# A general high order two-dimensional panel method

## TL;DR

This paper introduces a high-order, quadrature-free two-dimensional panel method optimized for airfoil design, balancing accuracy and computational efficiency, and provides an open-source implementation.

## Contribution

It presents a novel high-order panel method that is quadrature-free and integrates with a fast multipole method for improved efficiency.

## Key findings

- Method achieves high accuracy with reduced computational cost
- Trade-offs between approximation order and complexity are analyzed
- Open-source implementation available for practical use

## Abstract

We develop an efficient and high order panel method with applications in airfoil design. Through the use of analytic work and careful considerations near singularities our approach is quadrature-free. The resulting method is examined with respect to accuracy and efficiency and we discuss the different trade-offs in approximation order and computational complexity. A reference implementation within a package for a two-dimensional fast multipole method is distributed freely.