Efficient Implementation of Nonlinear Compact Schemes on Massively Parallel Platforms

@article{Ghosh2015EfficientIO,
  title={Efficient Implementation of Nonlinear Compact Schemes on Massively Parallel Platforms},
  author={Debojyoti Ghosh and Emil M. Constantinescu and Jed Brown},
  journal={SIAM J. Sci. Comput.},
  year={2015},
  volume={37}
}
Weighted nonlinear compact schemes are ideal for simulating compressible, turbulent flows because of their nonoscillatory nature and high spectral resolution. However, they require the solution to banded systems of equations at each time-integration step or stage. We focus on tridiagonal compact schemes in this paper. We propose an efficient implementation of such schemes on massively parallel computing platforms through an iterative substructuring algorithm to solve the tridiagonal system of… 

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References

SHOWING 1-10 OF 51 REFERENCES

A Higher-Order Compact Method in Space and Time Based on Parallel Implementation of the Thomas Algorithm

A novel method to parallelize high-order compact numerical algorithms for the solution of three-dimensional PDEs in a space?time domain that is driven by a communication and computation schedule instead of the usual “creative programming” approach is proposed.

Tera-Scalable Algorithms for Variable-Density Elliptic Hydrodynamics with Spectral Accuracy

This effort represents the first time that a high-order variable-density incompressible flow solver with species diffusion has demonstrated sustained performance in the TeraFLOPS range.

Practical Parallel Band Triangular System Solvers

A new algorithm for the fast solution of hnear recurrence systems, which is discussed in the form of band triangular linear systems, and variations on it which hold for certain special cases of practical interest are given.

A massively parallel multi-block hybrid compact-WENO scheme for compressible flows

Efficient Implementation of Weighted ENO Schemes

A new way of measuring the smoothness of a numerical solution is proposed, emulating the idea of minimizing the total variation of the approximation, which results in a fifth-order WENO scheme for the caser= 3, instead of the fourth-order with the original smoothness measurement by Liuet al.

An Efficient Parallel Algorithm for the Solution of a Tridiagonal Linear System of Equations

An efficient parallel algorithm is presented in which computation time grows as log 2, which can be used to solve recurrence relations of all orders.

Solving the compressible Navier-Stokes equations on up to 1.97 million cores and 4.1 trillion grid points

The use of hyperthreading is discussed, which significantly improves the parallel performance of the code of the Hybrid code, a finite-difference solver of the compressible Navier-Stokes equations on structured grids used for the direct numerical simulation of isotropic turbulence and its interaction with shock waves.

Implementation in ScaLAPACK of Divide-and-Conquer Algorithms forBanded and Tridiagonal Linear Systems

Comparison with existing dense-type methods shows that for areas of the problem parameter space with low bandwidth and/or high number of processors, the family of algorithms described here is superior.

Application of Compact-Reconstruction Weighted Essentially Nonoscillatory Schemes to Compressible Aerodynamic Flows

Compact-reconstruction weighted essentially nonoscillatory schemes have lower dissipation and dispersion errors as well as higher spectral resolution than weighted essentially nonoscillatory schemes
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