Related papers: Automated code generation for discontinuous Galerk…

This paper envisions an end-to-end program generation scenario using recurrent neural networks (RNNs): Users can express their intention in natural language; an RNN then automatically generates corresponding code in a…

We derive a posteriori error estimates for the hybridizable discontinuous Galerkin (HDG) methods, including both the primal and mixed formulations, for the approximation of a linear second-order elliptic problem on conforming simplicial…

We present a general framework to compute upper and lower bounds for linear-functional outputs of the exact solutions of the Poisson equation based on reconstructions of the field variable and flux for both the primal and adjoint problems.…

In this work, the authors introduce a generalized weak Galerkin (gWG) finite element method for the time-dependent Oseen equation. The generalized weak Galerkin method is based on a new framework for approximating the gradient operator.…

We propose an arbitrary-order discontinuous Galerkin method for second-order elliptic problem on general polygonal mesh with only one degree of freedom per element. This is achieved by locally solving a discrete least-squares over a…

This paper presents SimulatorCoder, an agent powered by large language models (LLMs), designed to generate and optimize deep neural network (DNN) accelerator simulators based on natural language descriptions. By integrating domain-specific…

We study discontinuous Galerkin approximations of the $p$--biharmonic equation from a variational perspective. We propose a discrete variational formulation of the problem based on a appropriate definition of a finite element Hessian and…

We present and analyze a new embedded--hybridized discontinuous Galerkin finite element method for the Stokes problem. The method has the attractive properties of full hybridized methods, namely an $H({\rm div})$-conforming velocity field,…

We present a high-order hybridizable discontinuous Galerkin method for the numerical solution of time-dependent three-phase flow in heterogeneous porous media. The underlying algorithm is a semi-implicit operator splitting approach that…

We introduce a family of mixed methods and discontinuous Galerkin discretisations designed to numerically solve the Oseen equations written in terms of velocity, vorticity, and Bernoulli pressure. The unique solvability of the continuous…

We develop a discontinuous Galerkin (DG) framework for automatically constructing adaptive basis sets for electronic structure calculations. By allowing basis functions to be discontinuous across element interfaces, our approach supports…

This paper discusses the upwinded local discontinuous Galerkin methods for the one-term/multi-term fractional ordinary differential equations (FODEs). The natural upwind choice of the numerical fluxes for the initial value problem for FODEs…

Automatic code generation from natural language descriptions can be highly beneficial during the process of software development. In this work, we propose GAP-Gen, a Guided Automatic Python Code Generation method based on Python syntactic…

Many software analysis methods have come to rely on machine learning approaches. Code segmentation - the process of decomposing source code into meaningful blocks - can augment these methods by featurizing code, reducing noise, and limiting…

Developing models that can automatically generate detailed code explanation can greatly benefit software maintenance and programming education. However, existing code-to-text generation models often produce only high-level summaries of code…

The idea of computer vision as the Bayesian inverse problem to computer graphics has a long history and an appealing elegance, but it has proved difficult to directly implement. Instead, most vision tasks are approached via complex…

Standard discontinuous Galerkin methods, based on piecewise polynomials of degree $ \qq=0,1$, are considered for temporal semi-discretization for second order hyperbolic equations. The main goal of this paper is to present a simple and…

Semiconductors form the backbone of modern electronics, with their manufacturing and testing relying on highly specialized equipment and domain-specific programming languages. Equipment languages such as the Algorithmic Pattern Generator…

Code generation aims to produce code that fulfills requirements written in natural languages automatically. Large language Models (LLMs) like ChatGPT have demonstrated promising effectiveness in this area. Nonetheless, these LLMs often fail…

The shallow water equations (SWE) are a commonly used model to study tsunamis, tides, and coastal ocean circulation. However, there exist various approaches to discretize and solve them efficiently. Which of them is best for a certain…