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Thermodynamic integration via Replica Exchange Hamiltonian Monte Carlo for faster sampling and model comparison Mingo Ndiwago, Damian ; ; Ley, Christophe et al Scientific Conference (2023, April 24) Detailed reference viewed: 60 (4 UL)Hierarchical a posteriori error estimation of Bank-Weiser type in the FEniCS Project Bulle, Raphaël ; Hale, Jack ; et al in Computers and Mathematics with Applications (2023), 131 In the seminal paper of Bank and Weiser [Math. Comp., 44 (1985), pp.283-301] a new a posteriori estimator was introduced. This estimator requires the solution of a local Neumann problem on every cell of ... [more ▼] In the seminal paper of Bank and Weiser [Math. Comp., 44 (1985), pp.283-301] a new a posteriori estimator was introduced. This estimator requires the solution of a local Neumann problem on every cell of the finite element mesh. Despite the promise of Bank-Weiser type estimators, namely locality, computational efficiency, and asymptotic sharpness, they have seen little use in practical computational problems. The focus of this contribution is to describe a novel implementation of hierarchical estimators of the Bank-Weiser type in a modern high-level finite element software with automatic code generation capabilities. We show how to use the estimator to drive (goal-oriented) adaptive mesh refinement and to mixed approximations of the nearly-incompressible elasticity problems. We provide comparisons with various other used estimators. An open-source implementation based on the FEniCS Project finite element software is provided as supplementary material. [less ▲] Detailed reference viewed: 146 (15 UL)Using replica exchange Hamiltonian Monte Carlo and thermodynamic integration for comparison of dynamic rainfall-runoff models Mingo Ndiwago, Damian ; ; Ley, Christophe et al Scientific Conference (2023, January 25) Detailed reference viewed: 58 (0 UL)An a posteriori error estimator for the spectral fractional power of the Laplacian Bulle, Raphaël ; ; Bordas, Stéphane et al in Computer Methods in Applied Mechanics and Engineering (2023), 407 We develop a novel a posteriori error estimator for the L2 error committed by the finite ele- ment discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes ... [more ▼] We develop a novel a posteriori error estimator for the L2 error committed by the finite ele- ment discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes advantage of the semi–discretization scheme using a rational approximation which allows to reformulate the fractional problem into a family of non–fractional parametric problems. The estimator involves applying the implicit Bank–Weiser error estimation strategy to each parametric non–fractional problem and reconstructing the fractional error through the same rational approximation used to compute the solution to the original fractional problem. We provide several numerical examples in both two and three-dimensions demonstrating the effectivity of our estimator for varying fractional powers and its ability to drive an adaptive mesh refinement strategy. [less ▲] Detailed reference viewed: 97 (9 UL)Towards assimilating SAR data into an anisotropic model of an underground aquifer Salehian Ghamsari, Sona ; van Dam, Tonie ; Hale, Jack Scientific Conference (2023) In this study, we aim to shed light on the feasibility of assimilating synthetic aperture radar (SAR) data into a partial differential equation-based model of a poroelastic homogeneous aquifer with ... [more ▼] In this study, we aim to shed light on the feasibility of assimilating synthetic aperture radar (SAR) data into a partial differential equation-based model of a poroelastic homogeneous aquifer with anisotropic hydraulic conductivity (AHC). Although other authors [1] have considered the problem of assimilating SAR data into a poroelastic model that uses an inhomogeneous isotropic random field model for hydraulic conductivity, to the best of our knowledge, our study is the first to consider assimilating SAR data into a poroelastic model with AHC. Our study is inspired by the work of [2] where an aquifer test is performed on the Anderson Junction aquifer in southwestern Utah. Due to the inherent preferential direction of the fractured sandstone at the Anderson Junction site, the ratio of hydraulic conductivity along the principal axes can be on the order of 24 to 1. We build an anisotropically conductive poroelastic finite element model of the Anderson Junction site that can predict the coupled fluid flow and mechanical displacements. Our results show that the effective elastic response of the aquifer on the Earth’s surface has an anisotropic nature driven by the underlying anisotropy in the fluid problem, even when the elasticity problem is assumed to be isotropic. We interpret these results in the context of using SAR data to improve the characterization of aquifer systems, like the Anderson Junction site, with strongly anisotropic behavior. The Doctoral Training Unit Data-driven computational modelling and applications (DRIVEN) is funded by the Luxembourg National Research Fund under the PRIDE programme (PRIDE17/12252781). [1] Amal Alghamdi. Bayesian inverse problems for quasi-static poroelasticity with application to ground water aquifer characterization from geodetic data. PhD thesis, 2020. https://repositories.lib.utexas.edu/handle/2152/86231. [2] Victor M. Heilweil and Paul A. Hsieh. Determining Anisotropic Transmissivity Using a Simplified Papadopulos Method. Groundwater, 44(5):749–753, 2006. 