Discrete and Continuous Adjoint Approaches to Estimate Boundary Heat Fluxes in Falling Films

A wavy falling film simulation is considered in which a liquid travels along one side of a thin metal foil that is heated electrically from the opposite side. The direct problem consists of a three-dimensional heat conduction equation on a cuboid domain representing the foil with suitable initial and boundary conditions. The inverse problem consists of determining the heat flux on the film side of the foil from a given distribution of the temperature on the heating side. Two different adjoint approaches for the solution of this inverse problem are compared. In the continuous adjoint approach, the adjoint problem is analytically derived from the direct problem and then discretized. In the discrete adjoint approach, the direct problem is discretized from which an adjoint code is generated by means of the reverse mode of automatic differentiation. Numerical experiments are reported demonstrating the advantages and disadvantages of the two approaches

A new metric enabling an exact hypergraph model for the communication volume in distributed-memory parallel applications

A hypergraph model for mapping applications with an all-neighbor communication pattern to distributed-memory computers is proposed, which originated in finite element triangulations. Rather than approximating the communication volume for linear algebra operations, this new model represents the communication volume exactly. To this end, a hypergraph partitioning problem is formulated where the objective function involves a new metric. This metric, the kðk 1Þ-metric, accurately models the communication volume for an all-neighbor communication pattern occurring in a concrete finite element application. It is a member of a more general class of metrics, which also contains more widely used metrics, such as the cut–net and the ðk 1Þ-metric. In addition, we develop a heuristic to minimize the communication volume in the new kðk 1Þ-metric. For the solution of several real-world finite element problems, experimental results based on this new heuristic demonstrate a small reduction in communication volume compared to a standard graph partitioner and do not show significant reductions in communication volume compared to a hypergraph partitioner using the common ðk 1Þ-metric. However, for this set of problems, the new approach does reduce actual communication times. As a by-product, we observe that it also tends to reduce the number of messages. Furthermore, the new approach dramatically reduces the communication volume for a set of sparse matrix problems that are more irregularly-structured than finite element problems

Influence of mounting on the optical surface figure in optical reference surfaces

The paper presents the effect of mechanical mounting of optical reference elements on their surface shape. Optical reference surfaces are key elements when traceable, highly accurate and precise optical surface measurements are required. In order to calibrate measuring instruments and compare the metrological capabilities of different metrology institutes, universities and other stakeholders, the reference artefacts were developed. Different measurement instruments require a different way of mounting and the reference artefacts are supposed to be useful for reliable and repeatable calibration of a great majority of the instruments worldwide. However, not only their shape was critical, but also the way of mounting was crucial. FEM analyses followed by experiments have revealed an unacceptable surface shape error in the order of hundreds of nanometres in the case of the commonly used screw mount, even for low applied torques. Other mounting options, such as the collet chuck or the Morse taper, are examined by means of FEM analysis and verified by interferometric measurements. It is shown that only the Morse taper can fulfil the strict criterion of less than 30 nm for surface shape deviation due to mounting, which is required in optical surface shape metrology.</jats:p

A new metric enabling an exact hypergraph model for the communication volume in distributed-memory parallel applications

A hypergraph model for mapping applications with an all-neighbor communication pattern to distributed-memory computers is proposed, which originated in finite element triangulations. Rather than approximating the communication volume for linear algebra operations, this new model represents the communication volume exactly. To this end, a hypergraph partitioning problem is formulated where the objective function involves a new metric. This metric, the kðk 1Þ-metric, accurately models the communication volume for an all-neighbor communication pattern occurring in a concrete finite element application. It is a member of a more general class of metrics, which also contains more widely used metrics, such as the cut–net and the ðk 1Þ-metric. In addition, we develop a heuristic to minimize the communication volume in the new kðk 1Þ-metric. For the solution of several real-world finite element problems, experimental results based on this new heuristic demonstrate a small reduction in communication volume compared to a standard graph partitioner and do not show significant reductions in communication volume compared to a hypergraph partitioner using the common ðk 1Þ-metric. However, for this set of problems, the new approach does reduce actual communication times. As a by-product, we observe that it also tends to reduce the number of messages. Furthermore, the new approach dramatically reduces the communication volume for a set of sparse matrix problems that are more irregularly-structured than finite element problems