Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms

DOI10.1016/j.jcp.2016.06.038zbMath1415.74049OpenAlexW2464593170WikidataQ47118666 ScholiaQ47118666MaRDI QIDQ2424425

Paris Perdikaris, Yue Yu, George Em. Karniadakis

Publication date: 24 June 2019

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2016.06.038

zbMATH Keywords

spectral element methodfluid-structure interactionfractional differential equationsbrain aneurysmfast convolution methodpatient-specific vasculature

Mathematics Subject Classification ID

Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Finite element methods applied to problems in solid mechanics (74S05) Linear constitutive equations for materials with memory (74D05) Biomechanics (92C10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Physiological flows (76Z05) Fractional partial differential equations (35R11)

Related Items

A self-singularity-capturing scheme for fractional differential equations, Multiscale and monolithic arbitrary Lagrangian-Eulerian finite element method for a hemodynamic fluid-structure interaction problem involving aneurysms, Shifted Legendre polynomials algorithm used for the dynamic analysis of viscoelastic pipes conveying fluid with variable fractional order model, Efficient and Accurate Numerical Methods Using the Accelerated Spectral Deferred Correction for Solving Fractional Differential Equations, A Degenerate Parabolic Logistic Equation, A stable fast time-stepping method for fractional integral and derivative operators, New iterative method for the solution of fractional damped Burger and fractional Sharma-Tasso-Olver equations, Almost oscillatory fractional differential equations, Predict Blood Pressure by Photoplethysmogram with the Fluid-Structure Interaction Modeling, Accurate and straightforward symplectic approach for fracture analysis of fractional viscoelastic media, Effect of Double-Frequency Excitation on a Fractional Model of Cerebral Aneurysm, An approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth data, A Unified Fast Memory-Saving Time-Stepping Method for Fractional Operators and Its Applications, A bi-fidelity surrogate modeling approach for uncertainty propagation in three-dimensional hemodynamic simulations, Existence results for a coupled system of fractional integro-differential equations with time-dependent delay, An H2N2 interpolation for Caputo derivative with order in \((1,2)\) and its application to time-fractional wave equations in more than one space dimension, One-dimensional haemodynamic model of a vascular network with fractional-order viscoelasticity, Implicit-explicit time integration of nonlinear fractional differential equations, Anomalous Diffusion with Caputo-Fabrizio Time Derivative: an Inverse Problem., A Time-Fractional Mean-Field Control Modeling Subdiffusive Advective Transport, Bi-Orthogonal fPINN: A Physics-Informed Neural Network Method for Solving Time-Dependent Stochastic Fractional PDEs, An Analysis of the Modified L1 Scheme for Time-Fractional Partial Differential Equations with Nonsmooth Data, Analysis of models for viscoelastic wave propagation, Stability analysis and numerical simulations via fractional calculus for tumor dormancy models, On the fundamental solutions of a discontinuous fractional boundary value problem, Efficient high order algorithms for fractional integrals and fractional differential equations, Unnamed Item, Mathematical model of atherosclerotic aneurysm, A continuum and computational framework for viscoelastodynamics. I: Finite deformation linear models, One-dimensional modeling of fractional flow reserve in coronary artery disease: uncertainty quantification and Bayesian optimization, Discontinuous fractional Sturm-Liouville problems with transmission conditions, A New Class of Semi-Implicit Methods with Linear Complexity for Nonlinear Fractional Differential Equations, AN OPERATOR-BASED APPROACH FOR THE CONSTRUCTION OF CLOSED-FORM SOLUTIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS, Solvability of fractional differential inclusion with a generalized Caputo derivative, Efficient Multistep Methods for Tempered Fractional Calculus: Algorithms and Simulations, Two finite difference methods based on an H2N2 interpolation for two-dimensional time fractional mixed diffusion and diffusion-wave equations, Exponential sum approximation for Mittag-Leffler function and its application to fractional Zener wave equation, Bifurcation in a New Fractional Model of Cerebral Aneurysm at the Circle of Willis, Approximate Solutions to Fractional Boundary Value Problems by Wavelet Decomposition Methods, A high-order partitioned fluid-structure interaction framework for vortex-induced vibration simulation, A non-local spectral transfer model and new scaling law for scalar turbulence

Cites Work

• Unnamed Item
• Unnamed Item
• Generalized fictitious methods for fluid-structure interactions: analysis and simulations
• A convergence study of a new partitioned fluid-structure interaction algorithm based on fictitious mass and damping
• Mixed spectral/\(hp\) element formulation for nonlinear elasticity
• BDF-like methods for nonlinear dynamic analysis
• A fully-coupled fluid-structure interaction simulation of cerebral aneurysms
• Discontinuous Galerkin method for an integro-differential equation modeling dynamic fractional order viscoelasticity
• Short memory principle and a predictor-corrector approach for fractional differential equations
• Computer modeling of cardiovascular fluid-structure interactions with the deforming-spatial-domain/stabilized space-time formulation
• Added-mass effect in the design of partitioned algorithms for fluid--structure problems
• Space-time fluid-structure interaction modeling of patient-specific cerebral aneurysms
• A semi‐local spectral/hp element solver for linear elasticity problems
• A Fast Time Stepping Method for Evaluating Fractional Integrals
• Influencing factors in image-based fluid-structure interaction computation of cerebral aneurysms
• Parallel Algorithms for Fluid-Structure Interaction Problems in Haemodynamics
• A Spectral Order Method for Inverting Sectorial Laplace Transforms
• Fluid-structure interaction problems with strong added-mass effect
• An Effective Fluid-Structure Interaction Formulation for Vascular Dynamics by Generalized Robin Conditions
• Adaptive, Fast, and Oblivious Convolution in Evolution Equations with Memory
• The Accurate Numerical Inversion of Laplace Transforms
• A modification of Talbot's method for the simultaneous approximation of several values of the inverse Laplace transform
• Fast Convolution for Nonreflecting Boundary Conditions
• On the Construction and Properties of $m$-step Methods for FDEs
• Fast and Oblivious Convolution Quadrature
• Spectral/hp Element Methods for Computational Fluid Dynamics
• The numerical solution of fractional differential equations: speed versus accuracy