, ON THE PARALLEL EFFICIENCY OF THE SOLVE PHASE WITH MULTIPLE SPARSE RIGHT-HAND SIDES
The transitive reduction of a directed graph, In: SIAM Journal on Computing, vol.1, pp.131-137, 1972. ,
Data Structures and Algorithms, 1983. ,
Improving multifrontal methods by means of block low-rank representations, In: SIAM Journal on Scientific Computing, vol.37, pp.1451-1474, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01237169
Fast 3D frequency-domain full waveform inversion with a parallel Block Low-Rank multifrontal direct solver: application to OBC data from the North Sea, In: Geophysics, vol.81, pp.363-383, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01349119
On the complexity of the Block Low-Rank multifrontal factorization, In: SIAM Journal on Scientific Computing, vol.39, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01672943
Performance and Scalability of the Block Low-Rank Multifrontal Factorization on Multicore Architectures, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01505070
An approximate minimum degree ordering algorithm, In: SIAM Journal on Matrix Analysis and Applications, vol.17, pp.886-905, 1996. ,
Analysis of the Solution Phase of a Parallel Multifrontal Approach, In: Parallel Computing, vol.36, pp.3-15, 2010. ,
URL : https://hal.archives-ouvertes.fr/inria-00413470
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling, In: SIAM Journal on Matrix Analysis and Applications, vol.23, pp.15-41, 2001. ,
URL : https://hal.archives-ouvertes.fr/hal-00808293
On computing inverse entries of a sparse matrix in an out-of-core environment, In: SIAM Journal on Scientific Computing, vol.34, pp.1975-1999, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00763556
Parallel computation of entries of A-1, In: SIAM Journal on Scientific Computing, vol.37, pp.268-284, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-00945082
Hybrid scheduling for the parallel solution of linear systems, Parallel Computing, vol.32, issue.2, pp.136-156, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-00358623
On Exploiting Sparsity of Multiple Right-Hand Sides in Sparse Direct Solvers ,
URL : https://hal.archives-ouvertes.fr/hal-01955659
Modeling 1D distributed-memory dense kernels for an asynchronous multifrontal sparse solver, High Performance Computing for Computational Science, VECPAR 201411th International Conference, pp.156-169, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01355356
An unsymmetrized multifrontal LU factorization, In: SIAM Journal on Matrix Analysis and Applications, vol.24, pp.553-569, 2002. ,
Bridging the gap between flat and hierarchical low-rank matrix formats: the multilevel BLR format, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01774642
A fast block low-rank dense solver with applications to finite-element matrices, In: Journal of Computational Physics, vol.304, pp.170-188, 2016. ,
Three-Dimensional Electromagnetic Modelling and Inversion from Theory to Application, In: Surveys in Geophysics, vol.26, issue.6, pp.1573-0956, 2005. ,
Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems, vol.63, 2008. ,
Sparse Marix Reordering Schemes for Browsing Hypertext, In: Lecture notes in applied mathematic, vol.32, pp.99-124, 1996. ,
ScaLAPACK Users' Guide, 1997. ,
Introduction to hierarchical matrices with applications, In: Engineering analysis with boundary elements, vol.27, pp.405-422, 2003. ,
Numerical Modelling in Geo-Electromagnetics: Advances and Challenges, In: Surveys in Geophysics, vol.31, issue.2, pp.225-245, 2010. ,
Ten years of marine CSEM for hydrocarbon exploration, In: GEOPHYSICS, vol.75, 2010. ,
Reducing the bandwidth of sparse symmetric matrices, Proceedings 24th National Conference of the Association for Computing Machinery, pp.157-172, 1969. ,
Algorithm 679: A set of Level 3 Basic Linear Algebra Subprograms, In: ACM Transactions on Mathematical Software, vol.16, pp.1-17, 1990. ,
On the number of nonzeros added when Gaussian elimination is performed on sparse random matrices, In: mathematics of computation, vol.28, pp.219-230, 1974. ,
, Direct Methods for Sparse Matrices, 2017.
