134 research outputs found

    FETI-DP algorithms for 2D Biot model with discontinuous Galerkin discretization

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    Dual-Primal Finite Element Tearing and Interconnecting (FETI-DP) algorithms are developed for a 2D Biot model. The model is formulated with mixed-finite elements as a saddle-point problem. The displacement u\mathbf{u} and the Darcy flux flow z\mathbf{z} are represented with P1P_1 piecewise continuous elements and pore-pressure pp with P0P_0 piecewise constant elements, {\it i.e.}, overall three fields with a stabilizing term. We have tested the functionality of FETI-DP with Dirichlet preconditioners. Numerical experiments show a signature of scalability of the resulting parallel algorithm in the compressible elasticity with permeable Darcy flow as well as almost incompressible elasticity.Comment: Accepted to the 27th International Conference on Domain Decomposition Methods (DD27), 8 pages. arXiv admin note: text overlap with arXiv:2211.1502

    BDDC preconditioners for virtual element approximations of the three-dimensional Stokes equations

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    The Virtual Element Method (VEM) is a novel family of numerical methods for approximating partial differential equations on very general polygonal or polyhedral computational grids. This work aims to propose a Balancing Domain Decomposition by Constraints (BDDC) preconditioner that allows using the conjugate gradient method to compute the solution of the saddle-point linear systems arising from the VEM discretization of the three-dimensional Stokes equations. We prove the scalability and quasi-optimality of the algorithm and confirm the theoretical findings with parallel computations. Numerical results with adaptively generated coarse spaces confirm the method's robustness in the presence of large jumps in the viscosity and with high-order VEM discretizations

    Formulation and analysis of a Schur complement method for fluid-structure interaction

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    This work presents a strongly coupled partitioned method for fluid-structure interaction (FSI) problems based on a monolithic formulation of the system which employs a Lagrange multiplier. We prove that both the semi-discrete and fully discrete formulations are well-posed. To derive a partitioned scheme, a Schur complement equation, which implicitly expresses the Lagrange multiplier and the fluid pressure in terms of the fluid velocity and structural displacement, is constructed based on the monolithic FSI system. Solving the Schur complement system at each time step allows for the decoupling of the fluid and structure subproblems, making the method non-iterative between subdomains. We investigate bounds for the condition number of the Schur complement matrix and present initial numerical results to demonstrate the performance of our approach, which attains the expected convergence rates.Comment: 27 pages, 4 figure

    Quasi-simultaneous coupling methods for partitioned problems in computational hemodynamics

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    The paper describes the numerical coupling challenges in multiphysics problems like the simulation of blood flow in compliant arteries. In addition to an iterative coupling between the fluid flow and elastic vessel walls, i.e. fluid-structure interaction, also the coupling between a detailed 3D local (arterial) flow model and a more global 0D model (representing a global circulation) is analyzed. Most of the coupling analysis is formulated in the more abstract setting of electrical-network models. Both, weak (segregated) and strong (monolithic) coupling approaches are studied, and their numerical stability limitations are discussed. Being a hybrid combination, the quasi-simultaneous coupling method, developed for partitioned problems in aerodynamics, is shown to be a robust and flexible approach for hemodynamic applications too

    Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference

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    The 6th ECCOMAS Young Investigators Conference YIC2021 will take place from July 7th through 9th, 2021 at Universitat Politècnica de València, Spain. The main objective is to bring together in a relaxed environment young students, researchers and professors from all areas related with computational science and engineering, as in the previous YIC conferences series organized under the auspices of the European Community on Computational Methods in Applied Sciences (ECCOMAS). Participation of senior scientists sharing their knowledge and experience is thus critical for this event.YIC 2021 is organized at Universitat Politécnica de València by the Sociedad Española de Métodos Numéricos en Ingeniería (SEMNI) and the Sociedad Española de Matemática Aplicada (SEMA). It is promoted by the ECCOMAS.The main goal of the YIC 2021 conference is to provide a forum for presenting and discussing the current state-of-the-art achievements on Computational Methods and Applied Sciences,including theoretical models, numerical methods, algorithmic strategies and challenging engineering applications.Nadal Soriano, E.; Rodrigo Cardiel, C.; Martínez Casas, J. (2022). Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. https://doi.org/10.4995/YIC2021.2021.15320EDITORIA

