A novel block non-symmetric preconditioner for mixed-hybrid finite-element-based flow simulations

In this work we propose a novel block preconditioner, labelled Explicit Decoupling Factor Approximation (EDFA), to accelerate the convergence of Krylov subspace solvers used to address the sequence of non-symmetric systems of linear equations originating from flow simulations in porous media. The flow model is discretized blending the Mixed Hybrid Finite Element (MHFE) method for Darcy's equation with the Finite Volume (FV) scheme for the mass conservation. The EDFA preconditioner is characterized by two features: the exploitation of the system matrix decoupling factors to recast the Schur complement and their inexact fully-parallel computation by means of restriction operators. We introduce two adaptive techniques aimed at building the restriction operators according to the properties of the system at hand. The proposed block preconditioner has been tested through an extensive experimentation on both synthetic and real-case applications, pointing out its robustness and computational efficiency

A Comparative Study Based on Patient-Specific Fluid-Structure Interaction Modeling of Cerebral Aneurysms

The Team for Advanced Flow Simulation and Modeling (T*AFSM) at Rice University has been developing techniques to address the computational challenges involved in fluid-structure interaction (FSI) modeling. The Stabilized Space-Time FSI (SSTFSI) core technologies, in conjunction with an array of special techniques, is used in a comparative study of patient-specific cerebral aneurysms. Ten cases, from three different locations, are studied, half of which were ruptured. The study compares the wall shear stress, oscillatory shear index, and the arterial-wall stress and stretch, with the original motivation of finding significant differences between ruptured and unruptured aneurysms. Simpler approaches to computer modeling of cerebral aneurysms are also compared to FSI modeling

Uncertainty Quantification for a Blood Pump Device with Generalized Polynomial Chaos Expansion

Nowadays, an increasing number of numerical modeling techniques, notably by means of the finite element method (FEM), are involved in the industrial design process and play a vital role in the area of the biomedical engineering. Particularly, the computational fluid dynamics (CFD) has become a promising tool for investigating the fluid behavior and has also been used to study the cardiovascular hemodynamics to predict the blood flow in the cardiovascular system over the recent decades. However, simulating a fluid in rotational frames is not trivial, as the classical fluid calculation considers that the geometry of the fluid domain does not alter along the time. In the meanwhile, due to the high rotating speed and the complex geometry of the ventricular assist device (VAD), a turbulent flow must be developed inside the pump housing. The Navier-Stokes equations are not applicable in respect of our available computing resource, additional assumptions and approaches are often applied as a means to model the eddy formation and cope with numerical instabilities. For many applications, there is still a big gap between the experimental data and the numerical results. Some of the discrepancies come especially from uncertain data which are used in the physical model, therefore, Uncertainty Quantification (UQ) comes into play. The Galerkin-based polynomial chaos expansion method delivers directly the mean and higher stochastic moments in a closed form. Due to the Galerkin projection’s properties, the spectral convergence is achieved. This thesis is dedicated to developing an efficient model to simulate the blood pump assuming uncertain parametric input sources. In a first step, we develop the shear layer update approach built on the Shear-Slip Mesh Update Method (SSMUM), our proposition facilitates the update procedure in parallel computing by forcing the local vector to retain the same structure. In a second step, we focus on the Variational Multiscale method (VMS) in order to handle the numerical instability and approximate the turbulent behavior in the blood. As a consequence of utilizing the intrusive Polynomial Chaos formulation, a highly coupled system needs to be solved in an efficient manner. Accordingly, we take advantage of the Multilevel preconditioner to precondition our stochastic Galerkin system, in which the Mean-based preconditioner is prescribed to be the smoother. Besides, the mean block is preconditioned with the Schur-Complement method, which leads to an acceleration of the solution process. Hence, by developing and combining the proposed solvers and preconditioners, dealing with a large coupled stochastic fluid problem on a modern computer architecture is then feasible. Furthermore, based on the stochastic solutions obtained from the previous described system, we obtain valuable information about the blood flow accompanied with certain level of confidence, which is beneficial for designing a new blood-handle device or improving the current model

Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference

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

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described