Related papers: Automated generation and symbolic manipulation of …
We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational…
We examine aspects of the computation of finite element matrices and vectors which are made possible by automated code generation. Given a variational form in a syntax which resembles standard mathematical notation, the low-level computer…
Code generation based software platforms, such as Firedrake, have become popular tools for developing complicated finite element discretisations of partial differential equations. We extended the code generation infrastructure in Firedrake…
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…
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…
We have developed a symbolic algebra approach to automatically produce, verify, and optimize computer code for the Fast Multipole Method (FMM) operators. This approach allows for flexibility in choosing a basis set and kernel, and can…
Physical units are fundamental to scientific computing. However, many finite element frameworks lack built-in support for dimensional analysis. In this work, we present a systematic framework for integrating physical units into the Unified…
Non-deterministic Finite Automata (NFA) represent regular languages concisely, increasing their appeal for applications such as word recognition. This paper proposes a new approach to generate NFA from an interaction language such as UML…
Deterministic and nondeterministic finite automata (DFAs and NFAs) are abstract models of computation commonly taught in introductory computing theory courses. These models have important applications (such as fast regular expression…
Tensor algebra finds applications in various domains, and these applications, especially when accelerated on spatial hardware accelerators, can deliver high performance and low power. Spatial hardware accelerator exhibits complex design…
Gauge-invariant polynomial functions of matrix and tensor variables capture combinatorial structures of gauge-string duality, which can be usefully organised using finite-dimensional associative algebras. I review recent work on eigenvalue…
Tensor algebra is essential for data-intensive workloads in various computational domains. Computational scientists face a trade-off between the specialization degree provided by dense tensor algebra and the algorithmic efficiency that…
We introduce flat automata for automatic generation of tokenizers. Flat automata are a simple representation of standard finite automata. Using the flat representation, automata can be easily constructed, combined and printed. Due to the…
The finite dimensional representations of associative quadratic algebras with three generators are investigated by using a technique based on the deformed parafermionic oscillator algebra. One application on the calculation of the…
Let $G$ be a group and let $X$ be an algebraic variety over an algebraically closed field $k$ of characteristic zero. Denote $A=X(k)$ the set of rational points of $X$. We investigate invertible algebraic cellular automata $\tau \colon A^G…
The method of direct computation of universal (fibred) product in the category of commutative associative algebras of finite type with unity over a field is given and proven. The field of coefficients is not supposed to be algebraically…
Biomolecular computation has emerged as an important area of computer science research due to its high information density, immense parallelism opportunity along with potential applications in cryptography, genetic engineering and…
FIAT (the FInite element Automatic Tabulator) provides a powerful Python library for the generation and evaluation of finite element basis functions on a reference element. This release paper describes recent improvements to FIAT aimed at…
Due to the works of S. Bozapalidis and A. Alexandrakis, there is a well-known characterization of recognizable weighted tree languages over fields in terms of finite-dimensionality of syntactic vector spaces. Here we prove a…
We propose a correspondence between certain multiband linear cellular automata - models of computation widely used in the description of physical phenomena - and endomorphisms of certain algebraic unipotent groups over finite fields. The…