Firedrake: Automating the finite element method by composing abstractions

ACM Transactions on Mathematical Software 43 (2016)

F Rathgeber, DA Ham, L Mitchell, M Lange, F Luporini, ATT McRae, GT Bercea, GR Markall, PHJ Kelly

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 centered on the composition of several existing and new abstractions for particular aspects of scientific computing. The result is a more complete separation of concerns that eases the incorporation of separate contributions from computer scientists, numerical analysts, and application specialists. These contributions may add functionality or improve performance. Firedrake benefits from automatically applying new optimizations. This includes factorizing mixed function spaces, transforming and vectorizing inner loops, and intrinsically supporting block matrix operations. Importantly, Firedrake presents a simple public API for escaping the UFL abstraction. This allows users to implement common operations that fall outside of pure variational formulations, such as flux limiters.



ATT Mcrae, G-T Bercea, L Mitchell, DA Ham, CJ Cotter

A structure-exploiting numbering algorithm for finite elements on extruded meshes, and its performance evaluation in Firedrake

Geoscientific Model Development 9 (2016) 3803-3815

GT Bercea, ATT McRae, DA Ham, L Mitchell, F Rathgeber, L Nardi, F Luporini, PHJ Kelly

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. Applications of extruded meshes include, but are not limited to, the representation of three-dimensional high aspect ratio domains employed by geophysical finite element simulations. These meshes are structured in the extruded direction. The algorithm presented here exploits this structure to avoid the performance penalty traditionally associated with unstructured meshes. We evaluate the implementation of this algorithm in the Firedrake finite element system on a range of low compute intensity operations which constitute worst cases for data layout performance exploration. The experiments show that having structure along the extruded direction enables the cost of the indirect data accesses to be amortized after 10-20 layers as long as the underlying mesh is well ordered. We characterize the resulting spatial and temporal reuse in a representative set of both continuous-Galerkin and discontinuous-Galerkin discretizations. On meshes with realistic numbers of layers the performance achieved is between 70 and 90% of a theoretical hardware-specific limit.

Improved seasonal prediction of the hot summer of 2003 over Europe through better representation of uncertainty in the land surface


DA MacLeod, HL Cloke, F Pappenberger, A Weisheimer

Human influence on climate in the 2014 southern England winter floods and their impacts


N Schaller, AL Kay, R Lamb, NR Massey, GJ van Oldenborgh, FEL Otto, SN Sparrow, R Vautard, P Yiou, I Ashpole, A Bowery, SM Crooks, K Haustein, C Huntingford, WJ Ingram, RG Jones, T Legg, J Miller, J Skeggs, D Wallom, A Weisheimer, S Wilson, PA Stott, MR Allen

Oceanic Stochastic Parameterizations in a Seasonal Forecast System


M Andrejczuk, FC Cooper, S Juricke, TN Palmer, A Weisheimer, L Zanna

Impact of springtime Himalayan-Tibetan Plateau snowpack on the onset of the Indian summer monsoon in coupled seasonal forecasts

CLIMATE DYNAMICS 47 (2016) 2709-2725

R Senan, YJ Orsolini, A Weisheimer, F Vitart, G Balsamo, TN Stockdale, E Dutra, FJ Doblas-Reyes, D Basang

The role of the tropical West Pacific in the extreme Northern Hemisphere winter of 2013/2014


PAG Watson, A Weisheimer, JR Knight, TN Palmer

The influence of the Gulf Stream on wintertime European blocking

CLIMATE DYNAMICS 47 (2016) 1545-1567

CH O'Reilly, S Minobe, A Kuwano-Yoshida

The signature of low-frequency oceanic forcing in the Atlantic Multidecadal Oscillation


CH O'Reilly, M Huber, T Woollings, L Zanna

Assessing the role of insulin-like growth factors and binding proteins in prostate cancer using Mendelian randomization: Genetic variants as instruments for circulating levels.

International journal of cancer 139 (2016) 1520-1533

C Bonilla, SJ Lewis, M-A Rowlands, TR Gaunt, G Davey Smith, D Gunnell, T Palmer, JL Donovan, FC Hamdy, DE Neal, R Eeles, D Easton, Z Kote-Jarai, AA Al Olama, S Benlloch, K Muir, GG Giles, F Wiklund, H Grönberg, CA Haiman, J Schleutker, BG Nordestgaard, RC Travis, N Pashayan, K-T Khaw, JL Stanford, WJ Blot, S Thibodeau, C Maier, AS Kibel, C Cybulski, L Cannon-Albright, H Brenner, J Park, R Kaneva, J Batra, MR Teixeira, H Pandha, PRACTICAL consortium, M Lathrop, RM Martin, JMP Holly

Circulating insulin-like growth factors (IGFs) and their binding proteins (IGFBPs) are associated with prostate cancer. Using genetic variants as instruments for IGF peptides, we investigated whether these associations are likely to be causal. We identified from the literature 56 single nucleotide polymorphisms (SNPs) in the IGF axis previously associated with biomarker levels (8 from a genome-wide association study [GWAS] and 48 in reported candidate genes). In ∼700 men without prostate cancer and two replication cohorts (N ∼ 900 and ∼9,000), we examined the properties of these SNPS as instrumental variables (IVs) for IGF-I, IGF-II, IGFBP-2 and IGFBP-3. Those confirmed as strong IVs were tested for association with prostate cancer risk, low (< 7) vs. high (≥ 7) Gleason grade, localised vs. advanced stage, and mortality, in 22,936 controls and 22,992 cases. IV analysis was used in an attempt to estimate the causal effect of circulating IGF peptides on prostate cancer. Published SNPs in the IGFBP1/IGFBP3 gene region, particularly rs11977526, were strong instruments for IGF-II and IGFBP-3, less so for IGF-I. Rs11977526 was associated with high (vs. low) Gleason grade (OR per IGF-II/IGFBP-3 level-raising allele 1.05; 95% CI: 1.00, 1.10). Using rs11977526 as an IV we estimated the causal effect of a one SD increase in IGF-II (∼265 ng/mL) on risk of high vs. low grade disease as 1.14 (95% CI: 1.00, 1.31). Because of the potential for pleiotropy of the genetic instruments, these findings can only causally implicate the IGF pathway in general, not any one specific biomarker.