A note on the work involved in no-fill sparse matrix factorization, In: IMA Journal of Numerical Analysis, vol.18, pp.1145-1151, 1983. ,
The multifrontal solution of indefinite sparse symmetric linear systems, In: ACM Transactions on Mathematical Software, vol.9, pp.302-325, 1983. ,
The multifrontal solution of unsymmetric sets of linear systems, In: SIAM Journal on Scientific and Statistical Computing, vol.5, pp.633-641, 1984. ,
The theory of elimination trees for sparse unsymmetric matrices, In: SIAM Journal on Matrix Analysis and Applications, vol.26, pp.686-705, 2005. ,
Remote sensing of hydrocarbon layers by seabed logging (SBL): Results from a cruise offshore Angola, In: The Leading Edge, vol.21, pp.972-982, 2002. ,
Nested dissection of a regular finite-element mesh, In: SIAM Journal on Numerical Analysis, vol.10, pp.345-363, 1973. ,
Predicting structure in sparse matrix computations, In: SIAM Journal on Matrix Analysis and Applications, vol.15, pp.62-79, 1994. ,
Elimination structures for unsymmetric sparse LU factors, In: SIAM Journal on Matrix Analysis and Applications, vol.14, pp.334-352, 1993. ,
An efficient algorithm to compute row and column counts for sparse cholesky factorization, In: SIAM Journal on Scientific Computing, vol.15, pp.1075-1091, 1994. ,
DOI : 10.2172/10177954
URL : https://digital.library.unt.edu/ark:/67531/metadc1450948/m2/1/high_res_d/7258591.pdf
, Matrix Computations, 2012.
A sparse matrix arithmetic based on H-matrices. Part I: introduction to H-matrices, In: Computing, vol.62, pp.10-485, 1999. ,
DOI : 10.1007/s006070050015
The next generation offshore CSEM acquisition system, SEG Technical Program Expanded Abstracts, pp.1194-1198, 2017. ,
DOI : 10.1190/segam2017-17725809.1
Delineating salt bodies with 3D CSEM technology, Salt Challenges in Hydrocarbon Exploration, SEG Annual Meeting Postconvention Workshop, 2015. ,
A frontal solution program for finite-element analysis, In: Int. Journal of Numerical Methods in Engineering, vol.2, pp.5-32, 1970. ,
METIS-A Software Package for Partitioning Unstructured Graphs, Partitioning Meshes, and Computing Fill-Reducing Orderings of Sparse Matrices-Version 4.0. University of Minnesota, 1998. ,
Basic Linear Algebra Subprograms for Fortran Usage, pp.308-323, 1979. ,
DOI : 10.1145/355841.355847
URL : http://hdl.handle.net/2060/19780018835
Modification of the Minimum Degree Algorithm by Multiple Elimination, In: ACM Transactions on Mathematical Software, vol.11, pp.141-153, 1985. ,
On the storage requirement in the out-of-core multifrontal method for sparse factorization, pp.127-148, 1986. ,
The multifrontal method for sparse matrix solution: Theory and Practice, pp.82-109, 1992. ,
DOI : 10.1137/1034004
The Role of Elimination Trees in Sparse Factorization, In: SIAM Journal on Matrix Analysis and Applications, vol.11, pp.134-172, 1990. ,
Block Low-Rank multifrontal solvers: complexity, performance, and scalability, 2017. ,
URL : https://hal.archives-ouvertes.fr/tel-01708791
Performance of greedy heuristics for sparse Cholesky factorization, In: SIAM Journal on Matrix Analysis and Applications, vol.20, pp.902-914, 1999. ,
Comparing large-scale 3D Gauss-Newton and BFGS CSEM inversions, SEG Technical Program Expanded Abstracts, pp.872-877, 2016. ,
DOI : 10.1190/segam2016-13858633.1
SCOTCH and LIBSCOTCH 5.0 User's guide, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00410327
A Mapping Algorithm for Parallel Sparse Cholesky Factorization, In: SIAM Journal on Scientific Computing, vol.14, issue.5, pp.1253-1257, 1993. ,
DOI : 10.1137/0914074
Reducing the Total Bandwidth of a Sparse Unsymmetric Matrix, In: SIAM Journal on Matrix Analysis and Applications, vol.28, issue.3, pp.805-821, 2006. ,
A Graph-Theoretic Study of the Numerical Solution of Sparse Positive Definite Systems of Linear Equations, Graph Theory and Computing, 1972. ,
Algorithmic aspects of vertex elimination on graphs, In: SIAM Journal on Computing, vol.5, pp.266-283, 1976. ,
DOI : 10.1137/0205021
Memory and performance issues in parallel multifrontal factorizations and triangular solutions with sparse right-hand sides, 2012. ,
URL : https://hal.archives-ouvertes.fr/tel-00785748
A new implementation of sparse Gaussian elimination, In: ACM Transactions on Mathematical Software, vol.8, pp.256-276, 1982. ,
DOI : 10.1145/356004.356006
A note on the solve phase of a multicore solver, 2010. ,
Large-scale 3D EM modeling with a Block Low-Rank multifrontal direct solver, In: Geophysical Journal International, vol.209, pp.1558-1571, 2017. ,
DOI : 10.1093/gji/ggx106
URL : https://hal.archives-ouvertes.fr/hal-01672952
Parallel triangular solution in the out-of-core multifrontal approach for solving large sparse linear systems, 2009. ,
Controlled-Source Electromagnetic Approaches for Hydrocarbon Exploration and Monitoring on Land, In: Surveys in Geophysics, vol.37, issue.1, pp.47-80, 2016. ,
DOI : 10.1007/s10712-015-9336-0
Inversion of seismic reflection data in the acoustic approximation, Geophysics 49, vol.8, pp.1259-1266, 1984. ,
Improving multifrontal solvers by means of algebraic block low-rank representations, 2013. ,
URL : https://hal.archives-ouvertes.fr/tel-00934939
Efficient Structured Multifrontal Factorization for General Large Sparse Matrices, In: SIAM Journal on Scientific Computing, vol.35, 2013. ,
DOI : 10.1137/120867032
Fast Algorithms for hierarchically semiseparable matrices, In: Numerical Linear Algebra with Applications, vol.17, pp.953-976, 2010. ,
DOI : 10.1002/nla.691
URL : http://crd.lbl.gov/~xiaoye/LBNL-62897.pdf
On Partitioning and Reordering Problems in a Hierarchically Parallel Hybrid Linear Solver, 2013 IEEE 27th International Parallel and Distributed Processing Symposium Workshops & PhD Forum (IPDPSW), pp.1391-1400, 2013. ,
DOI : 10.1109/ipdpsw.2013.170
URL : https://hal.archives-ouvertes.fr/hal-00923447
Computing the Minimum Fill-In is NP-Complete, In: SIAM Journal on Algebraic and Discrete Methods, vol.2, pp.77-79, 1981. ,
DOI : 10.1137/0602010
URL : http://dml.cz/bitstream/handle/10338.dmlcz/140775/Kybernetika_46-2010-4_4.pdf
, APPENDIX. BIBLIOGRAPHY
Interactively Cutting and Constraining Vertices in Meshes Using Augmented Matrices, In: ACM Trans. Graph, vol.35, issue.2, 2016. ,
DOI : 10.1145/2856317
URL : http://dl.acm.org/ft_gateway.cfm?id=2856317&type=pdf
AMPS: An Augmented Matrix Formulation for Principal Submatrix Updates with Application to Power Grids, In: SIAM Journal on Scientific Computing, vol.39, pp.809-827, 2017. ,
DOI : 10.1137/16m1082755
URL : http://arxiv.org/pdf/1706.03147
3D inversion of marine CSEM data using a fast finite-difference time-domain forward code and approximate hessian-based optimization, SEG Technical Program Expanded Abstracts, pp.614-618, 2008. ,
On Exploiting Sparsity of Multiple Right-Hand Sides in Sparse Direct Solvers, In: SIAM Journal on Scientific Computing, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01955659
, Articles in International Refereed Journals
Exploiting the sparsity of right-hand sides to improve the asymptotic complexity of low-rank sparse direct solvers, In: SIAM Journal on Scientific Computing ,
Efficient use of sparsity by direct solvers applied to 3D controlled-source EM problems ,
URL : https://hal.archives-ouvertes.fr/hal-01912713
, Abstracts in International Refereed Workshops
Fast direct solver for 3D marine controlled-source EM problems based on sparsity utilization and BLR approximation, 24th EM Induction Workshop EMIW2018, 2018. ,
Elimination Tree Flattening to Exploit Right-Hand Sides Sparsity, SIAM Workshop on Combinatorial Scientific Computing 2018. 2 pages extended abstract, 2018. ,
, Communications in International Conferences
Complexity and parallelism of the solution phase in sparse direct solvers, 10th International Workshop on Parallel Matrix Algorithms and Applications PMAA18, 2018. ,
Direct solution of sparse systems of linear equations with sparse multiple right-hand sides, In: Sparse Days. Cerfacs, 2017. ,
On the Solution Phase of Sparse Direct Solvers with Many Right-Hand Sides, SIAM Conference on Computational Science and Engineering (SIAM CSE17), 2017. ,
Avancées récentes et prochains défis de la phase de résolution pour les solveurs directs creux, 2017. ,
Performance of the Solution Phase: Recent Work and Perspectives, 2017. ,
Recent advances on the solution phase of sparse solvers with multiple sparse right-hand sides, In: MUMPS User's days. Inria, 2017. ,
When the Solution Phase is the Most Critical Part of Computation, Solveurs linéaires HPC pour les études industrielles, 2017. ,