Related papers: Automated code generation for discontinuous Galerk…
The finite element method, finite difference method, finite volume method and spectral method have achieved great success in solving partial differential equations. However, the high accuracy of traditional numerical methods is at the cost…
Traditionally, parsing has been a laborious and error-prone component of compiler development, and most parsers for full industrial programming languages are still written by hand. The author [Zim22] shows that automatic parser generation…
The digital transformation of automation places new demands on data acquisition and processing in industrial processes. Logical relationships between acquired data and cyclic process sequences must be correctly interpreted and evaluated. To…
Hybrid finite element methods such as hybridizable discontinuous Galerkin, hybrid high-order and weak Galerkin have emerged as powerful techniques for solving partial differential equations on general polytopal meshes. Despite their diverse…
This paper proposes a novel computational framework for the solution of geometrically parametrised flow problems governed by the Stokes equation. The proposed method uses a high-order hybridisable discontinuous Galerkin formulation and the…
Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…
Code generation, defined as automatically writing a piece of code to solve a given problem for which an evaluation function exists, is a classic hard AI problem. Its general form, writing code using a general language used by human…
A form compiler takes a high-level description of the weak form of partial differential equations and produces low-level code that carries out the finite element assembly. In this paper we present the Two-Stage Form Compiler (TSFC), a new…
The size and complexity of software applications is increasing at an accelerating pace. Source code repositories (along with their dependencies) require vast amounts of labor to keep them tested, maintained, and up to date. As the…
A new finite element method with discontinuous approximation is introduced for solving second order elliptic problem. Since this method combines the features of both conforming finite element method and discontinuous Galerkin (DG) method,…
Combinatorial evolution - the creation of new things through the combination of existing things - can be a powerful way to evolve rather than design technical objects such as electronic circuits. Intriguingly, this seems to be an ongoing…
We develop the general form of the variational multiscale method in a discontinuous Galerkin framework. Our method is based on the decomposition of the true solution into discontinuous coarse-scale and discontinuous fine-scale parts. The…
The proximal Galerkin finite element method is a high-order, low-iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of point-wise bound constraints in infinite-dimensional function spaces.…
This document describes an attempt to develop a compiler-based approach for computations with symmetric tensors. Given a computation and the symmetries of its input tensors, we derive formulas for random access under a storage scheme that…
We combine continuous and discontinuous Galerkin methods in the setting of a model diffusion problem. Starting from a hybrid discontinuous formulation, we replace element interiors by more general subsets of the computational domain -…
Automatic code generation for low-dimensional geometric algorithms is capable of producing efficient low-level software code through a high-level geometric domain specific language. Geometric Algebra (GA) is one of the most suitable…
Generating performant executables from high level languages is critical to software performance across a wide range of domains. Modern compilers perform this task by passing code through a series of well-studied optimizations at…
In this paper, we introduce a discontinuous Finite Element formulation on simplicial unstructured meshes for the study of free surface flows based on the fully nonlinear and weakly dispersive Green-Naghdi equations. Working with a new class…
In the prequel to this paper, we presented a systematic framework for processing spline spaces. In this paper, we take the results of that framework and provide a code generation pipeline that automatically generates efficient…
We introduce an immersed high-order discontinuous Galerkin method for solving the compressible Navier-Stokes equations on non-boundary-fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are…