TEST

Publications

Code

Loïc Gouarin and I have written a domain decomposition code in PETSc4py. It incorporates the GenEO coarse spaces (for Additive Schwarz and Neumann-Neumann) as well as adaptive multipreconditioned CG and AWG.

Articles

N. Spillane, D. Szyld.

New Convergence Analysis of GMRES with Weighted Norms, Preconditioning and Deflation, Leading to a New Deflation Space.

Preprint, 2023.

L. Gouarin, N. Spillane.

Fully algebraic domain decomposition preconditioners with adaptive spectral bounds.

Accepted for publication by Electronic Transactions on Numerical Analysis (ETNA), 2023.

N. Spillane.

Hermitian Preconditioning for a class of Non-Hermitian Linear Systems.

Accepted for publication by SIAM Journal on Scientific Computing (SISC), 2024.

N. Spillane.

An abstract theory of domain decomposition methods with coarse spaces of the GenEO family.

Preprint, 2021.

N. Spillane.

Toward a new fully algebraic preconditioner for symmetric positive definite problem.

26th International Domain Decomposition Conference, Dec 2020, HONG KONG, China, 2021.

C. Bovet, P. Gosselet, N. Spillane

Multipreconditioning for nonsymmetric problems: the case of orthomin and biCG.

C. R. Math. Acad. Sci. Paris 355, no. 3, 354–358, 2017.

C. Bovet, P. Gosselet, A. Parret-Fréaud, N. Spillane.

Adaptive multipreconditioned FETI: scalability results and robustness assessment.

Computers and Structures, 2017.

N. Spillane.

Algebraic Adaptive Multi Preconditioning applied to Restricted Additive Schwarz.

Proceedings of the DD23 conference, 2016.

N. Spillane.

An Adaptive Multi Preconditioned Conjugate Gradient Algorithm.

SIAM Journal on Scientific Computing, accepted, 2016. Preprint available online hal-01170059.

P. Gosselet, D. J. Rixen, F.-X. Roux, N. Spillane.

Simultaneous-FETI and Block-FETI: robust domain decomposition with multiple search directions.

International Journal for Numerical Methods in Engineering, 104(10):905–927, 2015.

N. Spillane, V. Dolean, P. Hauret, F. Nataf, C. Pechstein and R. Scheichl.

Abstract Robust Coarse Spaces for Systems of PDEs via Gereralized Eigenproblems in the Overlap.

Numerische Mathematik, 126(4):741–770, 2014.

N. Spillane, D. J. Rixen.

Automatic spectral coarse spaces for robust FETI and BDD algorithms.

International Journal for Numerical Methods in Engineering, 95(11):953–990, 2013.

N. Spillane, V. Dolean, P. Hauret, F. Nataf, C. Pechstein and R. Scheichl.

Achieving robustness through coarse space enrichment in the two level Schwarz framework.

Proceedings of Domain decomposition methods in science and engineering XXI, 2013.

N. Spillane, V. Dolean, P. Hauret, F. Nataf, D. J. Rixen.

Solving generalized eigenvalue problems on the interfaces to build a robust two level FETI method.

Comptes Rendus Mathematique, published online 04/10/13, (hal-00756840), 2013.

P. Jolivet, V. Dolean, F. Hecht, F. Nataf, C Prud'Homme, and N. Spillane.

High performance domain decomposition methods on massively parallel architectures with freefem++.

Journal of Numerical Mathematics, 20(3-4):287–302, 2012.

V. Dolean, F. Nataf, R. Scheichl, and N. Spillane.

Analysis of a two-level Schwarz method with coarse spaces based on local Dirichlet–to–Neumann maps.

Computational Methods in Applied Mechanics, 12(4), 2012.

N. Spillane, V. Dolean, P. Hauret, F. Nataf, C. Pechstein and R. Scheichl.

A robust two-level domain decomposition preconditioner for systems of PDEs.

Comptes Rendus Mathematique, 349(23-24):1255–1259, 2011.

F. Nataf, H. Xiang, V. Dolean, and N. Spillane.

A coarse space construction based on local Dirichlet to Neumann maps.

SIAM Journal on Scientific Computing, 33:1623–1642, 2011.

Phd thesis (2014)

Robust Domain Decomposition Methods for Symmetric Positive Definite Problems (manuscript).

I was a PhD student at Laboratoire Jacques Louis Lions in Paris between September 2010 and January 2014. My advisors were Frédéric Nataf (LJLL) and Patrice Hauret (Michelin).