190 research outputs found
A note on stress-driven anisotropic diffusion and its role in active deformable media
We propose a new model to describe diffusion processes within active
deformable media. Our general theoretical framework is based on physical and
mathematical considerations, and it suggests to use diffusion tensors directly
coupled to mechanical stress. A proof-of-concept experiment and the proposed
generalised reaction-diffusion-mechanics model reveal that initially isotropic
and homogeneous diffusion tensors turn into inhomogeneous and anisotropic
quantities due to the intrinsic structure of the nonlinear coupling. We study
the physical properties leading to these effects, and investigate mathematical
conditions for its occurrence. Together, the experiment, the model, and the
numerical results obtained using a mixed-primal finite element method, clearly
support relevant consequences of stress-assisted diffusion into anisotropy
patterns, drifting, and conduction velocity of the resulting excitation waves.
Our findings also indicate the applicability of this novel approach in the
description of mechano-electrical feedback in actively deforming bio-materials
such as the heart
HDGlab: An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB
This paper presents HDGlab, an open source MATLAB implementation of the hybridisable discontinuous Galerkin (HDG) method. The main goal is to provide a detailed description of both the HDG method for elliptic problems and its implementation available in HDGlab. Ultimately, this is expected to make this relatively new advanced discretisation method more accessible to the computational engineering community. HDGlab presents some features not available in other implementations of the HDG method that can be found in the free domain. First, it implements high-order polynomial shape functions up to degree nine, with both equally-spaced and Fekete nodal distributions. Second, it supports curved isoparametric simplicial elements in two and three dimensions. Third, it supports non-uniform degree polynomial approximations and it provides a flexible structure to devise degree adaptivity strategies. Finally, an interface with the open-source high-order mesh generator Gmsh is provided to facilitate its application to practical engineering problems
Competing mechanisms of stress-assisted diffusivity and stretch-activated currents in cardiac electromechanics
We numerically investigate the role of mechanical stress in modifying the
conductivity properties of the cardiac tissue and its impact in computational
models for cardiac electromechanics. We follow a theoretical framework recently
proposed in [Cherubini, Filippi, Gizzi, Ruiz-Baier, JTB 2017], in the context
of general reaction-diffusion-mechanics systems using multiphysics continuum
mechanics and finite elasticity. In the present study, the adapted models are
compared against preliminary experimental data of pig right ventricle
fluorescence optical mapping. These data contribute to the characterization of
the observed inhomogeneity and anisotropy properties that result from
mechanical deformation. Our novel approach simultaneously incorporates two
mechanisms for mechano-electric feedback (MEF): stretch-activated currents
(SAC) and stress-assisted diffusion (SAD); and we also identify their influence
into the nonlinear spatiotemporal dynamics. It is found that i) only specific
combinations of the two MEF effects allow proper conduction velocity
measurement; ii) expected heterogeneities and anisotropies are obtained via the
novel stress-assisted diffusion mechanisms; iii) spiral wave meandering and
drifting is highly mediated by the applied mechanical loading. We provide an
analysis of the intrinsic structure of the nonlinear coupling using
computational tests, conducted using a finite element method. In particular, we
compare static and dynamic deformation regimes in the onset of cardiac
arrhythmias and address other potential biomedical applications
Methods for Optimal Output Prediction in Computational Fluid Dynamics.
In a Computational Fluid Dynamics (CFD) simulation, not all data is of equal importance. Instead, the goal of the user is often to compute certain critical "outputs" -- such as lift and drag -- accurately. While in recent years CFD simulations have become routine, ensuring accuracy in these outputs is still surprisingly difficult. Unacceptable levels of output error arise even in industry-standard simulations, such as the steady flow around commercial aircraft. This problem is only exacerbated when simulating more complex, unsteady flows.
