Dohp aims to be a very efficient implementation of the hp-version of the finite element method. It exploits the tensor product structure of nodal bases on hexahedra to significantly reduce the memory requirements and computational cost compared to low-order elements. It uses Q1 elements on the nodes of the high-order basis to assemble a preconditioning matrix which is much sparser than Q2 elements. Preliminary results show that memory and solver runtime for arbitrary order (2-10 or so) is half that required by a standard Q2 approximation.
Dohp development is primarily focused on scalable solution of indefinite problems such as those found in incompressible flow and PDE-constrained optimization.
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