10.1111/j.1745-6584.2006.00210.x [less ▲] Detailed reference viewed: 105 (23 UL)Melt Instability Identification Using Unsupervised Machine Learning Algorithms ; ; et al in Macromolecular Materials and Engineering (2023) In industrial extrusion processes, increasing shear rates can lead to higher production rates. However, at high shear rates, extruded polymers and polymer compounds often exhibit melt instabilities ... [more ▼] In industrial extrusion processes, increasing shear rates can lead to higher production rates. However, at high shear rates, extruded polymers and polymer compounds often exhibit melt instabilities ranging from stick-slip to sharkskin to gross melt fracture. These instabilities result in challenges to meet the specifications on the extrudate shape. Starting with an existing published data set on melt instabilities in polymer extrusion, we assess the suitability of clustering, unsupervised machine learning algorithms combined with feature selection, to extract and identify hidden and important features from this data set, and their possible relationship with melt instabilities. The data set consists of both intrinsic features of the polymer as well as extrinsic features controlled and measured during an extrusion experiment. Using a range of commonly available clustering algorithms, it is demonstrated that the features related to only the intrinsic properties of the data set can be reliably divided into two clusters, and that in turn, these two clusters may be associated with either the stick-slip or sharkskin instability. Furthermore, using a feature ranking on both the intrinsic and extrinsic features of the data set, it is shown that the intrinsic properties of molecular weight and polydispersity are the strongest indicators of clustering. [less ▲] Detailed reference viewed: 49 (2 UL)SOniCS: Interfacing SOFA and FEniCS for advanced constitutive models Mazier, Arnaud ; ; et al Scientific Conference (2022, August) The Simulation Open Framework Architecture (SOFA) is a software environment for building simulations with a particular focus on real-time medical applications, e.g. surgery. Its scope is far broader than ... [more ▼] The Simulation Open Framework Architecture (SOFA) is a software environment for building simulations with a particular focus on real-time medical applications, e.g. surgery. Its scope is far broader than the FEniCS Project, encompassing e.g. rigid body dynamics, interfacing with haptic devices, contact and visualisation. Naturally, it also includes some finite element models of soft tissue mechanics, but these capabilities are currently ‘pre-baked’ and limited to a few simple constitutive models. The goal of this work is to incorporate state-of-the-art code generation tools from the FEniCS Project into SOFA in order to hugely increase SOFA’s capabilities in terms of soft tissue mechanics. To this end we have developed a new SOFA plugin named SOniCS. For adding a new material model in SOniCS, the user describes its strain energy density function using UFL (Unified Form Language) syntax. Then, using FFCx (FEniCSx Form Compiler) we generate the C code associated with the kernels corresponding to the automatically differentiated cell-local residual and stiffness forms. Finally, we assemble these kernels in SOFA into global tensors and solve the resulting non-linear systems of equations. The result is that it is now possible to straightforwardly implement complex material models such as the Holzapfel-Ogden anisotropic model into SOFA, and to use them alongside SOFA’s existing strong feature set in medical simulation. [less ▲] Detailed reference viewed: 156 (11 UL)Using Bayes factors to compare dynamical models of hydrological systems Mingo Ndiwago, Damian ; ; Ley, Christophe et al Scientific Conference (2022, June 05) Detailed reference viewed: 44 (10 UL)Inverse deformation analysis: an experimental and numerical assessment using the FEniCS Project Mazier, Arnaud ; ; et al in Engineering with Computers (2022) In this paper, we develop a framework for solving inverse deformation problems using the FEniCS Project finite-element software. We validate our approach with experimental imaging data acquired from a ... [more ▼] In this paper, we develop a framework for solving inverse deformation problems using the FEniCS Project finite-element software. We validate our approach with experimental imaging data acquired from a soft silicone beam under gravity. In contrast with inverse iterative algorithms that require multiple solutions of a standard elasticity problem, the proposed method can compute the undeformed configuration by solving only one modified elasticity problem. This modified problem has a complexity comparable to the standard one. The framework is implemented within an open-source pipeline enabling the direct and inverse deformation simulation directly