arXiv subjects

Jakub Kružík

Publications and source records attributed to Jakub Kružík.

4 recordsLinked to original sources

arXiv2026

Mixed-Precision Computing for Scientific Discovery: Formats, Co-Design, and Responsible Approximation

Reduced and mixed precision have moved from a niche optimization to a central design axis in scientific computing and engineering, driven by energy constraints, heterogeneous accelerators, and the convergence of simulation and machine learning. This paper organizes the landscape around seven coupled themes---number formats, floating-point emulation, emerging architectures, hardware/software co-design, relation to other approximations, software design, and precision as a multilevel resource ---and, for each theme, synthesizes the state of the art, future directions, and open questions. We emphasize \emph{energy per trusted solution} as the core objective, and we frame \say{recklessly responsible} computing as a pragmatic doctrine: exploit low precision aggressively, but with systematic detection, escalation, and certification pathways.

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arXiv2026

Accelerating MPGP-type Methods Through Preconditioning

This work investigates the acceleration of MPGP-type algorithms using preconditioning for the solution of quadratic programming problems. The preconditioning needs to be done only on the free set so as not to change the constraints. A variant of preconditioning restricted to the free set is the preconditioning in face. The inner preconditioner in preconditioning in face needs to be recomputed or updated every time the free set changes. Here, we investigate an approximate variant of preconditioning in face that computes the inner preconditioner only once. We analyze the error of the approximate variant, give a sharp bound on the condition number of the preconditioned operator, and provide numerical experiments demonstrating that very large speedups can be achieved by the approximate variant.

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arXiv2025

Convex optimization problems inspired by geotechnical stability analysis

This paper is motivated by the limit load, limit analysis and shear strength reduction methods, which are commonly employed in geotechnical stability analysis or similar applications. The aim is to make these methods more approachable by introducing a unified framework based on abstract convex optimization and its parametric studies. We establish suitable assumptions on the abstract problems that capture the selected features of these methods and facilitate rigorous theoretical investigation. Further, we propose continuation techniques tailored to the resulting parametric problem formulations and show that the developed abstract framework could also be useful outside the domain of geotechnical stability analysis. The main results are illustrated with analytical and numerical examples. The numerical example deals with a 3D slope stability problem.

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arXiv2024

On the parallel solution of hydro-mechanical problems with fracture networks and contact conditions

The paper presents a numerical method for simulating flow and mechanics in fractured rock. The governing equations that couple the effects in the rock mass and in the fractures are obtained using the discrete fracture-matrix approach. The fracture flow is driven by the cubic law, and the contact conditions prevent fractures from self-penetration. A stable finite element discretization is proposed for the displacement-pressure-flux formulation. The resulting nonlinear algebraic system of equations and inequalities is decoupled using a robust iterative splitting into the linearized flow subproblem, and the quadratic programming problem for the mechanical part. The non-penetration conditions are solved by means of dualization and an optimal quadratic programming algorithm. The capability of the numerical scheme is demonstrated on a benchmark problem for tunnel excavation with hundreds of fractures in 3D. The paper's novelty consists in a combination of three crucial ingredients: (i) application of discrete fracture-matrix approach to poroelasticity, (ii) robust iterative splitting of resulting nonlinear algebraic system working for real-world 3D problems, and (iii) efficient solution of its mechanical quadratic programming part with a large number of fractures in mutual contact by means of own solvers implemented into an in-house software library.

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