How do we build maintainable, robust, and performance-portable scientific
applications? This thesis argues that the answer to this software engineering
question in the context of the finite element method is through the use of
layers of Domain-Specific Languages (DSLs) to separate the various concerns in
the engineering of such codes.

Performance-portable software achieves high performance on multiple diverse
hardware platforms without source code changes. We demonstrate that finite
element solvers written in a low-level language are not performance-portable,
and therefore code must be specialised to the target architecture by a code
generation framework. A prototype compiler for finite element variational forms
that generates CUDA code is presented, and is used to explore how good
performance on many-core platforms in automatically-generated finite element
applications can be achieved. The differing code generation requirements for
multi- and many-core platforms motivates the design of an additional
abstraction, called PyOP2, that enables unstructured mesh applications to be
performance-portable.

We present a runtime code generation framework comprised of the Unified Form
Language (UFL), the FEniCS Form Compiler, and PyOP2. This toolchain separates
the succinct expression of a numerical method from the selection and
generation of efficient code for local assembly. This is further decoupled from
the selection of data formats and algorithms for efficient parallel
implementation on a specific target architecture.

We establish the successful separation of these concerns by demonstrating the
performance-portability of code generated from a single high-level source code
written in UFL across sequential C, CUDA, MPI and OpenMP targets. The
performance of the generated code exceeds the performance of comparable
alternative toolchains on multi-core architectures.