Solving Poisson's Equation on the Microsoft HoloLens

TL;DR

This paper introduces HoloFEM, a mixed reality application on Microsoft HoloLens that visualizes solutions to Poisson's equation using finite element methods, integrating real-world geometry for practical engineering applications.

Contribution

The paper presents a novel mixed reality tool that enables defining, solving, and visualizing Poisson's equation directly within the user's real environment.

Findings

Successful implementation of finite element method in mixed reality

Effective visualization of PDE solutions in real-world context

Potential applications in engineering and safety planning

Abstract

We present a mixed reality application (HoloFEM) for the Microsoft HoloLens. The application lets a user define and solve a physical problem governed by Poisson's equation with the surrounding real world geometry as input data. Holograms are used to visualise both the problem and the solution. The finite element method is used to solve Poisson's equation. Solving and visualising partial differential equations in mixed reality could have potential usage in areas such as building planning and safety engineering.