Productive and efficient computational science through domain-specific abstractions
File(s)
Author(s)
Rathgeber, Florian
Type
Thesis
Abstract
In an ideal world, scientific applications are computationally efficient,
maintainable and composable and allow scientists to work very productively. We
argue that these goals are achievable for a specific application field by
choosing suitable domain-specific abstractions that encapsulate domain
knowledge with a high degree of expressiveness.
This thesis demonstrates the design and composition of
domain-specific abstractions by abstracting the stages a scientist goes
through in formulating a problem of numerically solving a partial differential
equation. Domain knowledge is used to transform this problem into a different,
lower level representation and decompose it into parts which can be solved
using existing tools. A system for the portable solution of partial
differential equations using the finite element method on unstructured meshes
is formulated, in which contributions from different scientific communities
are composed to solve sophisticated problems.
The concrete implementations of these domain-specific abstractions are
Firedrake and PyOP2. Firedrake allows scientists to describe variational
forms and discretisations for linear and non-linear finite element problems
symbolically, in a notation very close to their mathematical models. PyOP2
abstracts the performance-portable parallel execution of local computations
over the mesh on a range of hardware architectures, targeting multi-core CPUs,
GPUs and accelerators. Thereby, a separation of concerns is achieved, in which
Firedrake encapsulates domain knowledge about the finite element method
separately from its efficient parallel execution in PyOP2, which in turn is
completely agnostic to the higher abstraction layer.
As a consequence of the composability of those abstractions, optimised
implementations for different hardware architectures can be
automatically generated without any changes to a single high-level
source. Performance matches or exceeds what is realistically attainable by
hand-written code. Firedrake and PyOP2 are combined to form a tool chain that
is demonstrated to be competitive with or faster than available alternatives
on a wide range of different finite element problems.
maintainable and composable and allow scientists to work very productively. We
argue that these goals are achievable for a specific application field by
choosing suitable domain-specific abstractions that encapsulate domain
knowledge with a high degree of expressiveness.
This thesis demonstrates the design and composition of
domain-specific abstractions by abstracting the stages a scientist goes
through in formulating a problem of numerically solving a partial differential
equation. Domain knowledge is used to transform this problem into a different,
lower level representation and decompose it into parts which can be solved
using existing tools. A system for the portable solution of partial
differential equations using the finite element method on unstructured meshes
is formulated, in which contributions from different scientific communities
are composed to solve sophisticated problems.
The concrete implementations of these domain-specific abstractions are
Firedrake and PyOP2. Firedrake allows scientists to describe variational
forms and discretisations for linear and non-linear finite element problems
symbolically, in a notation very close to their mathematical models. PyOP2
abstracts the performance-portable parallel execution of local computations
over the mesh on a range of hardware architectures, targeting multi-core CPUs,
GPUs and accelerators. Thereby, a separation of concerns is achieved, in which
Firedrake encapsulates domain knowledge about the finite element method
separately from its efficient parallel execution in PyOP2, which in turn is
completely agnostic to the higher abstraction layer.
As a consequence of the composability of those abstractions, optimised
implementations for different hardware architectures can be
automatically generated without any changes to a single high-level
source. Performance matches or exceeds what is realistically attainable by
hand-written code. Firedrake and PyOP2 are combined to form a tool chain that
is demonstrated to be competitive with or faster than available alternatives
on a wide range of different finite element problems.
Version
Open Access
Date Issued
2014-07
Date Awarded
2014-11
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Ham, David
Kelly, Paul
Sponsor
Engineering and Physical Sciences Research Council
Grant Number
EP/I00677X/1
Publisher Department
Computing
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)