@article {43269,
	title = {Algebraic multigrid methods for metric-perturbed coupled problems},
	journal = {SIAM J. Sci. Comput.},
	year = {2023},
	publisher = {SIAM},
	abstract = {We develop multilevel methods for interface-driven multiphysics problems that can be coupled across dimensions and where complexity and strength of the interface coupling deteriorates the performance of standard methods. We focus on solvers based on aggregation-based algebraic multigrid methods with custom smoothers that preserve the coupling information on each coarse level. We prove that with the proper choice of subspace splitting we obtain uniform convergence in discretization and physical parameters in the two-level setting. Additionally, we show parameter robustness and scalability with regards to number of the degrees of freedom of the system on several numerical examples related to the biophysical processes in the brain, namely the electric signalling in excitable tissue modeled by bidomain, EMI and reduced EMI equations.},
	url = {https://arxiv.org/abs/2305.06073},
	author = {Budisa, Ana and Hu, Xiaozhe and Kuchta, Miroslav and Mardal, Kent-Andre and Ludmil Tomov {Zikatanov}}
}
@inproceedings {42935,
	title = {Rational approximation preconditioners for multiphysics problems},
	journal = {Numerical Methods and Applications (NMA 2022)},
	volume = {13858},
	year = {2023},
	month = {05/2023},
	pages = {100-113},
	publisher = { Springer},
	edition = {Lecture Notes in Computer Science},
	address = {Cham},
	abstract = {We consider a class of mathematical models describing multiphysics phenomena interacting through interfaces. On such interfaces, the traces of the fields lie (approximately) in the range of a weighted sum of two fractional differential operators. We use a rational function approximation to precondition such operators. We first demonstrate the robustness of the approximation for ordinary functions given by weighted sums of fractional exponents. Additionally, we present more realistic examples utilizing the proposed preconditioning techniques in interface coupling between Darcy and Stokes equations.},
	keywords = {Multiphysics, preconditioning, Rational approximation},
	isbn = {978-3-031-32412-3},
	doi = {10.1007/978-3-031-32412-3_9},
	url = {https://doi.org/10.1007/978-3-031-32412-3_9},
	author = {Budisa, Ana and Hu, Xiaozhe and Kuchta, Miroslav and Mardal, Kent-Andre and Ludmil Tomov {Zikatanov}},
	editor = {Georgiev, Ivan and Datcheva, Maria and Georgiev, Krassimir and Nikolov, Geno}
}
@article {42936,
	title = {HAZniCS {\textendash} Software Components for Multiphysics Problems},
	journal = {ACM Transactions on Mathematical Software},
	year = {2022},
	publisher = {ACM},
	abstract = {We introduce the software toolbox HAZniCS for solving interface-coupled multiphysics problems. HAZniCS is a suite of modules that combines the well-known FEniCS framework for finite element discretization with solver and graph library HAZmath. The focus of the paper is on the design and implementation of a pool of robust and efficient solver algorithms which tackle issues related to the complex interfacial coupling of the physical problems often encountered in applications in brain biomechanics. The robustness and efficiency of the numerical algorithms and methods is shown in several numerical examples, namely the Darcy-Stokes equations that model flow of cerebrospinal fluid in the human brain and the mixed-dimensional model of electrodiffusion in the brain tissue.},
	author = {Budisa, Ana and Hu, Xiaozhe and Kuchta, Miroslav and Mardal, Kent-Andre and Ludmil Tomov {Zikatanov}}
}