In this thesis, we present a mesh adaptation strategy for unsteady problems that can automatically reduce errors in outputs of interest. This strategy applies to problems in which the computational domain deforms in time -- such as flapping-flight simulations -- and relies on an unsteady adjoint to identify regions of the mesh contributing most to the output error. This error is then driven down via refinement of the critical regions in both space and time. Here, we demonstrate this strategy on a series of flapping-wing problems in two and three dimensions, using high-order discontinuous Galerkin (DG) methods for both spatial and temporal discretizations. Compared to other methods, results indicate that this strategy can deliver a desired level of output accuracy with significant reductions in computational cost.
After concluding our work on mesh adaptation, we take a step back and investigate another idea for obtaining output accuracy: adapting the numerical method itself. In particular, we show how the test space of discontinuous finite element methods can be "optimized" to achieve accuracy in certain outputs or regions. In this work, we compute test functions that ensure accuracy specifically along domain boundaries. These regions -- which are vital to both scalar outputs (such as lift and drag) and distributions (such as pressure and skin friction) -- are often the most important from an engineering standpoint.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133418/1/kastsm_1.pd
Numerical modeling and open-source implementation of variational partition-of-unity localizations of space-time dual-weighted residual estimators for parabolic problems
In this work, we consider space-time goal-oriented a posteriori error
estimation for parabolic problems. Temporal and spatial discretizations are
based on Galerkin finite elements of continuous and discontinuous type. The
main objectives are the development and analysis of space-time estimators, in
which the localization is based on a weak form employing a partition-of-unity.
The resulting error indicators are used for temporal and spatial adaptivity.
Our developments are substantiated with several numerical examples.Comment: Changes in v2: - Updated the title - Reworked space-time function
spaces - Added cG(1) in time partition-of-unity - Added links to the now
published codes used for this work - Added further reference
Variational Multiscale Method with Flexible Fine-Scale Basis for Diffusion-Reaction Equation: Built-In a Posteriori Error Estimate and Heterogenous Coefficients
The diffusion-reaction equation develops sharp boundary and/or internal layers for the reaction-dominated case (i.e. singularly perturbed case). In this regime, spurious oscillations pollute the solution obtained with the Galerkin finite element method (FEM). To address this issue, we employ a stabilized Variational Multiscale (VMS) method that relies on an improved expression for the fine-scale stabilization parameter that is derived via the fine-scale variational formulation facilitated by the VMS framework. The flexible fine scale basis consists of enrichment functions which may be nonzero at element edges. The stabilization parameter thus derived has spatial variation over element interiors and along inter-element boundaries that helps model the rapid variation of the residual of the Euler-Lagrange equations over the domain. This feature facilitates consistent stabilization across boundary and internal layers as well as capturing anisotropic refinement effects. In addition, VMS methods come equipped with useful a posteriori error estimators. New numerical results are presented that show the performance of this VMS method with a flexible fine-scale basis for singularly perturbed diffusion-reaction equation. These include an evaluation of the built-in error estimate for homogenous domain, and an optional modification of the method for heterogeneous domains that may result in savings in the computational cost
The LifeV library: engineering mathematics beyond the proof of concept
LifeV is a library for the finite element (FE) solution of partial
differential equations in one, two, and three dimensions. It is written in C++
and designed to run on diverse parallel architectures, including cloud and high
performance computing facilities. In spite of its academic research nature,
meaning a library for the development and testing of new methods, one
distinguishing feature of LifeV is its use on real world problems and it is
intended to provide a tool for many engineering applications. It has been
actually used in computational hemodynamics, including cardiac mechanics and
fluid-structure interaction problems, in porous media, ice sheets dynamics for
both forward and inverse problems. In this paper we give a short overview of
the features of LifeV and its coding paradigms on simple problems. The main
focus is on the parallel environment which is mainly driven by domain
decomposition methods and based on external libraries such as MPI, the Trilinos
project, HDF5 and ParMetis.
Dedicated to the memory of Fausto Saleri.Comment: Review of the LifeV Finite Element librar
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