Benchmarking Northern Hemisphere midlatitude atmospheric synoptic variability in centennial reanalysis and numerical simulations


A Dell'Aquila, S Corti, A Weisheimer, H Hersbach, C Peubey, P Poli, P Berrisford, D Dee, A Simmons

Influence of the Eurasian snow on the negative North Atlantic Oscillation in subseasonal forecasts of the cold winter 2009/2010

Climate Dynamics 47 (2016) 1325-1334

YJ Orsolini, R Senan, F Vitart, G Balsamo, A Weisheimer, FJ Doblas-Reyes

© 2015, The Author(s). The winter 2009/2010 was remarkably cold and snowy over North America and across Eurasia, from Europe to the Far East, coinciding with a pronounced negative phase of the North Atlantic Oscillation (NAO). While previous studies have investigated the origin and persistence of this anomalously negative NAO phase, we have re-assessed the role that the Eurasian snowpack could have played in contributing to its maintenance. Many observational and model studies have indicated that the autumn Eurasian snow cover influences circulation patterns over high northern latitudes. To investigate that role, we have performed a suite of forecasts with the coupled ocean–atmosphere ensemble prediction system from the European Centre for Medium-Range Weather Forecasts. Pairs of 2-month ensemble forecasts with either realistic or else randomized snow initial conditions are used to demonstrate how an anomalously thick snowpack leads to an initial cooling over the continental land masses of Eurasia and, within 2 weeks, to the anomalies that are characteristic of a negative NAO. It is also associated with enhanced vertical wave propagation into the stratosphere and deceleration of the polar night jet. The latter then exerts a downward influence into the troposphere maximizing in the North Atlantic region, which establishes itself within 2 weeks. We compare the forecasted NAO index in our simulations with those from several operational forecasts of the winter 2009/2010 made at the ECWMF, and highlight the importance of relatively high horizontal resolution.

Turbulent-laminar patterns in shear flows without walls

Journal of Fluid Mechanics 791 (2016) R8-

M Chantry, LS Tuckerman, D Barkley

© 2016 Cambridge University Press. Turbulent-laminar intermittency, typically in the form of bands and spots, is a ubiquitous feature of the route to turbulence in wall-bounded shear flows. Here we study the idealised shear between stress-free boundaries driven by a sinusoidal body force and demonstrate quantitative agreement between turbulence in this flow and that found in the interior of plane Couette flow-the region excluding the boundary layers. Exploiting the absence of boundary layers, we construct a model flow that uses only four Fourier modes in the shear direction and yet robustly captures the range of spatiotemporal phenomena observed in transition, from spot growth to turbulent bands and uniform turbulence. The model substantially reduces the cost of simulating intermittent turbulent structures while maintaining the essential physics and a direct connection to the Navier-Stokes equations. We demonstrate the generic nature of this process by introducing stress-free equivalent flows for plane Poiseuille and pipe flows that again capture the turbulent-laminar structures seen in transition.

Calibrating Climate Change Time-Slice Projections with Estimates of Seasonal Forecast Reliability

JOURNAL OF CLIMATE 29 (2016) 3831-3840

M Matsueda, A Weisheimer, TN Palmer

Stochastic and Perturbed Parameter Representations of Model Uncertainty in Convection Parameterization*


HM Christensen, IM Moroz, TN Palmer

Bell's conspiracy, Schrödinger's black cat and global invariant sets.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences 373 (2015)

TN Palmer

A locally causal hidden-variable theory of quantum physics need not be constrained by the Bell inequalities if this theory also partially violates the measurement independence condition. However, such violation can appear unphysical, implying implausible conspiratorial correlations between the hidden variables of particles being measured and earlier determinants of instrumental settings. A novel physically plausible explanation for such correlations is proposed, based on the hypothesis that states of physical reality lie precisely on a non-computational measure-zero dynamically invariant set in the state space of the universe: the Cosmological Invariant Set Postulate. To illustrate the relevance of the concept of a global invariant set, a simple analogy is considered where a massive object is propelled into a black hole depending on the decay of a radioactive atom. It is claimed that a locally causal hidden-variable theory constrained by the Cosmological Invariant Set Postulate can violate the Clauser-Horne-Shimony-Holt inequality without being conspiratorial, superdeterministic, fine-tuned or retrocausal, and the theory readily accommodates the classical compatibilist notion of (experimenter) free will.

Impact of Initial Conditions versus External Forcing in Decadal Climate Predictions: A Sensitivity Experiment*

JOURNAL OF CLIMATE 28 (2015) 4454-4470

S Corti, T Palmer, M Balmaseda, A Weisheimer, S Drijfhout, N Dunstone, W Hazeleger, J Kroeger, H Pohlmann, D Smith, J-S von Storch, B Wouters

Opportunities for Energy Efficient Computing: A Study of Inexact General Purpose Processors for High-Performance and Big-data Applications


P Duben, J Schlachter, Parishkrati, S Yenugula, J Augustine, C Enz, K Palem, TN Palmer, IEEE


Significance 12 (2015) 2-7

H Christensen, B Tarran