All Outputs (21)

Bringing trimmed Serendipity methods to computational practice in Firedrake (2022)
Journal Article
Crum, J., Cheng, C., Ham, D. A., Mitchell, L., Kirby, R. C., Levine, J. A., & Gillette, A. (2022). Bringing trimmed Serendipity methods to computational practice in Firedrake. ACM Transactions on Mathematical Software, 48(1), 1-19. https://doi.org/10.1145/3490485

We present an implementation of the trimmed serendipity finite element family, using the open-source finite element package Firedrake. The new elements can be used seamlessly within the software suite for problems requiring H1, H(curl), or H(div)-con... Read More about Bringing trimmed Serendipity methods to computational practice in Firedrake.

PCPATCH: software for the topological construction of multigrid relaxation methods (2021)
Journal Article
Farrell, P. E., Knepley, M. G., Mitchell, L., & Wechsung, F. (2021). PCPATCH: software for the topological construction of multigrid relaxation methods. ACM Transactions on Mathematical Software, 47(3), 1-22. https://doi.org/10.1145/3445791

Effective relaxation methods are necessary for good multigrid convergence. For many equations, standard Jacobi and Gauß–Seidel are inadequate, and more sophisticated space decompositions are required; examples include problems with semidefinite terms... Read More about PCPATCH: software for the topological construction of multigrid relaxation methods.

A Reynolds-robust preconditioner for the Scott-Vogelius discretization of the stationary incompressible Navier-Stokes equations (2021)
Journal Article
Farrell, P. E., Mitchell, L., Scott, L. R., & Wechsung, F. (2021). A Reynolds-robust preconditioner for the Scott-Vogelius discretization of the stationary incompressible Navier-Stokes equations. The SMAI journal of computational mathematics, 7, 75-96. https://doi.org/10.5802/smai-jcm.72

Augmented Lagrangian preconditioners have successfully yielded Reynolds-robust preconditioners for the stationary incompressible Navier–Stokes equations, but only for specific discretizations. The discretizations for which these preconditioners have... Read More about A Reynolds-robust preconditioner for the Scott-Vogelius discretization of the stationary incompressible Navier-Stokes equations.

A study of vectorization for matrix-free finite element methods (2020)
Journal Article
Sun, T., Mitchell, L., Kulkarni, K., Klöckner, A., Ham, D. A., & Kelly, P. H. (2020). A study of vectorization for matrix-free finite element methods. International Journal of High Performance Computing Applications, 34(6), 629-644. https://doi.org/10.1177/1094342020945005

Vectorization is increasingly important to achieve high performance on modern hardware with SIMD instructions. Assembly of matrices and vectors in the finite element method, which is characterized by iterating a local assembly kernel over unstructure... Read More about A study of vectorization for matrix-free finite element methods.

Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond (2020)
Journal Article
Gibson, T. H., Mitchell, L., Ham, D. A., & Cotter, C. J. (2020). Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond. Geoscientific Model Development, 13(2), 735-761. https://doi.org/10.5194/gmd-13-735-2020

Within the finite element community, discontinuous Galerkin (DG) and mixed finite element methods have become increasingly popular in simulating geophysical flows. However, robust and efficient solvers for the resulting saddle point and elliptic syst... Read More about Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond.

Code generation for generally mapped finite elements (2019)
Journal Article
Kirby, R. C., & Mitchell, L. (2019). Code generation for generally mapped finite elements. ACM Transactions on Mathematical Software, 45(4), Article 41. https://doi.org/10.1145/3361745

Many classical finite elements such as the Argyris and Bell elements have long been absent from high-level PDE software. Building on recent theoretical work, we describe how to implement very general finite-element transformations in FInAT and hence... Read More about Code generation for generally mapped finite elements.

An augmented Lagrangian preconditioner for the 3D stationary incompressible Navier-Stokes equations at high Reynolds number (2019)
Journal Article
Farrell, P. E., Mitchell, L., & Wechsung, F. (2019). An augmented Lagrangian preconditioner for the 3D stationary incompressible Navier-Stokes equations at high Reynolds number. SIAM Journal on Scientific Computing, 41(5), A3073-A3096. https://doi.org/10.1137/18m1219370

In [M. Benzi and M. A. Olshanskii, SIAM J. Sci. Comput., 28 (2006), pp. 2095--2113] a preconditioner of augmented Lagrangian type was presented for the two-dimensional stationary incompressible Navier--Stokes equations that exhibits convergence almos... Read More about An augmented Lagrangian preconditioner for the 3D stationary incompressible Navier-Stokes equations at high Reynolds number.

