The Rycroft Group

For scientific computing and mathematical modeling

The Rycroft Group is part of the Department of Mathematics at University of Wisconsin–Madison. The group is led by Chris Rycroft and focuses on mathematical modeling and scientific computation, particularly for interdisciplinary applications in science and engineering.

The Rycroft Group works on a wide range of topics. A hallmark of the group's approach is to develop new computational methods while working directly with domain scientists. Three particular focus areas are listed below.

reference map simulation snapshots
Numerical methods for material mechanics

Many materials of scientific importance are hard to simulate, due to challenges resolving multiple phases or components, disparate timescales, and large deformations. We developed a new numerical method for bulk metallic glasses and used it to predict their failure properties, which were later verified experimentally. We co-developed the reference map technique, a new approach for simulating fluid–structure interaction.

crumpling simulation
Data-driven discovery

Many scientific fields are increasingly awash in data. We develop new computational approaches for processing data and extracting scientific insight, particularly those that combine traditional analysis and modeling with new machine learning methods. For example, we have a sequence of papers on the physics of crumpling, covering experimental observations, new machine learning approaches, and analysis and modeling.

Voronoi tessellation
Computational geometry

Geometry problems appear across many scales, from the arrangements of atoms to the structure of galaxies, and techniques for geometric analysis enter into many group projects. Chris Rycroft developed Voro++, a software library for calculating the Voronoi tessellation. The library is widely used, and the Rycroft Group has used it for problems as diverse as modeling insect wing patterning and finding materials for carbon dioxide capture.

The team

Rycroft Group photo, Feb 2020
Group photo, February 26, 2020.

The Rycroft Group currently consists of six graduate students, along with postdocs, undergraduates, and sabbatical visitors. Members have a diverse range of backgrounds and have education in applied mathematics, physics, engineering, and computer science. We also like obsessive color coordination!

Prior to summer 2022 the group was located at Harvard University, and some members of the group as still located at Harvard. We collaborate with a wide range of researchers, and we are involved with several collaborative centers such as the Harvard Quantitative Biology Initiative.

We also support teaching a wide range of courses at UW Madison and previously in the Harvard IACS master's program. In particular, from 2014–2021 Chris Rycroft taught and developed Applied Math 205 and Applied Math 225, a year-long graduate course sequence in scientific computing. Many previous and current group members have been involved in providing teaching support for these two courses.

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