arXiv subjects
Publications and source records attributed to Kent-Andre Mardal.
We study preconditioners for a model problem describing the coupling of two elliptic subproblems posed over domains with different topological dimension by a parameter dependent constraint. A pair of parameter robust and efficient preconditioners is proposed and analyzed. Robustness and efficiency of the preconditioners is demonstrated by numerical experiments.
Most Computational Fluid Dynamics (CFD) studies of hemodynamics in intracranial aneurysms are based on the assumption of laminar flow due to a relatively low (below 500) parent artery Reynolds number. A few studies have recently demonstrated the occurrence of transitional flow in aneurysms, but these studies employed special finite element schemes tailored to capture transitional nature of flow. In this study we investigate the occurrence of transition using a standard Lattice Boltzmann method (LBM). The LBM is used because of its computational efficiency, which in the present study allowed us to perform simulations at a higher resolution than has been done in the context of aneurysms before. The high space-time resolutions of 8μm and 0.11 μs resulted in nearly one billion cells and 9 million time steps per second and allowed us to quantify the turbulent kinetic energy at resolutions below the Kolmogorov scales. We perform an in-depth space and time refinement study on 2 aneurysms; one was previously reported laminar, while the other was reported transitional. Furthermore, we investigate the critical Reynolds number at which the flow transitions in aneurysms under time constant inflow conditions.
At the heart of any finite element simulation is the assembly of matrices and vectors from discrete variational forms. We propose a general interface between problem-specific and general-purpose components of finite element programs. This interface is called Unified Form-assembly Code (UFC). A wide range of finite element problems is covered, including mixed finite elements and discontinuous Galerkin methods. We discuss how the UFC interface enables implementations of variational form evaluation to be independent of mesh and linear algebra components. UFC does not depend on any external libraries, and is released into the public domain.
A uniform inf-sup condition related to a parameter dependent Stokes problem is established. Such conditions are intimately connected to the construction of uniform preconditioners for the problem, i.e., preconditioners which behave uniformly well with respect to variations in the model parameter as well as the discretization parameter. For the present model, similar results have been derived before, but only by utilizing extra regularity ensured by convexity of the domain. The purpose of this paper is to remove this artificial assumption. As a byproduct of our analysis, in the two dimensional case we also construct a new projection operator for the Taylor-Hood element which is uniformly bounded in $L^2$ and commutes with the divergence operator. This construction is based on a tight connection between a subspace of the Taylor-Hood velocity space and the lowest order Nedelec edge element.