https://github.com/mipals/boundaryintegralequations.jl

A simple package for solving Boundary Integral Equations using the (collocation) Boundary Element Method.
https://github.com/mipals/boundaryintegralequations.jl

acoustics bem boundary-element-method boundary-integral-equations

Last synced: about 2 months ago
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A simple package for solving Boundary Integral Equations using the (collocation) Boundary Element Method.

• Host: GitHub
• URL: https://github.com/mipals/boundaryintegralequations.jl
• Owner: mipals
• License: mit
• Created: 2022-04-21T09:09:02.000Z (over 2 years ago)
• Default Branch: main
• Last Pushed: 2024-03-15T06:39:04.000Z (10 months ago)
• Last Synced: 2024-03-15T07:44:26.295Z (10 months ago)
• Topics: acoustics, bem, boundary-element-method, boundary-integral-equations
• Language: Julia
• Homepage:
• Size: 520 MB
• Stars: 8
• Watchers: 1
• Forks: 0
• Open Issues: 1
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# BoundaryIntegralEquations.jl

| **Documentation** | **Tests** | **CodeCov** | **Lifecycle** | **Aqua** |

|:-----------------:|:---------:|:-----------:|:-------------:|:--------:|

|[![](https://img.shields.io/badge/docs-online-blue.svg)](https://mipals.github.io/BoundaryIntegralEquations.jl/dev/)| [![Build Status](https://github.com/mipals/BoundaryIntegralEquations.jl/actions/workflows/CI.yml/badge.svg?branch=main)](https://github.com/mipals/BoundaryIntegralEquations.jl/actions/workflows/CI.yml?query=branch%3Amain) | [![Coverage](https://codecov.io/gh/mipals/BoundaryIntegralEquations.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/mipals/BoundaryIntegralEquations.jl)| ![](https://img.shields.io/badge/Lifecycle-Unstable-yellow)| [![Aqua QA](https://raw.githubusercontent.com/JuliaTesting/Aqua.jl/master/badge.svg)](https://github.com/JuliaTesting/Aqua.jl) |

BoundaryIntegralEquations.jl provides the basic building blocks required for implementing Boundary Element Methods (BEMs). Currently, it supplies the discretization of the Kirchhoff–Helmholtz integral equation found in acoustical applications.

```math

\zeta(\mathbf{x})p(\mathbf{x}) + \int_\Gamma \frac{\partial G(\mathbf{x}, \mathbf{y})}{\partial \mathbf{n}(\mathbf{y})}p(\mathbf{y})\ \mathrm{d}S_\mathbf{y} -

    \mathrm{i} \rho_0 c k \int_\Gamma G(\mathbf{x},\mathbf{y})v_\mathbf{n}(\mathbf{y})\ \mathrm{d}S_\mathbf{y} = 0.

```

where 

```math 

    G(\mathbf{x},\mathbf{y}) = \frac{\exp\left(\mathrm{i}k\|\mathbf{x} - \mathbf{y}\|_2\right)}{4\pi\|\mathbf{x} - \mathbf{y}\|_2},

``` 

is the Green's function of the Helmholtz operator, $k$ is the wavenumber, $\rho_0$ is the ambient density and $c$ is the speed of sound.

The package supplies support for acceleration methods such as e.g. the Fast Multipole Method (FMM) and Hierarchical matrices. For the FMM the package utilizes the Flatiron Institute Fast Multipole Libraries ([2D](https://github.com/mipals/FMM2D.jl), [3D](https://github.com/flatironinstitute/FMM3D/tree/master/julia)) whereas for Hierarchical matrices it uses the [HMatrices.jl](https://github.com/WaveProp/HMatrices.jl) package.

## Installation

The package can be installed directly from GitHub 

```julia

using Pkg

Pkg.add(url="https://github.com/mipals/BoundaryIntegralEquations.jl")

```

## Mesh formats

* COMSOLs *.mphtxt* files (including entity description)

* `obj`, `stl`, `ply`, `off` and `2DM` through [MeshIO.jl](https://github.com/JuliaIO/MeshIO.jl).

## Similar Packages

* [BEAST.jl](https://github.com/krcools/BEAST.jl): Boundary Element Analysis and Simulation Toolkit. A general toolkit, with a focus on electromagnetics. Limitations with respect to element orders and only supplies Galerkin assembly. 

* [NESSie.jl](https://github.com/tkemmer/NESSie.jl): Nonlocal Electrostatics in Structured Solvents. A specialized package written specifically for Nonlocal protein eletrostatics.