Kevin Tew and Michael Scott

The mentored environment for isogeometric analysis (IGA) has trained engineering and computer science students to develop isogeometric numerical methods and accompanying software to solve challenging problems in science and engineering. The mentoring environment consisted of:

1. Weekly group meetings where research concepts were discussed, scientific literature was reviewed, and progress was monitored.
2. Pairing of students with a faculty members to develop IGA design-through-analysis methodologies.
3. Preparation of results for peer-reviewed publications.

Projects undertaken during the grant included the development of adaptive mesh refinement techniques for IGA, parameterized design approaches for analysis-suitable geometry, and T-spline-based beam, plate, and shell models for IGA. The Interdisciplinary Mentored Environment for Isogeometric Analysis included undergraduate, masters, doctoral, and postdoctoral students, working together to solve impactful and important problems in geometric design, structure preserving methods, adaptivity, and patient-specific modeling of prostate cancer.

Mentoring Environment Grant funds were used to mentor undergraduate and graduate students working in isogeometric analysis. The awarded MEG funds were used to further research into adaptivity techniques for computational meshes. Work centered around higher degree meshes, capable of supporting quadratic and cubic basis functions. Mesh coarsening was also investigated. Keith Rose, a civil engineering masters student completed his master’s project on adaptivity and graduated.

Before this MEG grant, state of the art coarsening required a global matrix solve. Investigations into mesh coarsening and adaptivity resulted in the publication ”Bzier projection: A unified approach for local projection and quadraturefree refinement and coarsening of NURBS and T-splines with particular application to isogeometric design and analysis” in the top journal Computer Methods in Applied Mechanics and Engineering.

The PI’s mentoring efforts have extend beyond the scope of the Mentoring Grant. Our most recent work has been with a BYU mechanical engineering undergraduate, Scot Wilcox and a PhD candidate from the University of A Coru˜na, Guillermo Lorenzo. Scot is working on a graphical interface specialized for isogeometric analysis as shown in figure 1. Scot is applying to the BYU Computer Science’s graduate program and plans on continuing to work with the BYU isogeometric group.

Guillermo is using isogeometric analysis for Tissue-scale, patient-specific modeling of prostate cancer growth. A pair of simulations results, figures 2 and 3, show simulated cancer growth and the adaptive mesh that was used to simulate the growth.

Mentored Environment for Isogeometric Analysis was a success both for the students and the faculty involved. We look to forward to conducting another Mentored Environment for Isogeometric Analysis in the future.

Figure 1: New graphical interface for conducting isogeometric analysis.

Figure 2: 3d simulation of prostate cancer growth.

Figure 3: 3d adaptive mesh of prostate cancer growth.