https://github.com/seissol/matrices

https://github.com/seissol/matrices

Last synced: about 1 month ago
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• Host: GitHub
• URL: https://github.com/seissol/matrices
• Owner: SeisSol
• License: bsd-3-clause
• Created: 2020-05-20T15:56:56.000Z (over 4 years ago)
• Default Branch: main
• Last Pushed: 2024-10-23T12:22:17.000Z (3 months ago)
• Last Synced: 2024-11-05T20:13:36.886Z (3 months ago)
• Language: Python
• Size: 290 KB
• Stars: 0
• Watchers: 7
• Forks: 0
• Open Issues: 1
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
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# 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`               |