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.