Interval Assignment for Volumes with Holes Page: 4 of 24
21 p.View a full description of this article.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
Introduction
The finite element method is a fundamental modeling technique with widespread use and
growing popularity in the engineering community. The technique uses a numerical approximation
of partial differential equations to model the effects of heat transfer, fluid flow, and stress for
objects with complex geometry. Much of the research into the finite element method focuses on
further automating the process, which would allow personnel with less training to use the process,
improve productivity, and achieve more accurate solutions.1 The most time part of using the finite
element method is the discretization of the model's geometry into finite elements, the process
known as mesh generation.
The quality of the mesh affects the accuracy and efficiency of the finite element method. In
practical cases, it is difficult to have perfectly shaped elements because many of the elements must
be distorted to fit the geometry. The quality of the depends on the technique, or "scheme", selected
to generate the mesh.
Mapping and submapping schemes are designed to place a structured mesh2 on surface and
volume geometry. The regular structure of the mapping and submapping meshes imposes
constraints on the mesh boundary: two sets of edges are paired and the number of mesh edges, or
"intervals", are constrained to be equal.
Surfaces are often connected to other surfaces by shared edges. The interval constraints
imposed on an edge can propagate across sets of mapped or submapped surfaces, thereby affecting
the meshes generated on distant surfaces.
The quality of a structured mesh depends on having roughly equally sized edges on its
sides. An interval count, which enhances the global quality of the final mesh, is desired. The
intervals assigned to the edges can be optimized through the use of linear programming
Upcoming Pages
Here’s what’s next.
Search Inside
This article can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Article.
BENZLEY, STEVEN; MITCHELL, SCOTT A. & SHEPHERD, JASON F. Interval Assignment for Volumes with Holes, article, September 7, 1999; Albuquerque, New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc627482/m1/4/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.