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Section: New Results

Cubature nodes for spectral element methods on symplicial meshes

Participants : Richard Pasquetti, Francesca Rapetti.

In a recent JCP paper (see [37]), a higher order triangular spectral element method (TSEM) is proposed to address seismic wave field modeling. The main interest of this TSEM is that the mass matrix is diagonal, so that an explicit time marching becomes very cheap. In [16], R. Pasquetti and F. Rapetti have compared this cubature points based method to the Fekete-Gauss one, that makes use of Fekete points for interpolation and of Gauss points for quadrature. Moreover, they have proposed an extension of this cubature TSEM to address elliptic PDEs with non homogeneous Neumann or Robin boundary conditions. More recently, the cubature TSEM has been experimented with isoparametric mappings to consider the case of non polygonal computational domains. In any cases it turns out that the cubature TSEM compares well with the Fekete-Gauss one.