A Quasi-Minimal Residual Variant of the Bi-CGSTAB Algorithm for Nonsymmetric Systems

Chan, Tony F.; Gallopoulos, Efstratios; Simoncini, Valeria; Szeto, Tedd; Tong, Charles

doi:10.1137/0915023

Cited by 101 publications

(54 citation statements)

References 14 publications

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“…QMRCGSTAB, denoted as QMR., is a solver of large nonsymmetric linear systems in subspace iteration method [18], and MVM calculates multiplication of two band matrices. The row max(computation density) is used to evaluate the relationship between computations and memory transfers.…”

Section: Discussionmentioning

confidence: 99%

Scientific Computing Applications on a Stream Processor

Zhang

Yang

Wang

et al. 2008

ISPASS 2008 - IEEE International Symposium on Performance Analysis of Systems and Software

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Stream processors, developed for the stream programming model, perform well on media applications. In this paper we examine the applicability of a stream processor to scientific computing applications. Eight scientific applications, each having different performance characteristics, are mapped to a stream processor. Due to the novelty of the stream programming model, we show how to map programs in a traditional language, such as FORTRAN. In a stream processor system, the management of system resources is the programmers' responsibility. We present several optimizations, which enable mapped programs to exploit various aspects of the stream processor architecture. Finally, we analyze the performance of the stream processor and the presented optimizations on a set of scientific computing applications. The stream programs are from 1.67 to 32.5 times faster than the corresponding FORTRAN programs on an Itanium 2 processor, with the optimizations playing an important role in realizing the performance improvement.

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Section: Discussionmentioning

confidence: 99%

Scientific Computing Applications on a Stream Processor

Zhang

Yang

Wang

et al. 2008

ISPASS 2008 - IEEE International Symposium on Performance Analysis of Systems and Software

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“…8, respectively. QMRCGSTAB [7] is a real application and used to solve large sparse linear systems with asymmetrical coefficient matrices with the Krylov subspace iteration method. MVM calculates the multiplication of two band matrices.…”

Section: Methodsmentioning

confidence: 99%

“…We also performed the test on a complete application, QMRCGSTAB [7]. It consists of 4 2-level loops.…”

Section: Complete Applicationmentioning

confidence: 99%

Exploiting loop-dependent stream reuse for stream processors

Yang

Zhang

Xue

et al. 2008

Proceedings of the 17th International Conference on Parallel Architectures and Compilation Techniques

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The memory access limits the performance of stream processors. By exploiting the reuse of data held in the Stream Register File (SRF), an on-chip storage, the number of memory accesses can be reduced. In current stream compilers reuse is only attempted for simple stream references, those whose start and end are known. Compiler analysis from outside of stream processors does not directly enable the consideration of other complex stream references. In this paper we propose a transformation to automatically optimize stream programs to exploit the reuse supplied by loop-dependent stream references. The transformation is based on three results: algorithms to recognize the reuse supplied by stream references, a new abstract expression called the Stream Reuse Graph (SRG) to depict the reuse and the optimization of the SRG for the transformation. Both the reuse between whole sequences accessed by stream references and that between partial sequences are exploited in the paper. In particular, the problem of exploiting partial stream reuse does not have its parallel in the traditional data reuse exploitation setting (for scalars and arrays). Finally, we have implemented our techniques using the StreamC/KernelC compiler for Imagine. Experimental results show a resultant speedup of 1.14 to 2.54 times using a range of typical stream processing application kernels.

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“…A comprehensive study of the numerical effectiveness for a new advanced group of conjugate gradient iterative solvers BICGSTAB (Van der Vorst, 1992), BICGSTAB2 (Steijpen et al, 1994), QMRSTAB (Chan et al, 1994), Chebyshev's solver (Manteuffel et al, 1995) was numerically examined by Varentsov (1999) and Fomenko (1999). All of these CG methods belong to the group of three-step methods, which provide the global minimization of the residual within certain iterations and give fast quasi-monotonic convergence.…”

Section: Solvers Of the Linear Systemmentioning

confidence: 99%

A new computation method for a staggered grid of 3D EM field conservative modeling

Fomenko¹,

Mogi

2014

Earth Planet Sp

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A new three-dimensional (3D) MT modeling scheme conserving electric current and magnetic flux is developed. The scheme is based on finite difference (FD) staggered rectangular non-uniform grid formulation for the secondary electric field with continuous components of tangential electric and normal magnetic fields, in contrast to existing FD algorithms with a discontinuous E-field at the face of the cells. The scheme leads to a sparse 13-band complex symmetrical system of linear equations, which is effectively solved by fast and stable conjugate gradient (CG) methods. The preconditioning procedure was used to decrease the condition of a number of an ill-conditioned matrix system by several orders and stably and quickly solves the matrix system. The special module for the correction of divergence-free current J greatly increased the speed of convergence and accuracy, especially at low frequencies and for high-contrast resistivity or conductivity structures. A special procedure was developed to improve the accuracy of tangential magnetic and vertical electrical components at the Earth's surface and at the interface with a large conductivity contrast. The validity of the new algorithm was demonstrated for difficult models with high-contrast resistivity structures including topography and for COMMEMI project models.

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A Quasi-Minimal Residual Variant of the Bi-CGSTAB Algorithm for Nonsymmetric Systems

Cited by 101 publications

References 14 publications

Scientific Computing Applications on a Stream Processor

Scientific Computing Applications on a Stream Processor

Exploiting loop-dependent stream reuse for stream processors

A new computation method for a staggered grid of 3D EM field conservative modeling

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