PyOP2: A High-Level Framework for Performance-Portable Simulations on Unstructured Meshes

Rathgeber, Florian; Markall, Graham; Mitchell, Lawrence; Loriant, Nicolas; Ham, David A.; Bertolli, Carlo; Kelly, Paul H. J.

doi:10.1109/sc.companion.2012.134

Cited by 62 publications

(56 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although well established finite element methods could be supported by such a declarative abstraction, it lacks the flexibility offered by frameworks such as OP2 for developing new applications/algorithms. Currently, a runtime code generation, compilation and execution framework that is based on Python, called PyOP2 [31], is being developed at Imperial College London to enable FEniCS declarations to use the OP2 back-ends. Thus, the performance results in this paper will be directly applicable to the performance of code written using FEniCS in the future.…”

Section: Related Workmentioning

confidence: 99%

Design and initial performance of a high-level unstructured mesh framework on heterogeneous parallel systems

et al. 2013

View full text Add to dashboard Cite

Section: Related Workmentioning

confidence: 99%

Design and initial performance of a high-level unstructured mesh framework on heterogeneous parallel systems

et al. 2013

View full text Add to dashboard Cite

“…Like the FEniCS Project [Logg et al, 2012;Alnaes et al, 2015], it is also built upon several scientific packages and can employ parallel computing tools across either CPUs or GPUs to obtain the solution. Two of its main leveraged components are the Unified Form Language (UFL) [Alnaes et al, 2014], used to declare finite element discretizations of variational forms, and the PyOP2 system [Rathgeber et al, 2012;Markall et al, 2013], used for the parallel assembly of the finite element discrete formulations. The main difference between the FEniCS and Firedrake project is that all data structures, linear solvers, non-linear solvers, and optimization solvers for the latter are provided entirely by the PETSc and TAO libraries.…”

Section: Appendix a Firedrake Projectmentioning

confidence: 99%

Variational inequality approach to enforcing the non-negative constraint for advection–diffusion equations

Chang

Nakshatrala

2017

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

These figures depict the concentration profiles of the advection-diffusion equation under the Discontinuous Galerkin formulation (left) and the Discontinuous Galerkin formulation with bounded constraints enforced through a variational inequality (right). Only the regions where concentrations meet the threshold of 0.5 and above are shown. Abstract. Predictive simulations are crucial for the success of many subsurface applications, and it is highly desirable to obtain accurate non-negative solutions for transport equations in these numerical simulations. To this end, optimization-based methodologies based on quadratic programming (QP) have been shown to be a viable approach to ensuring discrete maximum principles and the non-negative constraint for anisotropic diffusion equations. In this paper, we propose a computational framework based on the variational inequality (VI) which can also be used to enforce important mathematical properties (e.g., maximum principles) and physical constraints (e.g., the non-negative constraint). We demonstrate that this framework is not only applicable to diffusion equations but also to non-symmetric advection-diffusion equations. An attractive feature of the proposed framework is that it works with with any weak formulation for the advection-diffusion equations, including single-field formulations, which are computationally attractive. A particular emphasis is placed on the parallel and algorithmic performance of the VI approach across large-scale and heterogeneous problems. It is also shown that QP and VI are equivalent under certain conditions. State-of-the-art QP and VI solvers available from the PETSc library are used on a variety of steady-state 2D and 3D benchmarks, and a comparative study on the scalability between the QP and VI solvers is presented. We then extend the proposed framework to transient problems by simulating the miscible displacement of fluids in a heterogeneous porous medium and illustrate the importance of enforcing maximum principles for these types of coupled problems. Our numerical experiments indicate that VIs are indeed a viable approach for enforcing the maximum principles and the non-negative constraint in a large-scale computing environment. Also provided are Firedrake project files as well as a discussion on the computer implementation to help facilitate readers in understanding the proposed framework.

show abstract

“…UFL Unified Form Language [4,2], a domain-specific language for the specification of finite element variational forms. Firedrake also relies on PyOP2 [37] and COFFEE [30].…”

Section: Product Finite Elements Within Finite Element Exterior Calcumentioning

confidence: 99%

Automated Generation and Symbolic Manipulation of Tensor Product Finite Elements

McRae¹,

Bercea²,

Mitchell³

et al. 2016

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

Abstract. 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 implemented as an extension to the domain-specific language UFL, the Unified Form Language. This allows users to construct many finite element spaces beyond those supported by existing software packages. We have made corresponding extensions to FIAT, the FInite element Automatic Tabulator, to enable numerical tabulation of such spaces. This tabulation is consequently used during the automatic generation of low-level code that carries out local assembly operations, within the wider context of solving finite element problems posed over such function spaces. We have done this work within the code-generation pipeline of the software package Firedrake; we make use of the full Firedrake package to present numerical examples.

show abstract

PyOP2: A High-Level Framework for Performance-Portable Simulations on Unstructured Meshes

Cited by 62 publications

References 18 publications

Design and initial performance of a high-level unstructured mesh framework on heterogeneous parallel systems

Design and initial performance of a high-level unstructured mesh framework on heterogeneous parallel systems

Variational inequality approach to enforcing the non-negative constraint for advection–diffusion equations

Automated Generation and Symbolic Manipulation of Tensor Product Finite Elements

Contact Info

Product

Resources

About