4,817 research outputs found
Kranc: a Mathematica application to generate numerical codes for tensorial evolution equations
We present a suite of Mathematica-based computer-algebra packages, termed
"Kranc", which comprise a toolbox to convert (tensorial) systems of partial
differential evolution equations to parallelized C or Fortran code. Kranc can
be used as a "rapid prototyping" system for physicists or mathematicians
handling very complicated systems of partial differential equations, but
through integration into the Cactus computational toolkit we can also produce
efficient parallelized production codes. Our work is motivated by the field of
numerical relativity, where Kranc is used as a research tool by the authors. In
this paper we describe the design and implementation of both the Mathematica
packages and the resulting code, we discuss some example applications, and
provide results on the performance of an example numerical code for the
Einstein equations.Comment: 24 pages, 1 figure. Corresponds to journal versio
Combining Static and Dynamic Contract Checking for Curry
Static type systems are usually not sufficient to express all requirements on
function calls. Hence, contracts with pre- and postconditions can be used to
express more complex constraints on operations. Contracts can be checked at run
time to ensure that operations are only invoked with reasonable arguments and
return intended results. Although such dynamic contract checking provides more
reliable program execution, it requires execution time and could lead to
program crashes that might be detected with more advanced methods at compile
time. To improve this situation for declarative languages, we present an
approach to combine static and dynamic contract checking for the functional
logic language Curry. Based on a formal model of contract checking for
functional logic programming, we propose an automatic method to verify
contracts at compile time. If a contract is successfully verified, dynamic
checking of it can be omitted. This method decreases execution time without
degrading reliable program execution. In the best case, when all contracts are
statically verified, it provides trust in the software since crashes due to
contract violations cannot occur during program execution.Comment: Pre-proceedings paper presented at the 27th International Symposium
on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur,
Belgium, 10-12 October 2017 (arXiv:1708.07854
DOLFIN: Automated Finite Element Computing
We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness with efficient computation. Finite element variational forms may be expressed in near mathematical notation, from which low-level code is automatically generated, compiled and seamlessly integrated with efficient implementations of
computational meshes and high-performance linear algebra. Easy-to-use object-oriented interfaces to the library are provided in the form of a C++ library and a Python module. This paper discusses the mathematical abstractions and methods used in the design of the library and its implementation. A number of examples are presented to demonstrate the use of the library in application code
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