Krylov solvers preconditioned with the low-order red-black algorithm for the PN hybrid FEM for the INSTANT code

Yaqi Wang; Cristian Rabiti; Giuseppe Palmiotti

Krylov solvers preconditioned with the low-order red-black algorithm for the PN hybrid FEM for the INSTANT code

Yaqi Wang, Cristian Rabiti, Giuseppe Palmiotti

Nuclear Reactor Technology

Research output: Contribution to conference › Paper › peer-review

Abstract

This paper proposes a new set of Krylov solvers, CG and GMRes, as an alternative of the Red-Black (RB) algorithm on on solving the steady-state one-speed neutron transport equation discretized with PN in angle and hybrid FEM (Finite Element Method) in space. A pre conditioner with the low-order RB iteration is designed to improve their convergence. These Krylov solvers can reduce the cost of pre-assembling the response matrices greatly. Numerical results with the INSTANT code are presented in order to show that they can be a good supplement on solving the PN-HFEM system. (author)

Original language	American English
State	Published - May 8 2011
Event	International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering - Rio de Janeiro, Brazil Duration: May 8 2011 → May 12 2011

Conference

Conference	International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering
Abbreviated title	M&C 2011
Country/Territory	Brazil
City	Rio de Janeiro
Period	05/8/11 → 05/12/11

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title = "Krylov solvers preconditioned with the low-order red-black algorithm for the PN hybrid FEM for the INSTANT code",

abstract = "This paper proposes a new set of Krylov solvers, CG and GMRes, as an alternative of the Red-Black (RB) algorithm on on solving the steady-state one-speed neutron transport equation discretized with PN in angle and hybrid FEM (Finite Element Method) in space. A pre conditioner with the low-order RB iteration is designed to improve their convergence. These Krylov solvers can reduce the cost of pre-assembling the response matrices greatly. Numerical results with the INSTANT code are presented in order to show that they can be a good supplement on solving the PN-HFEM system. (author)",

author = "Yaqi Wang and Cristian Rabiti and Giuseppe Palmiotti",

year = "2011",

month = may,

day = "8",

language = "American English",

note = "International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering , M&C 2011 ; Conference date: 08-05-2011 Through 12-05-2011",

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Wang, Y, Rabiti, C & Palmiotti, G 2011, 'Krylov solvers preconditioned with the low-order red-black algorithm for the PN hybrid FEM for the INSTANT code', Paper presented at International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering , Rio de Janeiro, Brazil, 05/8/11 - 05/12/11. <https://inis.iaea.org/records/pbbna-z8963>

Krylov solvers preconditioned with the low-order red-black algorithm for the PN hybrid FEM for the INSTANT code. / Wang, Yaqi; Rabiti, Cristian; Palmiotti, Giuseppe.
2011. Paper presented at International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering , Rio de Janeiro, Brazil.

Research output: Contribution to conference › Paper › peer-review

TY - CONF

T1 - Krylov solvers preconditioned with the low-order red-black algorithm for the PN hybrid FEM for the INSTANT code

AU - Wang, Yaqi

AU - Rabiti, Cristian

AU - Palmiotti, Giuseppe

PY - 2011/5/8

Y1 - 2011/5/8

N2 - This paper proposes a new set of Krylov solvers, CG and GMRes, as an alternative of the Red-Black (RB) algorithm on on solving the steady-state one-speed neutron transport equation discretized with PN in angle and hybrid FEM (Finite Element Method) in space. A pre conditioner with the low-order RB iteration is designed to improve their convergence. These Krylov solvers can reduce the cost of pre-assembling the response matrices greatly. Numerical results with the INSTANT code are presented in order to show that they can be a good supplement on solving the PN-HFEM system. (author)

AB - This paper proposes a new set of Krylov solvers, CG and GMRes, as an alternative of the Red-Black (RB) algorithm on on solving the steady-state one-speed neutron transport equation discretized with PN in angle and hybrid FEM (Finite Element Method) in space. A pre conditioner with the low-order RB iteration is designed to improve their convergence. These Krylov solvers can reduce the cost of pre-assembling the response matrices greatly. Numerical results with the INSTANT code are presented in order to show that they can be a good supplement on solving the PN-HFEM system. (author)

M3 - Paper

T2 - International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering

Y2 - 8 May 2011 through 12 May 2011

ER -

Krylov solvers preconditioned with the low-order red-black algorithm for the PN hybrid FEM for the INSTANT code

Abstract

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