from imaging data. We use the high-level unified form language (UFL) of the FEniCS Project to express the finite-element model in variational form and to automatically derive the consistent Jacobian. Consequently, the design of the pipeline is flexible: for example, it allows the modification of the constitutive models by changing a single line of code. We include a complete working example showing the inverse deformation of a beam deformed by gravity as supplementary material. [less ▲] Detailed reference viewed: 246 (33 UL)SOniCS: Develop intuition on biomechanical systems through interactive error controlled simulations Mazier, Arnaud ; ; et al E-print/Working paper (2022) This new approach allows the user to experiment with model choices easily and quickly without requiring in-depth expertise, as constitutive models can be modified by one line of code only. This ease in ... [more ▼] This new approach allows the user to experiment with model choices easily and quickly without requiring in-depth expertise, as constitutive models can be modified by one line of code only. This ease in building new models makes SOniCS ideal to develop surrogate, reduced order mod- els and to train machine learning algorithms for uncertainty quantification or to enable patient-specific simulations. SOniCS is thus not only a tool that facilitates the development of surgical training simulations but also, and perhaps more importantly, paves the way to increase the intuition of users or otherwise non-intuitive behaviors of (bio)mechanical systems. The plugin uses new developments of the FEniCSx project enabling au- tomatic generation with FFCx of finite element tensors such as the local residual vector and Jacobian matrix. We validate our approach with nu- merical simulations such as manufactured solutions, cantilever beams, and benchmarks provided by FEBio. We reach machine precision accuracy and demonstrate the use of the plugin for a real-time haptic simulation involv- ing a surgical tool controlled by the user in contact with a hyperelastic liver. We include complete examples showing the use of our plugin for sim- ulations involving Saint Venant-Kirchhoff, Neo-Hookean, Mooney-Rivlin, and Holzapfel Ogden anisotropic models as supplementary material. [less ▲] Detailed reference viewed: 30 (1 UL)A hyper-reduction method using adaptivity to cut the assembly costs of reduced order models Hale, Jack ; ; Baroli, Davide et al in Computer Methods in Applied Mechanics and Engineering (2021), 380 At every iteration or timestep of the online phase of some reduced-order modelling schemes, large linear systems must be assembled and then projected onto a reduced order basis of small dimension. The ... [more ▼] At every iteration or timestep of the online phase of some reduced-order modelling schemes, large linear systems must be assembled and then projected onto a reduced order basis of small dimension. The projected small linear systems are cheap to solve, but assembly and projection are now the dominant computational cost. In this paper we introduce a new hyper-reduction strategy called reduced assembly (RA) that drastically cuts these costs. RA consists of a triangulation adaptation algorithm that uses a local error indicator to con- struct a reduced assembly triangulation specially suited to the reduced order basis. Crucially, this reduced assembly triangulation has fewer cells than the original one, resulting in lower assembly and projection costs. We demonstrate the efficacy of RA on a Galerkin-POD type reduced order model (RAPOD). We show performance increases of up to five times over the baseline Galerkin-POD method on a non-linear reaction-diffusion problem solved with a semi-implicit time-stepping scheme and up to seven times for a 3D hyperelasticity problem solved with a continuation Newton-Raphson algorithm. The examples are implemented in the DOLFIN finite element solver using PETSc and SLEPc for linear algebra. Full code and data files to produce the results in this paper are provided as supplementary material. [less ▲] Detailed reference viewed: 429 (54 UL)The FEniCS Project (SOFA Talk) Hale, Jack Presentation (2021, June 01) Detailed reference viewed: 51 (2 UL)Mechanistic modelling of astrocytic metabolism in physiological geometries reveals spatiotemporal effects potentially driving neurodegeneration Farina, Sofia ; ; Hale, Jack et al Presentation (2021, May) Detailed reference viewed: 122 (9 UL)Bubble-Enriched Smoothed Finite Element Methods for Nearly-Incompressible Solids ; ; Hale, Jack et al in Computer Modeling in Engineering and Sciences (2021), 127(2), 411-436 This work presents a locking-free smoothed finite element method (S-FEM) for the simulation of soft matter modelled by the equations of quasi-incompressible hyperelasticity. The proposed method overcomes ... [more ▼] This work presents a locking-free smoothed finite element method (S-FEM) for the simulation of soft matter modelled by the equations of quasi-incompressible hyperelasticity. The proposed method overcomes well-known issues of standard finite element methods (FEM) in the incompressible limit: the over-estimation of stiffness and sensitivity to severely distorted meshes. The concepts