Assessing the performance of the FEniCS Project on Graviton3

Presentation (2023, June 06)

We assess the performance of the FEniCS Project finite element solver on AWS Graviton3 instances, including compiler auto-vectorisation and MPI runs. Our results show that Graviton3 is competitive or ... [more ▼]

We assess the performance of the FEniCS Project finite element solver on AWS Graviton3 instances, including compiler auto-vectorisation and MPI runs. Our results show that Graviton3 is competitive or better performing for than state-of-the-art x86-64 HPC systems for various standard finite element methods. [less ▲]

Hierarchical a posteriori error estimation of Bank-Weiser type in the FEniCS Project

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 ▲]

Towards assimilating SAR data into an anisotropic model of an underground aquifer

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 ▲]

A Reissner-Mindlin plate formulation using symmetric Hu-Zhang elements via polytopal transformations

E-print/Working paper (2023)

In this work we develop new finite element discretisations of the shear-deformable Reissner--Mindlin plate problem based on the Hellinger-Reissner principle of symmetric stresses. Specifically, we use ... [more ▼]

In this work we develop new finite element discretisations of the shear-deformable Reissner--Mindlin plate problem based on the Hellinger-Reissner principle of symmetric stresses. Specifically, we use conforming Hu-Zhang elements to discretise the bending moments in the space of symmetric square integrable fields with a square integrable divergence. The latter results in highly accurate approximations of the bending moments M and in the rotation field being in the discontinuous Lebesgue space , such that the Kirchhoff-Love constraint can be satisfied for t tending to zero. In order to preserve optimal convergence rates across all variables for the case t tending to zero, we present an extension of the formulation using Raviart-Thomas elements for the shear stress. We prove existence and uniqueness in the continuous setting and rely on exact complexes for inheritance of well-posedness in the discrete setting. This work introduces an efficient construction of the Hu-Zhang base functions on the reference element via the polytopal template methodology and Legendre polynomials, making it applicable to hp-FEM. The base functions on the reference element are then mapped to the physical element using novel polytopal transformations, which are suitable also for curved geometries. The robustness of the formulations and the construction of the Hu-Zhang element are tested for shear-locking, curved geometries and an L-shaped domain with a singularity in the bending moments. Further, we compare the performance of the novel formulations with the primal-, MITC- and recently introduced TDNNS methods. [less ▲]

SOniCS: Interfacing SOFA and FEniCS for advanced constitutive models

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 ▲]

Inverse deformation analysis: an experimental and numerical assessment using the FEniCS Project

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 ▲]

A hyper-reduction method using adaptivity to cut the assembly costs of reduced order models

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 ▲]

Mechanistic modelling of astrocytic metabolism in physiological geometries reveals spatiotemporal effects potentially driving neurodegeneration

Presentation (2021, May)

A cut finite element method for spatially resolved energy metabolism models in complex neuro-cell morphologies with minimal remeshing

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 ▲]

A comparison of constitutive models for describing the flow of uncured styrene-butadiene rubber

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 ▲]