# A performance spectrum for parallel computational frameworks that solve PDEs

## TL;DR

This paper introduces a performance spectrum analysis method to evaluate and understand the efficiency and scalability of parallel computational frameworks for solving PDEs across different hardware and software configurations.

## Contribution

It proposes a versatile performance spectrum model for analyzing parallel PDE solvers, applicable to various hardware, software, and complex PDEs, enhancing performance understanding.

## Key findings

- Performance spectrum effectively analyzes scalability.
- Applicable to diverse hardware and PDE types.
- Helps identify bottlenecks in parallel PDE solvers.

## Abstract

Important computational physics problems are often large-scale in nature, and it is highly desirable to have robust and high performing computational frameworks that can quickly address these problems. However, it is no trivial task to determine whether a computational framework is performing efficiently or is scalable. The aim of this paper is to present various strategies for better understanding the performance of any parallel computational frameworks for solving PDEs. Important performance issues that negatively impact time-to-solution are discussed, and we propose a performance spectrum analysis that can enhance one's understanding of critical aforementioned performance issues. As proof of concept, we examine commonly used finite element simulation packages and software and apply the performance spectrum to quickly analyze the performance and scalability across various hardware platforms, software implementations, and numerical discretizations. It is shown that the proposed performance spectrum is a versatile performance model that is not only extendable to more complex PDEs such as hydrostatic ice sheet flow equations, but also useful for understanding hardware performance in a massively parallel computing environment. Potential applications and future extensions of this work are also discussed.