Westervelt Equation Simulation on Manifold using DEC

TL;DR

This paper presents a numerical method using discrete exterior calculus to simulate the Westervelt equation on manifolds, offering a geometric approach to ultrasound propagation modeling with implementation in C++.

Contribution

It introduces a novel application of discrete exterior calculus for solving the Westervelt equation on manifolds, extending finite difference methods to complex geometries.

Findings

Successfully implemented the algorithm in C++

Demonstrated the method's effectiveness on manifold geometries

Provided a new geometric framework for ultrasound simulation

Abstract

The Westervelt equation is a model for the propagation of finite amplitude ultrasound. The method of discrete exterior calculus can be used to solve this equation numerically. A significant advantage of this method is that it can be used to find numerical solutions in the discrete space manifold and the time, and therefore is a generation of finite difference time domain method. This algorithm has been implemented in C++.