3 edition of **Preconditioning for first-order spectral discretizations** found in the catalog.

Preconditioning for first-order spectral discretizations

- 183 Want to read
- 10 Currently reading

Published
**1986**
by National Aeronautics and Space Administration, Langley Research Center, For sale by the National Technical Information Service in Hampton, Va, [Springfield, Va
.

Written in English

- Iterative methods (Mathematics)

**Edition Notes**

Other titles | Preconditioning for first order spectral discretizations. |

Statement | Craig L. Streett, Michelle G. Macaraeg. |

Series | NASA technical memorandum -- 87619. |

Contributions | Macaraeg, Michelle G., Langley Research Center. |

The Physical Object | |
---|---|

Format | Microform |

Pagination | 1 v. |

ID Numbers | |

Open Library | OL14663756M |

Preconditioners for higher order finite element discretizations of H(div)-elliptic problem. Junxian Wang; Liuqiang Zhong; Shi Shu. School of Mathematical and Computational Sciences, Xiangtan University, Hunan , China. E-mails: [email protected] / [email protected] / [email protected] \Block-diagonal preconditioning for spectral stochastic nite element systems," with C. E. Powell, IMA Journal of Numerical Analysis {, \Convergence analysis of iterative solvers in inexact Rayleigh quotient iteration," with Fei Xue, SIAM Journal on Matrix Analysis and Applications ,

The hp finite element discretizations, in particular, by spectral elements of elliptic equations are given significant attention in current research and applications. This volume is the first to feature all components of Dirichlet?Dirichlet-type DD solvers for hp discretizations devised as numerical procedures which result in DD solvers that. Multigrid Algorithms for High-Order Discontinuous Galerkin Discretizations of the Compressible Navier-Stokes Equations Khosro Shahbazi;a Dimitri J. Mavriplis b Nicholas K. Burgess b aDivision of Applied Mathematics, Brown University, George Street, Providence, RI .

And then, a type of efficient algebraic multigrid (AMG) preconditioner is presented by combining both the coarsening techniques based on the distance matrix and the effective smoothing operators. The resulting preconditioned conjugate gradient (PCG) method is efficient for 3D nearly incompressible problems. @article{osti_, title = {Un-collided-flux preconditioning for the first order transport equation}, author = {Rigley, M. and Koebbe, J. and Drumm, C.}, abstractNote = {Two codes were tested for the first order neutron transport equation using finite element methods. The un-collided-flux solution is used as a preconditioner for each of these methods.

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Efficient solution of the equations from spectral discretizations is essential if the high-order accuracy of these methods is to be realized. A preconditioning scheme for first-order.

COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information Preconditioning for first-order spectral discretizations book resources to assist library staff as they consider how to handle.

Efficient solution of the equations from spectral discretizations is essential if the high-order accuracy of these methods is to be realized.

An illustration of an open book. Books. An illustration of two cells of a film strip. Preconditioning for first-order spectral discretization Item Preview remove-circle Share or Embed This Item.

The finding is even more valuable that this preconditioning can be applied on the conservative form of the Poisson’s equation, the one involved in some discretizations of variable density flows for instance. Several numerical experiments based on manufactured solutions demonstrate the accuracy of the discretization up to the by: 1.

Hence, an efficient preconditioner is necessary to improve the convergence of a numerical method whose number of iterations depends on the distributions of eigenvalues (see [9–12]).

Particularly, the lower-order finite element/difference preconditioning methods for spectral collocation/element methods have been reported ([9, 10, 13–17], etc.).Cited by: 1.

Based on these facts and previous results on the preconditioning of other components, fast domain decomposition algorithms for spectral discretizations are obtained. Read more Discover more. () Preconditioners for spectral discretizations of Helmholtz's equation with Sommerfeld boundary conditions.

Computer Methods in Applied Mechanics and Engineering() Fully discrete hp-finite elements: fast quadrature.

() Finite Element Preconditioning on Spectral Element Discretizations for Coupled Elliptic Equations. Journal of Applied Mathematics() Preconditioning Cubic Spline Collocation Methods for a Coupled Elliptic Equation.

Finite difference type preconditioners for spectral element discretizations based on Legendre-Gauss-Lobatto points are analyzed. The latter is employed for the approximation of uniformly elliptic partial differential problems.

