improved parallel preconditioners for multidisciplinary topology optimisations

Oktay, E.
Manguoğlu, Murat
Sivas, A. A.
Two commonly used preconditioners were evaluated for parallel solution of linear systems of equations with high condition numbers. The test cases were derived from topology optimisation applications in multiple disciplines, where the material distribution finite element methods were used. Because in this optimisation method, the equations rapidly become ill-conditioned due to disappearance of large number of elements from the design space as the optimisations progresses, it is shown that the choice for a suitable preconditioner becomes very crucial. In an earlier work the conjugate gradient (CG) method with a Block-Jacobi preconditioner was used, in which the number of CG iterations increased rapidly with the increasing number processors. Consequently, the parallel scalability of the method deteriorated fast due to the increasing loss of interprocessor information among the increased number of processors. By replacing the Block-Jacobi preconditioner with a sparse approximate inverse preconditioner, it is shown that the number of iterations to converge became independent of the number of processors. Therefore, the parallel scalability is improved.


Modified iterative methods for linear systems of equations
Karasözen, Bülent (1998-01-01)
An extension of the modified Jacobi and Gauss-Seidel methods for systems of linear equations has been introduced. The convergence properties of the proposed methods have been analyzed and compared with the classical and modified methods. The numerical results obtained for some linear systems show that the extended modified methods are superior to other modified iterative methods.
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Manguoğlu, Murat; Sameh, Ahmed H.; Tezduyar, Tayfun E. (2011-09-01)
Iterative solution of large sparse nonsymmetric linear equation systems is one of the numerical challenges in arterial fluid-structure interaction computations. This is because the fluid mechanics parts of the fluid + structure block of the equation system that needs to be solved at every nonlinear iteration of each time step corresponds to incompressible flow, the computational domains include slender parts, and accurate wall shear stress calculations require boundary layer mesh refinement near the arteria...
Rigorous Solutions of Electromagnetic Problems Involving Hundreds of Millions of Unknowns
Ergül, Özgür Salih (2011-02-01)
Accurate simulations of real-life electromagnetic problems with integral equations require the solution of dense matrix equations involving millions of unknowns. Solutions of these extremely large problems cannot be easily achieved, even when using the most powerful computers with state-of-the-art technology. Hence, many electromagnetic problems in the literature have been solved by resorting to various approximation techniques, without controllable error. In this paper, we present full-wave solutions of sc...
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Doǧru, K.; Aksel, M.h.; Tuncer, İsmail Hakkı (2008-12-01)
A parallel implementation of a previously developed finite volume algorithm for the solution of two-dimensional, unsteady, compressible Euler equations is given. The conservative form of the Euler equations is discretized with a second order accurate, one-step Lax-Wendroff scheme. Local time stepping is utilized in order to accelerate the convergence. For the parallel implementation of the method, the solution domain is partitioned into a number of subdomains to be distributed to separate processors for par...
Parallel computation of the diagonal of the inverse of a sparse matrix
Fasllija, Edona; Manguoğlu, Murat; Department of Computer Engineering (2017)
We consider the parallel computation of the diagonal of the inverse of a large sparse matrix. This problem is critical in many applications such as quantum mechanics and uncertainty quantification, where a subset of the entries of the inverse matrix, usually the diagonal, is required. A straightforward approach involves inverting the matrix explicitly and extracting the diagonal of the computed inverse. This approach, however, almost always is too costly for large sparse matrices since the inverse is often ...
Citation Formats
H. U. AKAY, E. Oktay, M. Manguoğlu, and A. A. Sivas, “Improved parallel preconditioners for multidisciplinary topology optimisations,” INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS, pp. 329–336, 2016, Accessed: 00, 2020. [Online]. Available: