Kruse, C., Sosonkina, M., Arioli, M., Tardieu, N. and Ruede, U. (2020) Parallel Performance of an Iterative Solver Based on the Golub-Kahan Bidiagonalization

[bibtex]

@ARTICLE{AR-PA-20-11,
author = {Kruse, C. and Sosonkina, M. and Arioli, M. and Tardieu, N. and Ruede, U. },
title = {Parallel Performance of an Iterative Solver Based on the Golub-Kahan Bidiagonalization},
year = {2020},
abstract = {We present an iterative method based on a generalization of the Golub-Kahan bidiagonalization for solving indenite matrices with a 2x2 block structure. We focus in particular on our recent implementation of the algorithm using the parallel numerical library PETSc. Since the algorithm is a nested solver, we investigate dierent choices for parallel inner solvers and show its strong scalability for two Stokes test problems. The algorithm is found to be scalable for large sparse problems.}}

Kruse, C., Sosonkina, M., Arioli, M., Tardieu, N. and Ruede, U. (2020) Parallel solution of saddle point systems with nested iterative solvers based on the Golub-Kahan Bidiagonalization

[bibtex]

@ARTICLE{AR-PA-20-17,
author = {Kruse, C. and Sosonkina, M. and Arioli, M. and Tardieu, N. and Ruede, U. },
title = {Parallel solution of saddle point systems with nested iterative solvers based on the Golub-Kahan Bidiagonalization},
year = {2020}}

Barucq, H., M'Barek, F., Kruse, C. and Tordeux, S. (2019) Sparsified discrete wave problem involving a radiation condition on a prolate spheroidal surface, IMA Journal of Numerical Analysis, doi: 10.1093/imanum/drz051

[bibtex]
[url] [pdf]

@ARTICLE{AR-PA-19-226,
author = {Barucq, H. and M'Barek, F. and Kruse, C. and Tordeux, S. },
title = {Sparsified discrete wave problem involving a radiation condition on a prolate spheroidal surface},
year = {2019},
doi = {10.1093/imanum/drz051},
journal = {IMA Journal of Numerical Analysis},
abstract = {We develop and analyse a high-order outgoing radiation boundary condition for solving three-dimensional scattering problems by elongated obstacles. This Dirichlet-to-Neumann condition is constructed using the classical method of separation of variables that allows one to define the scattered field in a truncated domain. It reads as an infinite series that is truncated for numerical purposes. The radiation condition is implemented in a finite element framework represented by a large dense matrix. Fortunately, the dense matrix can be decomposed into a full block matrix that involves the degrees of freedom on the exterior boundary and a sparse finite element matrix. The inversion of the full block is avoided by using a Sherman–Morrison algorithm that reduces the memory usage drastically. Despite being of high order, this method has only a low memory cost.},
pdf = {https://doi.org/10.1093/imanum/drz051},
url = {https://academic.oup.com/imajna/advance-article-abstract/doi/10.1093/imanum/drz051/5627734}}

Banks, H.T., Doumic, M. and Kruse, C. (2017) A numerical scheme for the early steps of nucleation-aggregation models, Journal of Mathematical Biology, 74 (1-2) , pp. 259–287, ISSN 0303-6812, doi: 10.1007/s00285-016-1026-0

[bibtex] [pdf]

@ARTICLE{AR-PA-17-326,
author = {Banks, H.T. and Doumic, M. and Kruse, C. },
title = {A numerical scheme for the early steps of nucleation-aggregation models},
year = {2017},
number = {1-2},
volume = {74},
pages = {259–287},
issn = {0303-6812},
doi = {10.1007/s00285-016-1026-0},
journal = {Journal of Mathematical Biology},
keywords = {Polymerization, Aggregation-fragmentation models, Finite volume schemes, Adaptive grid },
pdf = {https://doi.org/10.1007/s00285-016-1026-0}}

Arioli, M., Kruse, C., Ruede, U. and Tardieu, N. (2018) An iterative generalized Golub-Kahan algorithm for problems in structural mechanics, Cerfacs, Toulouse, France

[bibtex]

@TECHREPORT{TR-PA-18-159,
author = {Arioli, M. and Kruse, C. and Ruede, U. and Tardieu, N. },
title = {An iterative generalized Golub-Kahan algorithm for problems in structural mechanics},
year = {2018},
institution = {Cerfacs, Toulouse, France},
month = {8},
abstract = {This paper studies the Craig variant of the Golub-Kahan bidiagonalization algorithm as an iterative solver for linear systems with saddle point structure. Such symmetric indefinite systems in 2x2 block form arise in many applications, but standard iterative solvers are often found to perform poorly on them and robust preconditioners may not be available. Specifically, such systems arise in structural mechanics, when a semidefinite finite element stiffness matrix is augmented with linear multi-point constraints via Lagrange multipliers. Engineers often use such multi-point constraints to introduce boundary or coupling conditions into complex finite element models. The article will present a systematic convergence study of the Golub-Kahan algorithm for a sequence of test problems of increasing complexity, including concrete structures enforced with pretension cables and the coupled finite element model of a reactor containment building. When the systems are suitably transformed using augmented Lagrangians on the semidefinite block and when the constraint equations are properly scaled, the Golub-Kahan algorithm is found to exhibit excellent convergence that depends only weakly on the size of the model. The new algorithm is found to be robust in practical cases that are otherwise considered to be difficult for iterative solvers.}}