Fast static condensation: A linearly scaling operator for non-constant diffusivities

Kurzfassung

This paper derives a decomposition of the static condensed element operator for a spectral-element method for the Poisson equation for non-constant diffusivities. It allows to evaluate the static condensed element operator in O(n3 ) operations per element, where n is the number of points per hexahedral element, i.e. scaling linearly with the number of degrees of freedom in the full mesh. Numerical tests prove the exactness of the operator by comparing to the full operator, and runtime measurements demonstrate the linear scaling