LeXInt: GPU-accelerated Exponential Integrators package

TL;DR

LeXInt, written in a modular format, facilitates easy integration into any existing software package, and can be used for temporal integration of any differential equation, and can be used for temporal integration of any differential equation.

Abstract

We present an open-source CUDA-based package that consists of a compilation of exponential integrators where the action of the matrix exponential or the $\varphi_l$ functions on a vector is approximated using the method of polynomial interpolation at Leja points. Using a couple of test examples on an NVIDIA A100 GPU, we show that one can achieve significant speedups using CUDA over the corresponding CPU code. LeXInt, written in a modular format, facilitates easy integration into any existing software package, and can be used for temporal integration of any differential equation.

Figures (2)

• Figure 1: A flowchart demonstrating the structure and usage of LeXInt.
• Figure 2: The blue circles illustrate strong scaling for the linear diffusion--advection problem (top panel), linear diffusion--advection problem in the presence of sources (middle panel), and the Burgers' equation integrated using EXPRB32 (bottom panel). The configuration for simulations for the plots on the left half is $N_\mathrm{grid} = 2^{13} \times 2^{13}$, $T_f = 2\cdot10^{-7}$, and $\Delta t = 1 \cdot \Delta t_\mathrm{CFL}$, whilst for the right half, it is $N_\mathrm{grid} = 2^{14} \times 2^{14}$, $T_f = 2\cdot10^{-6}$, and $\Delta t = 100 \cdot \Delta t_\mathrm{CFL}$. All simulations were performed with a user-specified tolerance of $10^{-12}$ on Leonardo DCGP. The red line represents ideal strong scaling.