Fully automatic hp-adaptivity in three dimensions

Joint work with Leszek Demkowicz, David Pardo, Maciej Paszyński, Waldek Rachowicz and Adam Zdunek of the Swedish Defense Research Agency The backbone of this work is a Fortran 90 code supporting H1 and H(curl) conforming discretizations on 1-irregular hexahedral meshes - with the ability to refine anisotropically in both element size h and polynomial order p My principal contribution is a module supporting automatic, simultaneous hp-refinements, driven by the projection-based interpolation error of a reference (fine grid) solution Here are some animations of acoustic scattering from both smooth and geometrically singular obstacles Here are some animations of electromagnetic scattering from a thin box obstacle in a rectangular waveguide

Direct solvers for h and hp-adaptive finite elements

Joint work with Robert van de Geijn, Victor Eijkhout and Paulo Bientinesi Traditional direct solvers optimize the factorization of a single linear system by using graph partitioning algorithms to re-order the unknowns and identify supernodes Adaptive finite element methods require the solution of a sequence of linear systems generated by successive local refinement This project seeks to optimize the latter problem by using the natural ordering of unknowns dictated by the hierarchy of the mesh (nested substructuring) and storing the factors computed at each level With this approach, local mesh refinements require only local updates to the factorization

Elastic/acoustic waves in the human head

Joint work with Leszek Demkowicz, Maciej Paszyński, Jessica Zhang and Elizabeth and Marek Bleszynski of Monopole Research The cochlea is a fluid-filled cavity in the temporal bone of the skull, lined with tiny hairs that convert mechanical vibrations to electrical signals in the auditory nerve Under normal circumstances, acoustic waves travel into the ear canal and are transmitted from the ear drum to the oval window of the cochlea by a linkage of three small bones in the middle ear Underwater or in noisy environments, acoustic waves are also converted to elastic waves in the tissue and skull that reach the cochlea The goal of this project is to simulate both of these hearing mechanisms and determine the relative potential for damage to the cochlea Here are some preliminary computations for a layered elastic sphere