Automated shape differentiation in the Unified Form Language (2019)
Journal Article
Ham, D. A., Mitchell, L., Paganini, A., & Wechsung, F. (2019). Automated shape differentiation in the Unified Form Language. Structural and Multidisciplinary Optimization, 60(5), 1813-1820. https://doi.org/10.1007/s00158-019-02281-z

We discuss automating the calculation of weak shape derivatives in the Unified Form Language (JAMA 40(2):9:1–9:37 2014) by introducing an appropriate additional step in the pullback from physical to reference space that computes Gâteaux derivatives w... Read More about Automated shape differentiation in the Unified Form Language.

Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations (2018)
Journal Article
Kärnä, T., Kramer, S. C., Mitchell, L., Ham, D. A., Piggott, M. D., & Baptista, A. M. (2018). Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations. Geoscientific Model Development, 11(11), 4359-4382. https://doi.org/10.5194/gmd-11-4359-2018

Unstructured grid ocean models are advantageous for simulating the coastal ocean and river–estuary–plume systems. However, unstructured grid models tend to be diffusive and/or computationally expensive, which limits their applicability to real-life p... Read More about Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations.

TSFC: A Structure-Preserving Form Compiler (2018)
Journal Article
Homolya, M., Mitchell, L., Luporini, F., & Ham, D. A. (2018). TSFC: A Structure-Preserving Form Compiler. SIAM Journal on Scientific Computing, 40(3), C401-C428. https://doi.org/10.1137/17m1130642

A form compiler takes a high-level description of the weak form of partial differential equations and produces low-level code that carries out the finite element assembly. In this paper we present the Two-Stage Form Compiler (TSFC), a new form compil... Read More about TSFC: A Structure-Preserving Form Compiler.

Solver Composition Across the PDE/Linear Algebra Barrier (2018)
Journal Article
Kirby, R. C., & Mitchell, L. (2018). Solver Composition Across the PDE/Linear Algebra Barrier. SIAM Journal on Scientific Computing, 40(1), C76-C98. https://doi.org/10.1137/17m1133208

The efficient solution of discretizations of coupled systems of partial differential equations (PDEs) is at the core of much of numerical simulation. Significant effort has been expended on scalable algorithms to precondition Krylov iterations for th... Read More about Solver Composition Across the PDE/Linear Algebra Barrier.

Vertical slice modelling of nonlinear Eady waves using a compatible finite element method (2017)
Journal Article
Yamazaki, H., Shipton, J., Cullen, M. J., Mitchell, L., & Cotter, C. J. (2017). Vertical slice modelling of nonlinear Eady waves using a compatible finite element method. Journal of Computational Physics, 343, 130-149. https://doi.org/10.1016/j.jcp.2017.04.006

A vertical slice model is developed for the Euler–Boussinesq equations with a constant temperature gradient in the direction normal to the slice (the Eady–Boussinesq model). The model is a solution of the full three-dimensional equations with no vari... Read More about Vertical slice modelling of nonlinear Eady waves using a compatible finite element method.

Firedrake: automating the finite element method by composing abstractions (2016)
Journal Article
Rathgeber, F., Ham, D. A., Mitchell, L., Lange, M., Luporini, F., Mcrae, A. T., Bercea, G.-T., Markall, G. R., & Kelly, P. H. (2017). Firedrake: automating the finite element method by composing abstractions. ACM Transactions on Mathematical Software, 43(3), Article 24. https://doi.org/10.1145/2998441

Firedrake is a new tool for automating the numerical solution of partial differential equations. Firedrake adopts the domain-specific language for the finite element method of the FEniCS project, but with a pure Python runtime-only implementation cen... Read More about Firedrake: automating the finite element method by composing abstractions.

A structure-exploiting numbering algorithm for finite elements on extruded meshes, and its performance evaluation in Firedrake (2016)
Journal Article
Bercea, G.-T., McRae, A. T., Ham, D. A., Mitchell, L., Rathgeber, F., Nardi, L., Luporini, F., & Kelly, P. H. (2016). A structure-exploiting numbering algorithm for finite elements on extruded meshes, and its performance evaluation in Firedrake. Geoscientific Model Development, 9(10), 3803-3815. https://doi.org/10.5194/gmd-9-3803-2016

We present a generic algorithm for numbering and then efficiently iterating over the data values attached to an extruded mesh. An extruded mesh is formed by replicating an existing mesh, assumed to be unstructured, to form layers of prismatic cells.... Read More about A structure-exploiting numbering algorithm for finite elements on extruded meshes, and its performance evaluation in Firedrake.

