SCIENTIFIC COMPUTING AND IMAGING INSTITUTE
at the University of Utah

In this thesis, adjoint error estimation techniques are applied to complex elastohydrodynamic lubrication (EHL) problems. A functional is introduced, namely the friction, and justification is provided as to why this quantity, and hence its accuracy, is important. An iterative approach has been taken to develop understanding of the mechanisms at work. A series of successively complex cases are proposed, each with adjoint error estimation techniques applied to them. The first step is built up from a model free boundary problem, where the cavitation condition is captured correctly using a sliding mesh. The next problem tackled is a hydrodynamic problem, where non-linear viscosity and density are introduced. Finally, a full EHL line contact problem is introduced, where the surface deforms elastically under pressure. For each case presented, an estimate of a finer mesh friction, calculated from solutions obtained only on a coarse mesh, is corrected according to the adjoint error estimation technique. At each stage, care is taken to ensure that the error estimate is computed accurately when compared against the measured error in the friction.

Non-uniform meshes are introduced for the model free boundary problem. These nonuniform meshes are shown to give the same excellent predictions of the error as uniform meshes. Adaptive refinement is undertaken, with the mesh being refined using the adjoint error estimate. Results for this are presented for both the model free-boundary problem and the full EHL problem. This is shown to enable the accurate calculation of friction values using an order of magnitude fewer mesh points than with a uniform mesh.

Throughout this thesis, standard numerical techniques for calculating EHL solutions have been used. That is, regular mesh finite difference approximations have been used to discretise the problem, with multigrid used to efficiently solve the equations, and spatial adaptivity added through multigrid patches. The adjoint problems have been solved using standard linear algebra packages.

One of the most fundamental concepts in computer graphics is binary space subdivision. In its purest form, this concept leads to binary space partitioning trees (BSP trees) with arbitrarily oriented space partitioning planes. In practice, however, most algorithms use kd-trees-a special case of BSP trees that restrict themselves to axis-aligned planes-since BSP trees are believed to be numerically unstable, costly to traverse, and intractable to build well. In this paper, we show that this is not true. Furthermore, after optimizing our general BSP traversal to also have a fast kd-tree style traversal path for axis-aligned splitting planes, we show it is indeed possible to build a general BSP based ray tracer that is highly competitive with state of the art BVH and kd-tree based systems. We demonstrate our ray tracer on a variety of scenes, and show that it is always competitive with-and often superior to-state of the art BVH and kd-tree based ray tracers.

Keywords: rt, ray tracing, bsp tree

Visualization is often employed as part of the simulation science pipeline, it's the window through which scientists examine their data for deriving new science, and the lens used to view modeling and discretization interactions within their simulations. We advocate that as a component of the simulation science pipeline, visualization must be explicitly considered as part of the validation and verification (V&V) process. In this article, the authors define V&V in the context of computational science, discuss the role of V&V in the scientific process, and present arguments for the need for verifiable visualization.

With the continual increase in computing power, volumetric datasets with sizes ranging from only a few megabytes to petascale are generated thousands of times per day. Such data may come from an ordinary source such as simple everyday medical imaging procedures, while larger datasets may be generated from cluster-based scientific simulations or measurements of large scale experiments. In computer science an incredible amount of work worldwide is put into the efficient visualization of these datasets. As researchers in the field of scientific visualization, we often have to face the task of handling very large data from various sources. This data usually comes in many different data formats. In medical imaging, the DICOM standard is well established, however, most research labs use their own data formats to store and process data. To simplify the task of reading the many different formats used with all of the different visualization programs, we present a system for the efficient handling of many types of large scientific datasets (see Figure 1 for just a few examples). While primarily targeted at structured volumetric data, UVF can store just about any type of structured and unstructured data. The system is composed of a file format specification with a reference implementation of a reader. It is not only a common, easy to implement format but also allows for efficient rendering of most datasets without the need to convert the data in memory.