Publications by Simone Deparis

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Several models exist for the simulation of vascular flows; they span from simple circuit models to full three-dimensional ones that take into account detailed features of the blood and of the arterialwall. Eachmodel comeswith both benefits and drawbacks, the main denominator being a compromise between detailed resolution requirements versus computational time. We first present a fluid-structure interaction computationalmodelwhere both the fluid and the structure are three dimensional. In particular, the flu

We consider the numerical simulation of integrated heart models for the study of the cardiac functioning with particular emphasis on the coupling of the muscle contraction, the fluid dynamics of the left ventricle, and the interaction with the valves. We a ...

A Fluid–Structure Interaction (FSI) problem can be reinterpreted as a heterogeneous problem with two subdomains. It is possible to describe the coupled problem at the interface between the fluid and the structure, yielding a nonlinear Steklov–Poincaré problem. The linear system can be linearized by Newton iterations on the interface and the resulting linear problem can be solved by the preconditioned GMRES method. In this work we investigate the behavior of preconditioners of Neumann–Neumann and Dirichlet–N

We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier–Stokes equations. Our algorithm is based on an approximated domain-decomposition of the ...

In this work we are interested in the numerical solution of the steady incompressible Navier-Stokes equations for fluid flow in pipes with varying curvatures and cross-sections. We intend to compute a reduced basis approximation of the solution, employing ...

We are interested in the approximation of partial differential equations on domains decomposed into two (or several) subdomains featuring non-conforming interfaces. The non-conformity may be due to different meshes and/or different polynomial degrees used from the two sides, or even to a geometrical mismatch. Across each interface, one subdomain is identified as master and the other as slave. We consider Galerkin methods for the discretization (such as finite element or spectral element methods) that make u

In this work an iterative strategy to implicitly couple dimensionally-heterogeneous blood flow models accounting for the continuity of mean total normal stress at interface boundaries is developed. Conservation of mean total normal stress in the coupling o ...

The simulation of the physiological loading situation of arteries with moderate atherosclerotic plaque may provide additional indicators for medical doctors to estimate if the plaque is likely to rupture and if surgical intervention is required. In particular the transmural stresses are important in this context. They depend strongly on the mechanical response and thus, a predictive material model capturing all characteristics of the material behavior is required. Here, polyconvex strain energy functions ar

We propose a new approach for the data assimilation and simulation of anatomically correct left ventricle fluid dynamics based on cardiac magnetic resonance images. The movement of the ventricle is captured by a set of tracking points on the endocardium identified from a time series of magnetic resonance images. The displacement of the endocardium is interpolated using radial basis functions to produce a smooth global deformation field in both space and time. To regularize the motion of the fluid inside the

A geometrical multiscale model for blood flow through an ideal left ventricle and the main arteries is presented. The blood flow in the three-dimensional idealized left ventricle is solved through a monolithic fluid-structure interaction solver. To account for the interaction between the heart and the circulatory system the heart flow is coupled through an ideal valve with a network of viscoelastic one-dimensional models representing the arterial network. The geometrical multiscale approach used in this wor

Purpose: Connecting outflow cannula of LVAD to the aorta is an underexplored issue but may have considerable impact. In fact the hemodynamic modifications due to implantation in this region can cause thromboembolic events. It is therefore important to understand the flow pattern in this region and the way device interacts with the cardiovascular system. We present here the mathematical settings and results of a numerical model of the anastomosis between the outflow cannula of LVAD and the aorta. Methods: Th

The main goal of this work is to devise robust iterative strategies to partition the solution of the Navier-Stokes equations in a three-dimensional (3D) domain, into non overlapping 3D subdomains, which communicate through the exchange of averaged/integrat ...

