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## of High-Order Discretization of Linear Time-Dependent Problems

### Citations

2026 | GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
- Saad, Schultz
- 1986
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Citation Context ...ated Krylov subspace methods CG (Conjugate Gradient) and GMRES (Generalized Minimal Residual). The reader should refer to [4] and references therein for more detail. In this work, the GMRES algorithm =-=[1]-=-1 is used as the base algorithm however the statistical preconditioning proposed here can be readily applied to all Krylov subspace methods because they are based on matrix-vector multiplication. The ... |

510 |
Numerical Solution of Partial Differential Equations by the Finite Element Method. Cambridge University Press
- Johnson
- 1992
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Citation Context ...linear combination of the kth partial derivative in the ith direction, i.e. ∂k/∂xi k. When discretized using a suitable discretization method like Finite-Differences, Finite Elements or Finite Volume =-=[5]-=-, the resulting equations can be written in the following semi-discrete form d dt u = L u. (2) The fully discrete from is obtained after eq.(2) is discretized in time. There are many choices available... |

293 |
Numerical Methods for Ordinary Differential Equations
- Butcher
- 2003
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Citation Context ... can be written in the following semi-discrete form d dt u = L u. (2) The fully discrete from is obtained after eq.(2) is discretized in time. There are many choices available for time-discretization =-=[6]-=-. However a common step in these algorithms, which is the most costly part of the solution, is simply an Euler implicit scheme presented below un+1 − un ∆t = Lun+1, (3) which leads to the solution of ... |

251 | Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods
- Barrett, Berry, et al.
- 1994
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Citation Context ... from stationary methods including Jacobi, Gauss-Seidel, SOR to more sophisticated Krylov subspace methods CG (Conjugate Gradient) and GMRES (Generalized Minimal Residual). The reader should refer to =-=[4]-=- and references therein for more detail. In this work, the GMRES algorithm [1]1 is used as the base algorithm however the statistical preconditioning proposed here can be readily applied to all Krylov... |

190 | Jacobian-free Newton-Krylov methods: a survey of approaches and applications
- Knoll, Keyes
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Citation Context ...is situation a full implicit solution procedure is avoided to prevent the problem of storing the full Jacobian matrix. Yet still another possibility is available by using a matrix-free implementation =-=[7]-=-. In this approach the matrix A is never computed/stored but eq.(4) is solved by replacing the matrixvector product in the GMRES algorithm with residual computation. However the only disadvantage of t... |

44 |
Introduction to Linear Regression Analysis”, 4th Edition
- Montgomery, Peck, et al.
- 2006
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Citation Context ...essors. As the GMRES progress and more matrix-vector multiplications are performed, a standard model selection procedure, like backward elimination, might be used to eliminate inappropriate regressors=-=[3, 2]-=-. This would result in optimum model which might result in optimum speed-up of the convergence of the GMRES algorithm. However this approach has two expensive parts that should be analyzed mathematica... |

2 |
Large-Eddy Simulations of Turbulence”, Cambridge Univ
- Lesieur, Mtais, et al.
- 2005
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Citation Context ...ge that it does not fit in the physical memory of the current machines. This situation typically happens in Large Eddy Simulation (LES) or Direct Numerical Simulations (DNS) of a turbulent fluid flow =-=[8]-=-. In this situation a full implicit solution procedure is avoided to prevent the problem of storing the full Jacobian matrix. Yet still another possibility is available by using a matrix-free implemen... |

1 |
Lecture Note Applied Statistical Methods
- Gao
- 2013
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Citation Context ...essors. As the GMRES progress and more matrix-vector multiplications are performed, a standard model selection procedure, like backward elimination, might be used to eliminate inappropriate regressors=-=[3, 2]-=-. This would result in optimum model which might result in optimum speed-up of the convergence of the GMRES algorithm. However this approach has two expensive parts that should be analyzed mathematica... |