of cell-based, edge-based and node-based S-FEMs are extended in this paper to three-dimensions. Additionally, a cubic bubble function is utilized to improve accuracy and stability. For the bubble function, an additional displacement degree of freedom is added at the centroid of the element. Several numerical studies are performed demonstrating the stability and validity of the proposed approach. The obtained results are compared with standard FEM and with analytical solutions to show the effectiveness of the method. [less ▲] Detailed reference viewed: 184 (4 UL)A cut finite element method for spatially resolved energy metabolism models in complex neuro-cell morphologies with minimal remeshing Farina, Sofia ; ; Hale, Jack et al in Advanced Modeling and Simulation in Engineering Sciences (2021), 8 A thorough understanding of brain metabolism is essential to tackle neurodegenerative diseases. Astrocytes are glial cells which play an important metabolic role by supplying neurons with energy. In ... [more ▼] A thorough understanding of brain metabolism is essential to tackle neurodegenerative diseases. Astrocytes are glial cells which play an important metabolic role by supplying neurons with energy. In addition, astrocytes provide scaffolding and homeostatic functions to neighboring neurons and contribute to the blood–brain barrier. Recent investigations indicate that the complex morphology of astrocytes impacts upon their function and in particular the efficiency with which these cells metabolize nutrients and provide neurons with energy, but a systematic understanding is still elusive. Modelling and simulation represent an effective framework to address this challenge and to deepen our understanding of brain energy metabolism. This requires solving a set of metabolic partial differential equations on complex domains and remains a challenge. In this paper, we propose, test and verify a simple numerical method to solve a simplified model of metabolic pathways in astrocytes. The method can deal with arbitrarily complex cell morphologies and enables the rapid and simple modification of the model equations by users also without a deep knowledge in the numerical methods involved. The results obtained with the new method (CutFEM) are as accurate as the finite element method (FEM) whilst CutFEM disentangles the cell morphology from its discretisation, enabling us to deal with arbitrarily complex morphologies in two and three dimensions. [less ▲] Detailed reference viewed: 207 (18 UL)Dynamic composition of solvers for coupled problems in DOLFINx Rehor, Martin ; Hale, Jack Presentation (2021, March 22) Recent developments in DOLFINx allow for the block assembly of linear algebraic systems arising from discretisations of coupled partial differential equations. Each algebraic block represents a subproblem ... [more ▼] Recent developments in DOLFINx allow for the block assembly of linear algebraic systems arising from discretisations of coupled partial differential equations. Each algebraic block represents a subproblem associated with a coupling of the unknown fields. Designing and implementing robust and scalable solution and preconditioning strategies for block-structured linear systems is an active area of research. In this contribution we show how DOLFINx can now exploit one of the most significant features of PETSc; the dynamic composition of the hierarchical solver and preconditioner options at runtime, see Brown et al [1]. The idea is inspired by the work of Kirby and Mitchell [2] that was originally implemented in the Firedrake Project. One of the most significant benefits of the approach is the possibility to construct advanced preconditioners that require structure beyond a purely algebraic problem description, eg the pressure-convection-diffusion (PCD) approximation of the Schur complement for the Navier–Stokes equations, see Silvester et al [3]. We illustrate the capabilities of our implementation on examples ranging from incompressible flow of a viscous fluid, through temperature-driven convection, to flows described by rate-type viscoelastic fluid models. References [1] J. Brown, M. G. Knepley, D. A. May, L. C. McInnes, and B. Smith, "Composable Linear Solvers for Multiphysics," in 2012 11th International Symposium on Parallel and Distributed Computing, Munich, Germany, Jun. 2012, pp. 55–62, doi: 10.1109/ISPDC.2012.16. [2] R. C. Kirby and L. Mitchell, "Solver Composition Across the PDE/Linear Algebra Barrier," SIAM J. Sci. Comput., vol. 40, no. 1, pp. C76–C98, 2017, doi: 10.1137/17M1133208. [3] H. C. Elman, D. J. Silvester, and A. J. Wathen, Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics. 2014, doi: 10.1093/acprof:oso/9780199678792.001.0001. Acknowledgements The present work is supported by the National Research Fund, Luxembourg in the frame of the Industrial Fellowship project RIFLE (13754363). The experiments presented in this work were carried out using the HPC facilities of the University of Luxembourg. [less ▲] Detailed reference viewed: 159 (10 UL)A comparison of constitutive models for describing the flow of uncured styrene-butadiene rubber Rehor, Martin ; Gansen, Alex ; et al in Journal of Non-Newtonian Fluid Mechanics (2020), 286 Uncured styrene-butadiene rubber (SBR) can be modelled as a viscoelastic material with at least two different relaxation mechanisms. In this paper we compare multi-mode constitutive models combining two ... [more ▼] Uncured styrene-butadiene rubber (SBR) can be modelled as a viscoelastic material with at least two different relaxation mechanisms. In this paper we compare multi-mode constitutive models combining two viscoelastic modes (linear and/or nonlinear) in three possible ways. Our particular choice of the two modes was inspired by models originally developed to describe the response of asphalt binders. We select the model that best fits the experimental data obtained from a modified stress relaxation experiment in the torsional configuration of the plate-plate rheometer. The optimisation of the five model parameters for each model is achieved by minimising the weighted least-squares distance between experimental observations and the computer model output using a tree-structured Parzen estimator algorithm to find an initial guess, followed by further optimisation using the Nelder-Mead simplex algorithm. The results show that the model combining the linear mode and the nonlinear mode is the most suitable variant to describe the observed behavior of SBR in the given regime. The predictive capabilities of the three models are further examined in changed experimental and numerical configurations. Full data and code to produce the figures in this article are included as supplementary material. [less ▲] Detailed reference viewed: 283 (29 UL)Removing the saturation assumption in Bank-Weiser error estimator analysis in dimension three Bulle, Raphaël ; ; Hale, Jack et al in Applied Mathematics Letters (2020), 107 We provide a new argument proving the reliability of the Bank-Weiser estimator for Lagrange piecewise linear finite elements in both dimension two and three. The extension to dimension three constitutes ... [more ▼] We provide a new argument proving the reliability of the Bank-Weiser estimator for Lagrange piecewise linear finite elements in both dimension two and three. The extension to dimension three constitutes the main novelty of our study. In addition, we present a numerical comparison of the Bank-Weiser and residual estimators for a three-dimensional test case. [less ▲] Detailed reference viewed: 174 (41 UL)Inverse simulation for retrieving the undeformed position for hyperelastic materials : application to breast simulations Mazier, Arnaud ; ; et al Scientific Conference (2020, July) The rest position, as well as any associated internal stresses in soft organs, are usually unknown when solving biomechanics problems. In addition, the initial geometry of a specific organ, obtained from ... [more ▼] The rest position, as well as any associated internal stresses in soft organs, are usually unknown when solving biomechanics problems. In addition, the initial geometry of a specific organ, obtained from medical images, is affected by external forces. An example is breast MRI performed prior to cancer surgery. During the imaging routine, the breast is elongated in prone position in order to better view the tumor. However, during surgery, the patient is in supine position, which causes the breast to rest in a completely different state. To simulate this state from the prone stance, the rest configuration is needed as well as the pre-stress mapping of the organs [1]. To tackle this problem, iterative algorithms have been proposed such as Sellier’s method [2]. In this fixed-point approach, the rest configuration is updated by multiple forward calculations then repeated until the error (between the updated and target configuration) reaches an established threshold. The method presents many benefits e.g. easy implementation and fast convergence. However, convergence issues appear at large deformations induced for instance by hyperelastic material formulations. In this work, we develop a simple formulation and a robust solution procedure for inverse deformation problems in soft-tissue biomechanics using the FEniCS Project finite element solver. In contrast with iterative algorithms, our method can solve with a single simulation the rest position without computing multiple solutions of the forward problem. For a fixed convergence tolerance, our physics-based algorithm is about ten times faster and better handles large deformations than Sellier’s method [2]. Moreover, no additional direct deformation simulations from the rest configuration are required to compute stresses in the organ. The framework is implemented within an open-source pipeline enabling the seamless, fully parallelized, direct and inverse deformation simulation of organs directly from segmented images. The pipeline is also designed to be flexible to user’s needs: for example, it allows the modification of the constitutive models by changing a single line of code. [less ▲] Detailed reference viewed: 434 (47 UL)Practical aspects of the Bank-Weiser estimator implementation and Biomechanics applications. Bulle, Raphaël ; Bordas, Stéphane ; et al Scientific Conference (2020, July) Detailed reference viewed: 113 (8 UL) |
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