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 $\Phi_{k(p,q)}$, 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 $\Psi_{k(p,q,r)}$, 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
$M_{kl}$	$\int_T \Psi_k \Psi_l dx$	M3
	$\int_T \Phi_k \Phi_l dx$	M2
$F_{kl}^{-,j}$	$\int_T \Psi_k \Psi_l dx$	rT