BEAST.jl

This Julia package, the boundary element analysis and simulation toolkit (BEAST), provides routines to convert integral and differential equations to linear systems of equations via the boundary element method (BEM) and the finite element method (FEM). To this end, the (Petrov-) Galerkin method is employed.

Currently, the focus is on equations encountered in classical electromagnetism, where frequency and time domain equations are covered. Several operators, basis functions, and geometry representations are implemented.

Note

SI units and for time-harmonic simulations a time convention of $\mathrm{e}^{\,\mathrm{j}\omega t}$ are used everywhere.

Tip

To use the code have a look at the general usage.

However, the code is designed such that users can easily hook into the code at any level and implement new features. To do so, have a look at the internals documentation and the contribution guidelines. Design goals are extendability and a performant execution.

Installation

Installing BEAST is done by entering the package manager (enter ] at the julia REPL) and issuing:

pkg> add BEAST

Overview

The following operators, basis functions, and geometry representations are implemented. To see details and all variations, have a look at the corresponding sections of this documentation.

Operators

Boundary Integral operators
- Maxwell (3D)
  - Single Layer (time-harmonic & time-domain)
  - Double Layer (time-harmonic & time-domain)
- Helmholtz (2D & 3D)
  - Single Layer
  - Double Layer
Volume Integral operators
- Maxwell
  - Single Layer (time-harmonic)
  - Double Layer (time-harmonic)
Local Operators
- Identity (+ variations thereof)

Basis functions

Spatial
- Low Order
  - Raviart-Thomas / Rao-Wilton-Glisson
  - Buffa-Christiansen
  - Brezzi-Douglas-Marini
- High Order
  - Graglia-Wilton-Peterson (GWP)
  - B-Spline based

Temporal
- Lagrange?
- ...

Geometry Representations

Low Order ("flat")
- Triangular
- Quadrilaterals
- Tetrahedra

High Order (curvilinear)
- NURBS-surfaces