Bruno Carpentieri

By Bruno Carpentieri

Part of the book: Trends in Electromagnetism

By Bruno Carpentieri and Aldo Bonfiglioli

Implicit methods based on the Newton’s rootfinding algorithm are receiving an increasing attention for the solution of complex Computational Fluid Dynamics (CFD) applications due to their potential to converge in a very small number of iterations. This approach requires fast convergence acceleration techniques in order to compete with other conventional solvers, such as those based on artificial dissipation or upwind schemes, in terms of CPU time. In this chapter, we describe a multilevel variable-block Schur-complement-based preconditioning for the implicit solution of the Reynolds-averaged Navier-Stokes equations using unstructured grids on distributed-memory parallel computers. The proposed solver detects automatically exact or approximate dense structures in the linear system arising from the discretization, and exploits this information to enhance the robustness and improve the scalability of the block factorization. A complete study of the numerical and parallel performance of the solver is presented for the analysis of turbulent Navier-Stokes equations on a suite of three-dimensional test cases.

Part of the book: Computational Fluid Dynamics

By Salvatore Ventre, Bruno Carpentieri, Gaspare Giovinco, Antonello Tamburrino, Fabio Villone and Guglielmo Rubinacci

We present iterative solution strategies for solving efficiently Magneto-Quasi-Static (MQS) problems expressed in terms of an integral formulation based on the electric vector potential. Integral formulations give rise to discrete models characterized by linear systems with dense coefficient matrices. Iterative Krylov subspace methods combined with fast compression techniques for the matrix-vector product operation are the only viable approach for treating large scale problems, such as those considered in this study. We propose a fully algebraic preconditioning technique built upon the theory of H2-matrix representation that can be applied to different integral operators and to changes in the geometry, only by tuning a few parameters. Numerical experiments show that the proposed methodology performs much better than the existing one in terms of ability to reduce the number of iterations of a Krylov subspace method, especially for fast transient analysis.

Part of the book: Advances in Fusion Energy Research

By Mudassir Shams and Bruno Carpentieri

In this study, we propose a novel hybrid numerical optimization technique that combines iterative methods with a butterfly optimization scheme to solve nonlinear equations. The iterative methods, characterized by cubic convergence order, refine local solutions, while the butterfly optimization scheme enables global search. Our approach aims to improve efficiency and robustness by mitigating sensitivity to initial guesses. We conduct a local convergence analysis in Banach space and estimate convergence radii to guide the selection of initial values. The proposed technique is evaluated through engineering applications, demonstrating superior performance compared to classical methods and other optimization schemes such as particle swarm optimization, sperm swarm optimization, and ant line optimization.

Part of the book: Nonlinear Systems and Matrix Analysis

By Bruno Carpentieri

Part of the book: Quantum Computing

By Mudassir Shams and Bruno Carpentieri

The complexity of the nonlinear eigenvalue problem is too great for traditional analytical methods, particularly in engineering applications where dynamic behaviors and material nonlinearities are crucial. For this reason, this chapter presents a novel hybrid parallel technique based on multiplicative calculus as an effective way to handle scale-invariant processes without dealing with sum divergence issues. It offers improved precision and computational stability, making it especially appropriate for complex systems where ratios—rather than differences—are crucial. The results are verified in the nonlinear dynamical analysis of frame structures, a highly relevant applied engineering problem involving substantial deformations and material nonlinearities. The proposed formulation achieves a convergence order of three. The numerical findings reveal that our method performs better than existing strategies in the literature, with considerable improvements in residual error, computational efficiency, stability, and CPU time. These findings show the method’s potential application in handling real-world engineering challenges such as dynamic structural analysis.

Part of the book: Bridging Eigenvalue Theory and Practice