 |
| Titel |
A Spectral Element Discretisation on Unstructured Triangle / Tetrahedral Meshes for Elastodynamics |
| VerfasserIn |
Dave A. May, Alice-A. Gabriel |
| Konferenz |
EGU General Assembly 2017
|
| Medientyp |
Artikel
|
| Sprache |
en
|
| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 19 (2017) |
| Datensatznummer |
250148913
|
| Publikation (Nr.) |
 EGU/EGU2017-13218.pdf |
|
|
|
|
|
| Zusammenfassung |
| The spectral element method (SEM) defined over quadrilateral and hexahedral
element geometries has proven to be a fast, accurate and scalable approach to study
wave propagation phenomena. In the context of regional scale seismology and or
simulations incorporating finite earthquake sources, the geometric restrictions associated
with hexahedral elements can limit the applicability of the classical quad./hex.
SEM.
Here we describe a continuous Galerkin spectral element discretisation defined over
unstructured meshes composed of triangles (2D), or tetrahedra (3D). The method uses a
stable, nodal basis constructed from PKD polynomials and thus retains the spectral accuracy
and low dispersive properties of the classical SEM, in addition to the geometric versatility
provided by unstructured simplex meshes. For the particular basis and quadrature rule we
have adopted, the discretisation results in a mass matrix which is not diagonal, thereby
mandating linear solvers be utilised. To that end, we have developed efficient solvers and
preconditioners which are robust with respect to the polynomial order (p), and
possess high arithmetic intensity. Furthermore, we also consider using implicit time
integrators, together with a p-multigrid preconditioner to circumvent the CFL condition.
Implicit time integrators become particularly relevant when considering solving
problems on poor quality meshes, or meshes containing elements with a widely varying
range of length scales - both of which frequently arise when meshing non-trivial
geometries.
We demonstrate the applicability of the new method by examining a number of two- and
three-dimensional wave propagation scenarios. These scenarios serve to characterise the
accuracy and cost of the new method. Lastly, we will assess the potential benefits of
using implicit time integrators for regional scale wave propagation simulations. |
|
|
|
|
|
|