A Multithreaded Recursive and Nonrecursive Parallel Sparse Direct Solver

2016-01-01
Sparse linear system of equations often arises after discretization of the partial differential equations (PDEs) such as computational fluid dynamics, material science, and structural engineering. There are, however, sparse linear systems that are not governed by PDEs, some examples of such applications are circuit simulations, power network analysis, and social network analysis. For solution of sparse linear systems one can choose using either a direct or an iterative method. Direct solvers are based on some factorization of the coefficient matrix such as the LU, QR, or singular value decompositions and are known to be robust. Classical preconditioned iterative solvers, on the other hand, are not as robust as direct solvers and finding an effective preconditioner is often problem dependent. Due to their sequential nature, direct solvers often have limited parallel scalability. In this chapter, we present a new parallel recursive sparse direct solver that is based on the sparse DS factorization. We implement our algorithm using MIT's Cilk programming language which is also a part of the Intel C++ compiler. We show the scalability and robustness of our algorithm and compare it to Pardiso direct solver.
ADVANCES IN COMPUTATIONAL FLUID-STRUCTURE INTERACTION AND FLOW SIMULATION: NEW METHODS AND CHALLENGING COMPUTATIONS

Suggestions

Optimization of the array geometry for direction finding
Özaydın, Seval; Koç, Seyit Sencer; Tanık, Yalçın; Department of Electrical and Electronics Engineering (2003)
In this thesis, optimization of the geometry of non-uniform arrays for direction finding yielding unambiguous results is studied. A measure of similarity between the array response vectors is defined. In this measure, the effects of antenna array geometry, source placements and antenna gains are included as variable parameters. Then, assuming that the antenna gains are known and constant, constraints on the similarity function are developed and described to result in unambiguous configurations and maximum r...
A parallel sparse algorithm targeting arterial fluid mechanics computations
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 Analysis of Double-Negative Materials with the Multilevel Fast Multipole Algorithm
Ergül, Özgür Salih (2012-02-01)
We present rigorous analysis of double-negative materials (DNMs) with surface integral equations and the multilevel fast multipole algorithm (MLFMA). Accuracy and efficiency of numerical solutions are investigated when DNMs are formulated with two recently developed formulations, i.e., the combined tangential formulation (CTF) and the electric and magnetic current combined-field integral equation (JMCHE). Simulation results on canonical objects are consistent with previous results in the literature on ordin...
An interactive preference based multiobjective evolutionary algorithm for the clustering problem
Demirtaş, Kerem; Özdemirel, Nur Evin; Karasakal, Esra; Department of Industrial Engineering (2011)
We propose an interactive preference-based evolutionary algorithm for the clustering problem. The problem is highly combinatorial and referred to as NP-Hard in the literature. The goal of the problem is putting similar items in the same cluster and dissimilar items into different clusters according to a certain similarity measure, while maintaining some internal objectives such as compactness, connectivity or spatial separation. However, using one of these objectives is often not sufficient to detect differ...
Approximate Chernoff Fusion of Gaussian Mixtures Using Sigma-Points
Gunay, Melih; Orguner, Umut; Demirekler, Mübeccel (2014-07-10)
Covariance intersection (CI) is a method used for consistent track fusion with unknown correlations. The well-known generalization of CI to probability density functions is known as Chernoff fusion. In this paper, we propose an approximate approach for the Chernoff fusion of Gaussian mixtures based on a sigma-point approximation of the underlying densities. The resulting general density fusion rule yields a closed form cost function and an analytical fused density for Gaussian mixtures. The proposed method ...
Citation Formats
E. S. Bölükbaşı, “A Multithreaded Recursive and Nonrecursive Parallel Sparse Direct Solver,” ADVANCES IN COMPUTATIONAL FLUID-STRUCTURE INTERACTION AND FLOW SIMULATION: NEW METHODS AND CHALLENGING COMPUTATIONS, pp. 283–292, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/35667.