Related papers: COFFEE: an Optimizing Compiler for Finite Element …
COFFEE (ConFormal Field Equation Evolver) is a Python package primarily developed to numerically evolve systems of partial differential equations over time using the method of lines. It includes a variety of time integrators and finite…
We propose a kernel compression method for solving Distributed-Order (DO) Fractional Partial Differential Equations (DOFPDEs) at the cost of solving corresponding local-in-time PDEs. The key concepts are (1) discretization of the integral…
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…
Code generation has largely improved development efficiency in the era of large language models (LLMs). With the ability to follow instructions, current LLMs can be prompted to generate code solutions given detailed descriptions in natural…
Building on the successes of local kernel methods for approximating the solutions to partial differential equations (PDE) and the evaluation of definite integrals (quadrature/cubature), a local estimate of the error in such approximations…
Finite element method (FEM) is one of the most important numerical methods in modern engineering design and analysis. Since traditional serial FEM is difficult to solve large FE problems efficiently and accurately, high-performance parallel…
In recent years, high performance scientific computing on graphics processing units (GPUs) have gained widespread acceptance. These devices are designed to offer massively parallel threads for running code with general purpose. There are…
We present BEE, a compiler which enables to encode finite domain constraint problems to CNF. Using BEE both eases the encoding process for the user and also performs transformations to simplify constraints and optimize their encoding to…
In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches,…
We examine the effect of using complexity-reducing relations to generate optimized code for the evaluation of finite element variational forms. The optimizations are implemented in a prototype code named FErari, which has been integrated as…
We present a prototypical linear algebra compiler that automatically exploits domain-specific knowledge to generate high-performance algorithms. The input to the compiler is a target equation together with knowledge of both the structure of…
We present a high-level domain-specific language (DSL) interface to drive an adaptive incomplete $k$-d tree-based framework for finite element (FEM) solutions to PDEs. This DSL provides three key advances: (a) it abstracts out the…
The paper presents investigations on the implementation and performance of the finite element numerical integration algorithm for first order approximations and three processor architectures, popular in scientific computing, classical CPU,…
In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics…
The coffea framework provides a new approach to High-Energy Physics analysis, via columnar operations, that improves time-to-insight, scalability, portability, and reproducibility of analysis. It is implemented with the Python programming…
Particle breakage due to collisional interactions plays a vital role in the development of several phenomena in science and engineering. The nonlinear collisional breakage equations (NCBEs) are a significant set of equations in this…
In this paper, we introduce the Phantom Domain Finite Element Method (PDFEM), a novel computational approach tailored for the efficient analysis of heterogeneous and composite materials. Inspired by fictitious domain methods, this method…
The ultimate goal of any numerical scheme for partial differential equations (PDEs) is to compute an approximation of user-prescribed accuracy at quasi-minimal computational time. To this end, algorithmically, the standard adaptive finite…
The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for finite element discretizations. MFEM supports numerous types of finite element methods and is the discretization engine powering many computational…
The computational cost of concurrent multiscale finite element methods is dominated by the repeated solution of microscopic representative volume element (RVE) problems at macroscopic quadrature points. In this work, we introduce a…