SeisSol Matrices

Basis functions

We use the basis functions based on Jacobi polynomials as explained in appendix A of J. de la Puente, ‘Seismic Wave Simulation for Complex Rheologies on Unstructured Meshes’, PhD-Thesis, Ludwig-Maximilians-Universität München, Munich, 2008.

On triangles, we denote the polynomials as ${\mathrm{\Phi }}_{k(p,q)}$, where $k$ is a multiindex, based on $p$ and $q$. If we use basis functions for order $\mathcal{O}$, we have $\frac{1}{2}\times \mathcal{O}\times (\mathcal{O}+1)$ basis functions.

On tetrahedrons, we denote the polynomials as ${\mathrm{\Psi }}_{k(p,q,r)}$, where $l$ is a multiindex, based on $p$, $q$ and $r$. If we use basis functions for order $\mathcal{O}$, we have $\frac{1}{6}\times \mathcal{O}\times (\mathcal{O}+1)\times (\mathcal{O}+2)$ basis functions.

Matrices

Discountinuos Galerkin matrices

Notation	Formula	SeisSol
$M_{kl}$	${\int }_T{\mathrm{\Psi }}_k{\mathrm{\Psi }}_{l}dx$	M3
	${\int }_T{\mathrm{\Phi }}_k{\mathrm{\Phi }}_{l}dx$	M2
$F_{kl}^{-,j}$	${\int }_T{\mathrm{\Psi }}_k{\mathrm{\Psi }}_{l}dx$	rT

Usage

Use poetry to install or use the package. In particular, consider the commands

# install
poetry install
# format files
poetry run black src
# run unit tests
poetry run coverage run -m nose2