# Publications

## 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).

## Code

## Articles

L. Gouarin, N. Spillane.

Fully algebraic domain decomposition preconditioners with adaptive spectral bounds.

*Preprint, 2021.*

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.

*Preprint, 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.*