Automated Generation and Symbolic Manipulation of Tensor Product Finite Elements (2016)
Journal Article
McRae, A., Bercea, G.-T., Mitchell, L., Ham, D., & Cotter, C. (2016). Automated Generation and Symbolic Manipulation of Tensor Product Finite Elements. SIAM Journal on Scientific Computing, 38(5), S25-S47. https://doi.org/10.1137/15m1021167

We describe and implement a symbolic algebra for scalar and vector-valued finite elements, enabling the computer generation of elements with tensor product structure on quadrilateral, hexahedral, and triangular prismatic cells. The algebra is impleme... Read More about Automated Generation and Symbolic Manipulation of Tensor Product Finite Elements.

Efficient Mesh Management in Firedrake Using PETSc DMPlex (2016)
Journal Article
Lange, M., Mitchell, L., Knepley, M. G., & Gorman, G. J. (2016). Efficient Mesh Management in Firedrake Using PETSc DMPlex. SIAM Journal on Scientific Computing, 38(5), S143-S155. https://doi.org/10.1137/15m1026092

The use of composable abstractions allows the application of new and established algorithms to a wide range of problems, while automatically inheriting the benefits of well-known performance optimizations. This work highlights the composition of the... Read More about Efficient Mesh Management in Firedrake Using PETSc DMPlex.

High level implementation of geometric multigrid solvers for finite element problems: Applications in atmospheric modelling (2016)
Journal Article
Mitchell, L., & Müller, E. H. (2016). High level implementation of geometric multigrid solvers for finite element problems: Applications in atmospheric modelling. Journal of Computational Physics, 327, 1-18. https://doi.org/10.1016/j.jcp.2016.09.037

The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated (mixed) finite element di... Read More about High level implementation of geometric multigrid solvers for finite element problems: Applications in atmospheric modelling.

Exploring the Thread-level Parallelisms for the Next Generation Geophysical Fluid Modelling Framework Fluidity-ICOM (2013)
Journal Article
Guo, X., Gorman, G., Lange, M., Mitchell, L., & Weiland, M. (2013). Exploring the Thread-level Parallelisms for the Next Generation Geophysical Fluid Modelling Framework Fluidity-ICOM. Procedia engineering, 61, 251-257. https://doi.org/10.1016/j.proeng.2013.08.012

In this paper, we highlight our progress in implementing a hybrid OpenMP-MPI version of the unstructured finite element appli- cation Fluidity-ICOM. We demonstrate that utilising non-blocking algorithms and libraries are critical to mixed-mode applic... Read More about Exploring the Thread-level Parallelisms for the Next Generation Geophysical Fluid Modelling Framework Fluidity-ICOM.

Parallel classification and feature selection in microarray data using SPRINT (2012)
Journal Article
Mitchell, L., Sloan, T. M., Mewissen, M., Ghazal, P., Forster, T., Piotrowski, M., & Trew, A. (2014). Parallel classification and feature selection in microarray data using SPRINT. Concurrency and Computation: Practice and Experience, 26(4), 854-865. https://doi.org/10.1002/cpe.2928

The statistical language R is favoured by many biostatisticians for processing microarray data. In recent times, the quantity of data that can be obtained in experiments has risen significantly, making previously fast analyses time consuming or even... Read More about Parallel classification and feature selection in microarray data using SPRINT.

Accelerating Cardiac Bidomain Simulations Using Graphics Processing Units (2012)
Journal Article
Neic, A., Liebmann, M., Hoetzl, E., Mitchell, L., Vigmond, E., Haase, G., & Plank, G. (2012). Accelerating Cardiac Bidomain Simulations Using Graphics Processing Units. IEEE Transactions on Biomedical Engineering, 59(8), 2281-2290. https://doi.org/10.1109/tbme.2012.2202661

Anatomically realistic and biophysically detailed multiscale computer models of the heart are playing an increasingly important role in advancing our understanding of integrated cardiac function in health and disease. Such detailed simulations, howev... Read More about Accelerating Cardiac Bidomain Simulations Using Graphics Processing Units.