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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.