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Access status: Open Access ,
Modular fem framework »ModFEM« for generic scientific parallel simulations
(Wydawnictwa AGH, 2013) Michalik, Kazmimierz; Banaś, Krzysztof; Płaszewski, Przemysław; Cybułka, Paweł
We present the design for, and implementation of, aflexible and robust parallel modular finite element (FEM) framework called ModFEM. The designis based on reusable modules which use narrow and well-defined interfaces to cooperate. At the top of the architecture, there are problem - dependent modules. Problem - dependent modules can be additionally grouped together by »super-modules«. The structure allows for reusing the sequential code for parallel environments, and also supports solving multi-physics and multi-scale problems.
Access status: Open Access ,
Efficient simulations of large-scale convective heat transfer problems
(Wydawnictwa AGH, 2021) Goik, Damian; Banaś, Krzysztof; Bielański, Jan Gustaw; Chłoń, Kazimierz
We describe an approach for efficient solution of large-scale convective heat transfer problems that are formulated as coupled unsteady heat conduction and incompressible fluid-flow equations. The original problem is discretized over time using classical implicit methods, while stabilized finite elements are used for space discretization. The algorithm employed for the discretization of the fluid-flow problem uses Picard’s iterations to solve the arising nonlinear equations. Both problems (the heat transfer and Navier–Stokes equations) give rise to large sparse systems of linear equations. The systems are solved by using an iterative GMRES solver with suitable preconditioning. For the incompressible flow equations, we employ a special preconditioner that is based on an algebraic multigrid (AMG) technique. This paper presents algorithmic and implementation details of the solution procedure, which is suitably tuned – especially for ill-conditioned systems that arise from discretizations of incompressible Navier–Stokes equations. We describe a parallel implementation of the solver using MPI and elements from the PETSC library. The scalability of the solver is favorably compared with other methods, such as direct solvers and the standard GMRES method with ILU preconditioning.
Access status: Open Access ,
Artificial intelligence-enhanced algebraic multigrid for 3D finite element simulations
(Wydawnictwa AGH, 2026) Goik, Damian; Banaś, Krzysztof
The paper presents preliminary investigations into a strategy for solving linear systems resulting from 3D finite element simulations, based on the algebraic multigrid (AMG) method, enhanced using artificial intelligence techniques. In particular, we adapt to 3D problems the algorithm presented in Luz et al. (2020) for using a graph neural network to create the prolongation and restriction operators in a way that will improve convergence. The process of training the network proceeds on the basis of a set of system matrices obtainedfor tasks much smaller in scale than the target problem to be solved. Learning is aimed at decreasing the spectral radius of the error propagation matrix after applying modified prolongation and restriction. We describe some implementation details of the solver developed based on the presented strategy and show several numerical examples of its application for medium-sized problems.

Banaś, Krzysztof

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