Parallel black box \mathcal {H}-LU preconditioning for elliptic boundary value problems

Hierarchical ( $\mathcal {H}$ -) matrices provide a data-sparse way to approximate fully populated matrices. The two basic steps in the construction of an $\mathcal {H}$ -matrix are (a) the hierarchical construction of a matrix block partition, and (b) the blockwise approximation of matrix data by low rank matrices. In the context of finite element discretisations of elliptic boundary value problems, $\mathcal {H}$ -matrices can be used for the construction of preconditioners such as approximate $\mathcal {H}$ -LU factors. In this paper, we develop a new black box approach to construct the necessary partition. This new approach is based on the matrix graph of the sparse stiffness matrix and no longer requires geometric data associated with the indices like the standard clustering algorithms. The black box clustering and a subsequent $\mathcal {H}$ -LU factorisation have been implemented in parallel, and we provide numerical results in which the resulting black box $\mathcal {H}$ -LU factorisation is used as a preconditioner in the iterative solution of the discrete (three-dimensional) convection-diffusion equation.     

Audio peer feedback to promote deep learning in online education

We investigated the relation between providing and receiving audio peer feedback with a deep approach to learning within online education. Online students were asked to complete peer feedback assignments. Data through a questionnaire with 108 respondents and 14 interviews were used to measure to what extent deep learning was perceived and why. Results support the view that both providing and receiving audio peer feedback indeed promote deep learning. As a consequence of the peer feedback method, the following student mechanisms were triggered: “feeling personally committed,” “probing back and forth,” and “understanding one's own learning process.” Particularly important for both providing and receiving feedback is feeling personally committed. Results also show that mechanisms were a stronger predictor for deep learning when providing than when receiving. Given the context in which instructors face an increasing number of students and a high workload, students may be supported by online audio peer feedback as a method to choose a deep approach to learning.     

Roll-to-roll hot embossing of microstructures

In this paper we present a new roll-to-roll embossing process allowing the replication of micro patterns with feature sizes down to 0.5 μm. The embossing process can be run in ‘continuous mode’ as well as in ‘discontinuous mode’. Continuous hot embossing is suitable for the continuous output of micro patterned structures. Discontinuous hot embossing has the advantage that it is not accompanied by waste produced during the initial hot embossing phase. This is because in ‘discontinuous mode’, embossing does not start before the foil has reached the target temperature. The foil rests between two parallel heating plates and foil movement and embossing starts only after the part of the foil resting between the heating plates has reached a thermal steady state. A new type of embossing master is used which is based on flexible silicon substrates. The embossing pattern with sub-μm topographic resolution is prepared on silicon wafers by state of the art lithography and dry etching techniques. The wafers are thinned down to a thickness of 40 μm, which guarantees the mechanical flexibility of the embossing masters. Up to 20 individual chips with a size of 20 × 20 mm2 were assembled on a roller. Embossing experiments with COC foils showed a good replication of the silicon master structures in the foil. The maximum depth of the embossed holes was about 70% of the master height.     

Optimizing Code Generation from SSA Form: A Comparison Between Two Formal Correctness Proofs in Isabelle/HOL

Correctness of compilers is a vital precondition for the correctness of the software translated by them. In this paper, we present two approaches for the formalization of static single assignment (SSA) form together with two corresponding formal proofs in the Isabelle/HOL system, each showing the correctness of code generation. Our comparison between the two proofs shows that it is very important to find adequate formalizations in formal proofs since they can simplify the verification task considerably. Our formal correctness proofs do not only verify the correctness of a certain class of code generation algorithms but also give us sufficient, easily checkable correctness criteria characterizing correct compilation results obtained from implementations (compilers) of these algorithms. These correctness criteria can be used in a compiler result checker.     

Ordering Techniques for Two- and Three-Dimensional Convection-Dominated Elliptic Boundary Value Problems

Multigrid methods with simple smoothers have been proven to be very successful for elliptic problems with no or only moderate convection. In the presence of dominant convection or anisotropies as it might appear in equations of computational fluid dynamics (e.g. in the Navier-Stokes equations), the convergence rate typically decreases. This is due to a weakened smoothing property as well as to problems in the coarse grid correction. In order to obtain a multigrid method that is robust for convection-dominated problems, we construct efficient smoothers that obtain their favorable properties through an appropriate ordering of the unknowns. We propose several ordering techniques that work on the graph associated with the (convective part of the) stiffness matrix. The ordering algorithms provide a numbering together with a block structure which can be used for block iterative methods. We provide numerical results for the Stokes equations with a convective term illustrating the improved convergence properties of the multigrid algorithm when applied with an appropriate ordering of the unknowns. Received July 12, 1999; revised October 1, 1999     

High Reliefs from 3D Scenes

We present a method for synthesizing high reliefs, a sculpting technique that attaches 3D objects onto a 2D surface within a limited depth range. The main challenges are the preservation of distinct scene parts by preserving depth discontinuities, the fine details of the shape, and the overall continuity of the scene. Bas relief depth compression methods such as gradient compression and depth range compression are not applicable for high relief production. Instead, our method is based on differential coordinates to bring scene elements to the relief plane while preserving depth discontinuities and surface details of the scene. We select a user‐defined number of attenuation points within the scene, attenuate these points towards the relief plane and recompute the positions of all scene elements by preserving the differential coordinates. Finally, if the desired depth range is not achieved we apply a range compression. High relief synthesis is semi‐automatic and can be controlled by user‐defined parameters to adjust the depth range, as well as the placement of the scene elements with respect to the relief plane.