    Scalable Domain Decomposition for Parallel Solution of 3D Finite Element Multibody Rotorcraft Aeromechanics

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    A specialized mesh partitioner is developed for large-scale multibody three-dimensional finite element models. This partitioner enables modern domain decomposition algorithms to be leveraged for the parallel solution of complex, multibody, three-dimensional finite element-based rotor structural dynamics problems. The partitioner works with any domain decomposition algorithm, but contains special features for FETI-DP, a state-of-the-art iterative substructuring algorithm. The algorithm was implemented into an aeroelastic rotor solver X3D, with several modifications to improve performance. The parallel solver was applied to two practical test cases: the NASA Tiltrotor Aeroacoustic Model (TRAM) and the NASA Rotor Optimization for the Advancement of Mars eXploration (ROAMX) rotor blade. The mesh partitioner was developed from two sets of requirements: one standard to any domain decomposition algorithm and one specific to the FETI-DP method. The main feature of the partitioner is the ability to robustly partition any multibody structure, but with several special features for rotary-wing structures. The NASA TRAM, a 1/4 scale V-22 model, was specially released by NASA as a challenge test case. This model contained four flexible parts, six joints, nearly twenty composite material decks, a fluid-structure interface, and trim control inputs. The solver performance was studied for three test problems of increasing complexity: 1) an elementary beam, 2) the isolated TRAM blade, and 3) the TRAM blade and hub assembly. A key conclusion is that the use of a skyline solver for the coarse problem eliminates the coarse problem scalability barrier. Overall, the principle barrier of computational time that prevented the use of high-fidelity three-dimensional structures in rotorcraft is thus resolved. The two selected cases provided a template for how 3D structures should be used in the future. A detailed aeromechanical analysis of the NASA TRAM rotor was conducted. The solver was validated against experimental results in hover. The stresses in the blade and hub components were examined, illustrating the unique benefit of 3D structures. The NASA ROAMX blade was the first rotor blade to our knowledge designed exclusively with 3D structures. The torsional stability, blade loads, blade deformations, and 3D stresses/strains were evaluated for multiple blade designs before the final selection. The aeroelastic behavior of this blade was studied in steady and unsteady hover. Inertial effects were found to dominate over aerodynamics on Mars. The rotor blade was found to have sufficient factor of safety and damping for all test conditions. Over 20 thousand cases were executed with detailed stresses/strains as means of downselection, demonstrating the efficiency and utility of the parallel solver, and providing a roadmap for its use in future designs

    Stable discretizations and IETI-DP solvers for the Stokes system in multi-patch Isogeometric Analysis

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    We are interested in a fast solver for the Stokes equations, discretized with multi-patch Isogeometric Analysis. In the last years, several inf-sup stable discretizations for the Stokes problem have been proposed, often the analysis was restricted to single-patch domains. We focus on one of the simplest approaches, the isogeometric Taylor--Hood element. We show how stability results for single-patch domains can be carried over to multi-patch domains. While this is possible, the stability strongly depends on the shape of the geometry. We construct a Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) solver that does not suffer from that effect. We give a convergence analysis and provide numerical tests

    Multigrid and saddle-point preconditioners for unfitted finite element modelling of inclusions

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    In this work, we consider the modeling of inclusions in the material using an unfitted finite element method. In the unfitted methods, structured background meshes are used and only the underlying finite element space is modified to incorporate the discontinuities, such as inclusions. Hence, the unfitted methods provide a more flexible framework for modeling the materials with multiple inclusions. We employ the method of Lagrange multipliers for enforcing the interface conditions between the inclusions and matrix, this gives rise to the linear system of equations of saddle point type. We utilize the Uzawa method for solving the saddle point system and propose preconditioning strategies for primal and dual systems. For the dual systems, we review and compare the preconditioning strategies that are developed for FETI and SIMPLE methods. While for the primal system, we employ a tailored multigrid method specifically developed for the unfitted meshes. Lastly, the comparison between the proposed preconditioners is made through several numerical experiments
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