In wave propagation problems, finite difference methods implemented on staggered grids are commonly used to avoid checkerboard patterns and to improve accuracy in the approximation of short-wavelength components of the solutions. In this study, we develop a mimetic finite difference (MFD) method on staggered grids for transport operators with divergence-free advective field that is proven to be energy-preserving in wave problems. This method mimics some characteristics of the summation-by-parts (SBP) operat

In this work, we address the numerical solution of fluid-structure interaction problems. This issue is particularly difficulty to tackle when the fluid and the solid densities are of the same order, for instance as it happens in hemodynamic applications, since fully implicit coupling schemes are required to ensure stability of the resulting method. Thus, at each time step, we have to solve a highly nonlinear coupled system, since the fluid domain depends on the unknown displacement of the structure. Standar

We introduce a two-level preconditioner for the efficient solution of large scale saddle point linear systems arising from the finite element (FE) discretization of parametrized Stokes equations. This preconditioner extends the Multi Space Reduced Basis (M ...

In this work we introduce a new two-level preconditioner for the efficient solution of large scale linear systems arising from the discretization of parametrized PDEs. The proposed preconditioner combines in a multiplicative way a reduced basis solver, which plays the role of coarse component, and a "traditional" fine grid preconditioner, such as one-level Additive Schwarz, block Gauss-Seidel or block Jacobi preconditioners. The coarse component is built up on a new Multi Space Reduced Basis (MSRB) method t

Cardiovascular diseases are the first cause of death in industrialized countries. It is now widely established that blood fluid dynamics and its interaction with the vascular wall play an essential role in the development and evolution of vascular pathologies. Mathematical modeling and numerical simulation are precious tools which may help to understand biomechanical phenomena in both physiological and pathological states and can lead to the development of new therapies or to assist physicians in clinical d

Background Research shows that active pedagogies could play an important role in achieving more equitable outcomes for diverse groups of students in Science, Technology, Engineering, and Mathematics (STEM). Although flipped classes are a popular active met ...

In this work a numerical strategy to address the solution of the blood flow in one-dimensional arterial networks through a topology-based decomposition is presented. Such decomposition results in the local analysis of the blood flow in simple arterial segm ...

We analyze the numerical performance of a preconditioning technique recently proposed in [1] for the efficient solution of parametrized linear systems arising from the finite element (FE) discretization of parameter-dependent elliptic partial differential ...

Simone Deparis

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Fluid-structure interaction for vascular flows: From supercomputers to laptops

Coupled models for integrated heart simulations: a numerical study of the fluid dynamics in the left ventricle

A Comparison of Preconditioners for the Steklov–Poincaré Formulation of the Fluid-Structure Coupling in Hemodynamics

Model order reduction of flow based on a modular geometrical approximation of blood vessels

Stabilized reduced basis approximation of incompressible three-dimensional Navier–Stokes equations in parametrized deformed domains

MATHICSE Technical Report : INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutations of PDEs on subdomains featuring non-conforming interfaces

On the continuity of mean total normal stress in geometrical multiscale cardiovascular problems

Aspects of Arterial Wall Simulations: Nonlinear Anisotropic Material Models and Fluid Structure Interaction

Multiscale fluid-structure interaction simulation of anatomically correct left ventricle fluid dynamics with fictitious elastic structure regularization

Geometrical multiscale model of an idealized left ventricle with fluid-structure interaction effects coupled to a one-dimensional viscoelastic arterial network

Numerical Fluid-Structure Interaction Model for the Connection of Outflow Cannula of LVAD to the Aorta

Algorithms for the partitioned solution of weakly coupled fluid models for cardiovascular flows

Mimetic finite difference schemes for transport operators with divergence-free advective field and applications to plasma physics

Acceleration of a fixed point algorithm for fluid-structure interaction using transpiration conditions

Multi space reduced basis preconditioners for parametrized Stokes equations

MATHICSE Technical Report : Multi space reduced basis preconditioners for large-scale parametrized PDEs

Efficient Solution of Fluid-Structure Interaction Problems in Computational Hemodynamics

Gender, prior knowledge, and the impact of a flipped linear algebra course for engineers over multiple years

A two-level time step technique for the partitioned solution of one-dimensional arterial networks

A numerical investigation of multi space reduced basis preconditioners for parametrized elliptic advection-diffusion equations