# Landau Collision Integral Solver with Adaptive Mesh Refinement on Emerging Architectures

## TL;DR

This paper presents a high-order finite element solver for the Landau collision integral in fusion plasmas, optimized with adaptive mesh refinement and vectorization for emerging architectures like Intel Xeon Phi.

## Contribution

It introduces a fully conservative, adaptive finite element discretization of the Landau integral optimized for vector processing on modern architectures.

## Key findings

- Achieves up to 22% of peak flop rate on Knights Landing
- Develops algorithms for efficient memory usage and vectorization
- Demonstrates effective adaptive mesh refinement for plasma simulations

## Abstract

The Landau collision integral is an accurate model for the small-angle dominated Coulomb collisions in fusion plasmas. We investigate a high order accurate, fully conservative, finite element discretization of the nonlinear multi-species Landau integral with adaptive mesh refinement using the PETSc library (www.mcs.anl.gov/petsc). We develop algorithms and techniques to efficiently utilize emerging architectures with an approach that minimizes memory usage and movement and is suitable for vector processing. The Landau collision integral is vectorized with Intel AVX-512 intrinsics and the solver sustains as much as 22% of the theoretical peak flop rate of the Second Generation Intel Xeon Phi, Knights Landing, processor.