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Creators/Authors contains: "Kuchta, Miroslav"

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  1. ; ; ; (, Computers mathematics with applications)
    We introduce and analyze a coupled hybridizable discontinuous Galerkin/discontinuous Galerkin (HDG/DG) method for porous media in which we allow fully and partly immersed faults, and faults that separate the domain into two disjoint subdomains. We prove well-posedness and present an a priori error analysis of the discretization. Numerical examples verify our analysis. 
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    Free, publicly-accessible full text available December 15, 2026
  2. ; ; (, SIAM Journal on Numerical Analysis)
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  3. ; ; ; ; (, SIAM journal on scientific computing)
    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 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 regard to the number of the degrees of freedom of the system on several numerical examples related to the biophysical processes in the brain, namely, the electric signaling in excitable tissue modeled by bidomain, the extracellular-membrane-intracellular (EMI) model, and reduced EMI equations. 
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    Accepted Manuscript Full Text Available
  4. ; ; ; ; (, ACM Transactions on Mathematical Software)
    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 this article is on the design and implementation 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 the flow of cerebrospinal fluid in the human brain and the mixed-dimensional model of electrodiffusion in the brain tissue. 
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    Full Text Available 
  5. ; ; ; ; (, the Tenth International Conference on Numerical Methods and Applications, Lecture Notes in Computer Science)
    Georgiev, Ivan; Datcheva, Maria; Georgiev, Krassimir; Nikolov, Geno (Ed.)
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