@misc {42968,
	title = {Fractional Laplacians and Hybridized DG},
	howpublished = {Simula{\textquoteright}s Workshop on computational mechanics models on domains of heterogeneous dimensionality, Split, Croatia},
	year = {2022},
	author = {Kuchta, Miroslav and Budisa, Ana and Hu, Xiaozhe and Ludmil Tomov {Zikatanov} and Mardal, Kent-Andre}
}
@article {27769,
	title = {Block preconditioners for mixed-dimensional discretization of flow in fractured porous media},
	journal = {Computational Geosciences},
	year = {2020},
	month = {07/2020},
	publisher = { Springer},
	abstract = {In this paper, we are interested in an efficient numerical method for the mixed-dimensional approach to modeling single-phase flow in fractured porous media. The model introduces fractures and their intersections as lower-dimensional structures, and the mortar variable is used for flow coupling between the matrix and fractures. We consider a stable mixed finite element discretization of the problem, which results in a parameter-dependent linear system. For this, we develop block preconditioners based on the well-posedness of the discretization choice. The preconditioned iterative method demonstrates robustness with regard to discretization and physical parameters. The analytical results are verified on several examples of fracture network configurations, and notable results in reduction of number of iterations and computational time are obtained.},
	issn = {1420-0597},
	doi = {10.1007/s10596-020-09984-z},
	url = {https://link.springer.com/article/10.1007/s10596-020-09984-z},
	author = {Budisa, Ana and Hu, Xiaozhe}
}
@article {27770,
	title = {Mixed-Dimensional Auxiliary Space Preconditioners},
	journal = {SIAM Journal on Scientific Computing},
	volume = {42},
	year = {2020},
	month = {10/2020},
	pages = {A3367 - A3396},
	publisher = {SIAM},
	abstract = {This work introduces nodal auxiliary space preconditioners for discretizations of mixed-dimensional partial differential equations. We first consider the continuous setting and generalize the regular decomposition to this setting. With the use of conforming mixed finite element spaces, we then expand these results to the discrete case and obtain a decomposition in terms of nodal Lagrange elements. In turn, nodal preconditioners are proposed analogous to the auxiliary space preconditioners of Hiptmair and Xu [SIAM J. Numer. Anal., 45 (2007), pp. 2483--2509]. Numerical experiments show the performance of this preconditioner in the context of flow in fractured porous media.},
	issn = {1064-8275},
	doi = {10.1137/19M1292618},
	url = {https://epubs.siam.org/doi/pdf/10.1137/19M1292618},
	author = {Budisa, Ana and Wietse M. {Boon} and Hu, Xiaozhe}
}
@article {budisa2022haznics,
	title = {HAZniCS{\textendash}Software Components for Multiphysics Problems},
	journal = {arXiv preprint arXiv:2210.13274},
	publisher = {Arxiv},
	author = {Budisa, Ana and Hu, Xiaozhe and Kuchta, Miroslav and Mardal, Kent-Andre and Ludmil Tomov {Zikatanov}}
}
@article {budisa2022rational,
	title = {Rational approximation preconditioners for multiphysics problems},
	journal = {arXiv preprint arXiv:2209.11659},
	publisher = {Arxiv},
	author = {Budisa, Ana and Hu, Xiaozhe and Kuchta, Miroslav and Mardal, Kent-Andre and Ludmil Tomov {Zikatanov}}
}