In this work, it is shown that the condition number of the resulting preconditioned system is bounded independently of both of the polynomial degrees. Readers will discover new analysis results for both the well-known basic DD solvers and some DD methods recently devised by the authors, e.g., for elliptic problems with varying chaotically piecewise constant orthotropism without restrictions on the finite aspect hp finite element discretizations, in particular, by spectral elements.

Fig. 2 shows that when the preconditioner is a block-plus-diagonal matrix, the iteration diverges. For this problem, a block-plus-pentadiagonal preconditioner is needed. The off-diagonal elements of the second derivative are half the size of the diagonal elements in the limit that the row or column index n is large.

Download: Download high-res image (KB). Earlier, for spectral elements, only fast solvers obtained with the use of special preconditioners in factored form were known. The most intricate part of the algorithm is the inter-subdomain Schur complement preconditioning by inexact iterative solver employing two preconditioners -- preconditioner-solver and preconditioner-multiplicator.

yield efficient solution of the preconditioning operator. Variations of the Beam and Warming scheme (refs. 3, 4) are popular for such solutions. However, the advection terms in this scheme are central differenced. Elementary analysis of preconditioning first-order.

Korneev V., Rytov A. () Fast Domain Decomposition Algorithms for Discretizations of 3-d Elliptic Equations by Spectral Elements. In: Langer U., Discacciati M., Keyes D.E., Widlund O.B., Zulehner W. (eds) Domain Decomposition Methods in Science and Engineering XVII. Lecture Notes in Computational Science and Engineering, vol Olson L.N., Hesthaven J.S., Wilcox L.C.

() Developments in Overlapping Schwarz Preconditioning of High-Order Nodal Discontinuous Galerkin Discretizations. In: Widlund O.B., Keyes D.E. (eds) Domain Decomposition Methods in Science and Engineering XVI. Lecture Notes in Computational Science and Engineering, vol Springer, Berlin, Heidelberg.

Block-diagonal preconditioning for spectral stochastic finite element systems by Catherine E. Powell, Howard C. Elman, Deterministic models of fluid flow and the transport of chemicals in flows in heterogeneous porous media incorporate PDEs whose material parameters are assumed to be known exactly.

An algebraic multigrid (AMG) with aggregation technique to coarsen is applied to construct a better preconditioner for solving Helmholtz equations in this paper. The solution process consists of constructing the preconditioner by AMG and solving the preconditioned Helmholtz problems by Krylov subspace methods.

In the setup process of AMG, we employ the double pairwise. 2 Preconditioning by the upstream scheme From the one-dimensional •nodel problem it can be seen that for e • 0 wb first have to find a good preconditioner for the derivative operator du Here we employ the first order upstream scheme (L•up) for preconditioning, i.e., or __ _._ dx a(x•+•)- u(xi) if xi+•.

The discretization is performed by second-order finite difference schemes (fi-schemes) where the second-order upstream scheme is combined with the standard central scheme. Higher order discretizations with spectral methods are also considered.

For preconditioning the usual first-order upstream scheme is employed. Preconditioning for first-order spectral discretization. By M. Macaraeg and C. Streett. Abstract. Efficient solution of the equations from spectral discretizations is essential if the high-order accuracy of these methods is to be realized.

Direct solution of these equations is rarely feasible, thus iterative techniques are required. Hybrid discretization methods based on a domain decomposition exploiting continuous symmetries present in parts of the model aim at a reduction of the computational cost of the related numerical simulations.

The resulting linear systems of equations arising from, e.g., the coupling of finite elements (FE) and spectral elements (SE), are sparse and symmetric. .First-Order Transport Problems: Physics-based block preconditioner: A solution strategy for fluid-structure interaction using the unified continuum formulation, quasi-direct coupling, and nested block preconditioning spectral fractional Laplacian: A Fast Solver for the Fractional Helmholtz Equation.D.

Funaro, E. Rothman, Preconditioning Matrices for the Pseudo-Spectral Approximation of First Order Operators, in Finite Element Analysis in Fluids (T. J. Chung & G. R. Karr Eds., UAH Press, Huntsville ), pp. D. Funaro, Convergence Analysis for Pseudo Spectral Multidomain Approximations of Linear Advection Equations, IMA J.

Numer.