Biosspheres

A Python-based solver for Laplace and Helmholtz scattering by multiple disjoint spheres, utilizing spherical harmonic decomposition and local multiple trace formulations.

Its main routines are for:

• Computing boundary integral operators evaluated and tested against spherical harmonics.
• Building Calderón operators.
• Solving transmission problems using the multiple trace formulation.

Tested with python 3.9

Installation

We recommend to install the package in its own python environment.

Via pip

The package is available in TestPyPi.

For the minimum installation:

pip install --index-url https://test.pypi.org/simple/ --extra-index-url https://pypi.org/simple/ biosspheres

For the installation including the dependencies necessary for running jupyter notebooks:

pip install --index-url https://test.pypi.org/simple/ --extra-index-url https://pypi.org/simple/ biosspheres[all]

Docker

The biosspheres-notebook Docker image is configured to run biosspheres with Python 3.10. This can be done running:

docker run -v $(pwd):/root/shared -w "/root/shared" -p 8888:8888 pescapil/biosspheres-notebook

Additional comments

The file requirements.txt has the list of required package for biosspheres to work, they can be installed using pip install -r requirements.txt

How to use

See the Jupyter notebook examples in the folder "notebooks" to see how biosspheres can be used.

Contributing

Read the file CONTRIBUTING.md and also see the Jupyter notebooks.

Acknowledgments

External packages used in biosspheres

numpy

Library for arrays, vectors and matrices in dense format, along with routines of linear algebra, norm computation, dot product, among others. It also computes functions like sine, cosine, exponential, etc.

• Web page.
• GitHub repository.
• Documentation.

scipy

• Web page.
• GitHub repository.
• Documentation.

scipy.special

Library for special functions, as the spherical Bessel and spherical Hankel functions.

scipy.sparse

Library for sparse arrays.

pyshtools

All Legendre's functions are computed using the package pyshtools (documentation of pyshtools).

• Web page and documentation.
• GitHub repository of SHTOOLS.

matplotlib

Library used in the examples for plotting.

• Web page.
• GitHub repository.
• Documentation.