Application and accuracy of the parallel diagonal dominant algorithm

Sun, Xian-He

doi:10.1016/0167-8191(95)00018-j

Cited by 40 publications

(53 citation statements)

References 15 publications

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“…arising in CFD applications [11]. j=17 has been chosen for the Reduced PDD algorithm to reach the single precision accuracy, 10…”

Section: Resultsmentioning

confidence: 99%

“…(PDEs) rely on solving a sequence of tridiagonal systems. In addition to PDEs, tridiagonal systems also arise in many other applications [11]. Three parallel tridiagonal solvers, the Parallel Partition LU (PPT), the Parallel Diagonal Dominant (PDD), and the Reduced Parallel Diagonal Dominant (RPDD, Reduced PDD) algorithms, are used to confirm the analytical results.…”

Section: Tridiagonal Solvers: a Case Studymentioning

confidence: 97%

“…Three parallel tridiagonal solvers, the Parallel Partition LU (PPT), the Parallel Diagonal Dominant (PDD), and the Reduced Parallel Diagonal Dominant (RPDD, Reduced PDD) algorithms, are used to confirm the analytical results. Interested readers may refer to [12] and [11] for details of the algorithms, especially for accuracy analysis and extension of these algorithms to solve periodic systems and general banded linear systems. Only computation and communication count of the algorithms are presented here for scalability analysis.…”

Section: Tridiagonal Solvers: a Case Studymentioning

confidence: 99%

“…In the Reduced PDD algorithm, only j elements of the partition vectors need to be computed for the final modification. Formulas for computing the integer j can be found in [11], depending on particular circumstances.…”

Section: Operation Comparisonmentioning

confidence: 99%

“…The scalability analysis of the PDD algorithm for solving single systems can be found in [11]. In the following, we give a scalability analysis of the PDD algorithm for solving systems with multiple right sides, where the number of right sides does not increase with the ensemble size and the LU factorization of the matrix is not considered.…”

Section: Scalability Analysismentioning

confidence: 99%

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Scalability versus Execution Time in Scalable Systems

Sun

2002

Journal of Parallel and Distributed Computing

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Parallel programming is elusive. The relative performance of different parallel implementations varies with machine architecture, system and problem size. How to compare different implementations over a wide range of machine architectures and problem sizes has not been well addressed due to its difficulty. Scalability has been proposed in recent years to reveal scaling properties of parallel algorithms and machines. In this paper, the relation between scalability and execution time is carefully studied. The concepts of crossing point analysis and range comparison are introduced. Crossing point analysis finds slow/fast performance crossing points of parallel algorithms and machines. Range comparison compares performance over a wide range of ensemble and problem size via scalability and crossing point analysis. Three algorithms from scientific computing are implemented on an Intel Paragon and an IBM SP2 parallel computer. Experimental and theoretical results show how the combination of scalability, crossing point analysis, and range comparison provides a practical solution for scalable performance evaluation and prediction. While our testings are conducted on homogeneous parallel computers, the proposed methodology applies to heterogeneous and network computing as well. © 2002 Elsevier Science (USA)

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“…arising in CFD applications [11]. j=17 has been chosen for the Reduced PDD algorithm to reach the single precision accuracy, 10…”

Section: Resultsmentioning

confidence: 99%

Section: Tridiagonal Solvers: a Case Studymentioning

confidence: 97%

Section: Tridiagonal Solvers: a Case Studymentioning

confidence: 99%

Section: Operation Comparisonmentioning

confidence: 99%

Section: Scalability Analysismentioning

confidence: 99%

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Scalability versus Execution Time in Scalable Systems

Sun

2002

Journal of Parallel and Distributed Computing

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Performance comparison of a set of periodic and non-periodic tridiagonal solvers on SP2 and Paragon parallel computers

Sun

Moitra

1997

Concurrency: Pract. Exper.

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Various tridiagonal solvers have been proposed in recent years for different parallel platforms. In this paper, the performance of three tridiagonal solvers, namely, the parallel partition LU algorithm, the parallel diagonal dominant algorithm, and the reduced diagonal dominant algorithm, is studied. These algorithms are designed for distributed‐memory machines and are tested on an Intel Paragon and an IBM SP2 machine. Measured results are reported in terms of execution time and speedup. Analytical studies are conducted for different communication topologies and for different tridiagonal systems. The measured results match the analytical results closely. In addition to addressing implementation issues, performance considerations such as problem sizes and models of speedup are also discussed. © 1997 John Wiley & Sons, Ltd.

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Using staggered grids with characteristic boundary conditions when solving compressible reactive Navier–Stokes equations

Albin

D'Angelo

2011

Numerical Methods in Fluids

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SUMMARYA specific (hybrid) arrangement of variables is discussed to solve reactive compressible Navier-Stokes equations on staggered-like grids with high-order finite difference schemes. The objective is to improve the numerical flow solution at boundaries. Hybrid arrangement behaviour is compared with 'pure' colocated and staggered strategies. Classical Fourier analysis shows accuracy to be significantly improved in the hybrid case. One-dimensional laminar flame test demonstrates increased robustness (in terms of mesh resolution), whereas computation of 1D exiting pressure wave propagation gives evidence that the method also improves accuracy in the prediction of non-reflecting outflows, compared e.g. with the fully staggered scheme of (J. Comput. Phy. 2003). Multidimensional extension is illustrated through turbulent 2D planar and 3D expanding flames simulations.

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Application and accuracy of the parallel diagonal dominant algorithm

Cited by 40 publications

References 15 publications

Scalability versus Execution Time in Scalable Systems

Scalability versus Execution Time in Scalable Systems

Performance comparison of a set of periodic and non-periodic tridiagonal solvers on SP2 and Paragon parallel computers

Using staggered grids with characteristic boundary conditions when solving compressible reactive Navier–Stokes equations

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