arXiv subjects

Gordon L. Kindlmann

Publications and source records attributed to Gordon L. Kindlmann.

3 recordsLinked to original sources

arXiv2019

Point Movement in a DSL for Higher-Order FEM Visualization

Scientific visualization tools tend to be flexible in some ways (e.g., for exploring isovalues) while restricted in other ways, such as working only on regular grids, or only on unstructured meshes (as used in the finite element method, FEM). Our work seeks to expose the common structure of visualization methods, apart from the specifics of how the fields being visualized are formed. Recognizing that previous approaches to FEM visualization depend on efficiently updating computed positions within a mesh, we took an existing visualization domain-specific language, and added a mesh position type and associated arithmetic operators. These are orthogonal to the visualization method itself, so existing programs for visualizing regular grid data work, with minimal changes, on higher-order FEM data. We reproduce the efficiency gains of an earlier guided search method of mesh position update for computing streamlines, and we demonstrate a novel ability to uniformly sample ridge surfaces of higher-order FEM solutions defined on curved meshes.

cs.GR↗

arXiv2018

Compiling Diderot: From Tensor Calculus to C

Diderot is a parallel domain-specific language for analysis and visualization of multidimensional scientific images, such as those produced by CT and MRI scanners. In particular, it supports algorithms where tensor fields (i.e., functions from 3D points to tensor values) are used to represent the underlying physical objects that were scanned by the imaging device. Diderot supports higher-order programming where tensor fields are first-class values and where differential operators and lifted linear-algebra operators can be used to express mathematical reasoning directly in the language. While such lifted field operations are central to the definition and computation of many scientific visualization algorithms, to date they have required extensive manual derivations and laborious implementation. The challenge for the Diderot compiler is to effectively translate the high-level mathematical concepts that are expressible in the surface language to a low-level and efficient implementation in C. This paper describes our approach to this challenge, which is based around the careful design of an intermediate representation (IR), called EIN, and a number of compiler transformations that lower the program from tensor calculus to C while avoiding combinatorial explosion in the size of the IR. We describe the challenges in compiling a language like Diderot, the design of EIN, and the transformation used by the compiler. We also present an evaluation of EIN with respect to both compiler efficiency and quality of generated code.

cs.PL↗

arXiv2014

Helicity conservation by flow across scales in reconnecting vortex links and knots

The conjecture that helicity (or knottedness) is a fundamental conserved quantity has a rich history in fluid mechanics, but the nature of this conservation in the presence of dissipation has proven difficult to resolve. Making use of recent advances, we create vortex knots and links in viscous fluids and simulated superfluids and track their geometry through topology changing reconnections. We find that the reassociation of vortex lines through a reconnection enables the transfer of helicity from links and knots to helical coils. This process is remarkably efficient, owing to the anti-parallel orientation spontaneously adopted by the reconnecting vortices. Using a new method for quantifying the spatial helicity spectrum, we find that the reconnection process can be viewed as transferring helicity between scales, rather than dissipating it. We also infer the presence of geometric deformations which convert helical coils into even smaller scale twist, where it may ultimately be dissipated. Our results suggest that helicity conservation plays an important role in fluids and related fields, even in the presence of dissipation.

physics.flu-dyn↗