Browsing by Subject "Iterative method"

Now showing 1 - 4 of 4

Open Access
Decompositional analysis of Kronecker structured Markov chains
(Kent State University, 2008) Bao, Y.; Bozkur, I. N.; Dayar, T.; Sun, X.; Trivedi, K. S.
This contribution proposes a decompositional iterative method with low memory requirements for the steadystate analysis ofKronecker structured Markov chains. The Markovian system is formed by a composition of subsystems using the Kronecker sum operator for local transitions and the Kronecker product operator for synchronized transitions. Even though the interactions among subsystems, which are captured by synchronized transitions, need not be weak, numerical experiments indicate that the solver benefits considerably from weak interactions among subsystems, and is to be recommended specifically in this case. © 2008, Kent State University.
Open Access
Efficient methods for electromagnetic characterization of 2-D geometries in stratified media
(1997) Çalışkan, Fatma
Numerically efficient method of moments (MoM) algorithms are developed for and applied to 2-D geometries in multilayer media. These are, namely, the spatial-domain MoM in conjunction with the closed-from Green's functions, the spectral-domain MoM using the generalized pencil of functions (GPOF) algorithm and a FFT algorithm to evaluate the MoM matrix entries. These approaches are mainly to improve the computational efficiency of the evaluation of the MoM matrix entries. Among these, the spectral-domain MoM using the GPOF algorithm is the most efficient approach for printed multilayer geometries. The assessment of the efficiency of this method is performed on several problems, by comparing the matrix fill times for these three approaches. In addition a new iterative algorithm is developed to solve the MoM matrix equation, which is based on dividing a large object into subregions and solving the matrix equation on each subregion by considering the effects of other regions. This iterative algorithm is applied to some large geometries and is compared to a traditional LU decomposition algorithm for the assessment of its numerical efficiency. It is observed that the iterative algorithm is numerically more efficient as compared to the LU decomposition.
Open Access
Encapsulating multiple communication-cost metrics in partitioning sparse rectangular matrices for parallel matrix-vector multiplies
(SIAM, 2004) Uçar, B.; Aykanat, Cevdet
This paper addresses the problem of one-dimensional partitioning of structurally unsymmetric square and rectangular sparse matrices for parallel matrix-vector and matrix-transpose-vector multiplies. The objective is to minimize the communication cost while maintaining the balance on computational loads of processors. Most of the existing partitioning models consider only the total message volume hoping that minimizing this communication-cost metric is likely to reduce other metrics. However, the total message latency (start-up time) may be more important than the total message volume. Furthermore, the maximum message volume and latency handled by a single processor are also important metrics. We propose a two-phase approach that encapsulates all these four communication-cost metrics. The objective in the first phase is to minimize the total message volume while maintaining the computational-load balance. The objective in the second phase is to encapsulate the remaining three communication-cost metrics. We propose communication-hypergraph and partitioning models for the second phase. We then present several methods for partitioning communication hypergraphs. Experiments on a wide range of test matrices show that the proposed approach yields very effective partitioning results. A parallel implementation on a PC cluster verifies that the theoretical improvements shown by partitioning results hold in practice.
Open Access
Partitioning sparse matrices for parallel preconditioned iterative methods
(Society for Industrial and Applied Mathematics, 2007) Uçar, B.; Aykanat, Cevdet
This paper addresses the parallelization of the preconditioned iterative methods that use explicit preconditioners such as approximate inverses. Parallelizing a full step of these methods requires the coefficient and preconditioner matrices to be well partitioned. We first show that different methods impose different partitioning requirements for the matrices. Then we develop hypergraph models to meet those requirements. In particular, we develop models that enable us to obtain partitionings on the coefficient and preconditioner matrices simultaneously. Experiments on a set of unsymmetric sparse matrices show that the proposed models yield effective partitioning results. A parallel implementation of the right preconditioned BiCGStab method on a PC cluster verifies that the theoretical gains obtained by the models hold in practice. © 2007 Society for Industrial and Applied Mathematics.