Introduction

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.

Documentation

• Documentation for the latest stable version.
• Documentation for the development version.

Hello World

To solve scattering of a time-harmonic electromagnetic plane wave by a perfectly conducting sphere:

using CompScienceMeshes
using BEAST

# --- basis functions
Γ  = meshsphere(1.0, 2.5)   # triangulate sphere of radius one
RT = raviartthomas(Γ)       # define basis functions

# --- operators & excitation
𝑇 = Maxwell3D.singlelayer(wavenumber=2.0)                             # integral operator
𝐸 = Maxwell3D.planewave(direction=x̂, polarization=ẑ, wavenumber=2.0)  # excitation
𝑒 = (n × 𝐸) × n # tangential part

# --- compute the RHS and system matrix
e = assemble(𝑒, RT)         # assemble RHS
T = assemble(𝑇, RT, RT)     # assemble system matrix

# --- solve
u = T \ -e

# ... post processing ...