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

Kurzfassung

This paper derives a decomposition of the condensed part of the element operator for second-order elliptic equations with non-constant diffusivities that are generated via a tensor product. It allows to implement the static condensation operator in O(n^3 n_e) , where n is the number of points per direction and n_e the number of elements, i.e. scaling linearly with the number of degrees of freedom in the full mesh. Runtime tests demonstrate the linear scaling and beneficial behavior compared to matrix-matrix implementations.