Exasim: Generating Discontinuous Galerkin Codes for Numerical Solutions of Partial Differential Equations on Graphics Processors

TL;DR

Exasim is an open-source tool that automatically generates high-performance discontinuous Galerkin codes for solving parametrized PDEs on CPUs and GPUs, integrating high-level scripting with low-level optimized code.

Contribution

It introduces a flexible code generation framework combining high-level scripting languages with low-level C++ for efficient PDE solutions on heterogeneous hardware.

Findings

Enables high-order DG discretizations on GPUs and CPUs

Provides scalable reduced basis preconditioners and solvers

Achieves efficient and accurate PDE approximations

Abstract

This paper presents an overview of the functionalities and applications of Exasim, an open-source code for generating high-order discontinuous Galerkin codes to numerically solve parametrized partial differential equations (PDEs). The software combines high-level and low-level languages to construct parametrized PDE models via Julia, Python or Matlab scripts and produce high-performance C++ codes for solving the PDE models on CPU and Nvidia GPU processors with distributed memory. Exasim provides matrix-free discontinuous Galerkin discretization schemes together with scalable reduced basis preconditioners and Newton-GMRES solvers, making it suitable for accurate and efficient approximation of wide-ranging classes of PDEs.