IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences
Parallel Solver for 3-D Full-Stokes Ice Sheet Modeling

A Parallel Solver for 3-D Full-Stokes Ice Sheet Modeling: Simulation results of the temperature evolution of a Greenland ice sheet after 10 years (Ju et al.).

A Parallel Solver for 3-D Full-Stokes Ice Sheet Modeling 2

A Parallel Solver for 3-D Full-Stokes Ice Sheet Modeling: Zoom-in of a region close to the ice sheet edge (Ju et al.).

“Trident”-shaped branched tube formation

Time evolution of “trident”-shaped branched
tube formation
via fusion of uniluminal vascular
spheroids in a KMC simulation. Top: the
cross-sectional views. Red: smooth muscle
cells; Green: endothelial cells; Blue: lumen
particles (see enlargement). Bottom: the external
views. (Y. Sun, X. Yang and Q. Wang)

Computational Analysis of Biofabrication

Computational Analysis of Biofabrication Morphogenesis of a Branching Vascular Construct: Vascular construct made of a layer-by-layer deposition in a designed Y-shape pattern (Q. Wang et al.).

Fifth Roots

Fifth Roots: Take a random walk in the complex plane starting from 0, each step an equiprobable fifth root of unity. Ten steps later, there's a circle centered at your destination whose area is proportional to your probability of being there. Other than two minor modifications (taking the fifth power of all points and inflating the atom at zero), this is the distribution of complex homogeneous eigenvalues of the all-ones 10X10X10X10X10X10 hypermatrix. (Joshua Cooper with Aaron Dutle.)

Spheres in Lattice

Monochromatic Boxes in Color Grids: What is the size of the smallest box (left) so that, if the elements are colored with two colors, there must be a nontrivial "subgrid" (right) all in one color? (See Cooper et al.)

Adaptivity and Variational Stabilization for Convection-Diffusion

Adaptivity and Variational Stabilization for Convection-Diffusion Equations: Every fourth adaptive cycle of Algorithm 1 with modification at the outflow boundary starting from cycle 3 for the test problem (3.25) with $\epsilon = 5 \cdot 10^{-3}$. The first row depicts the finite element solution $u _ h$. The second row displays the corresponding grids of $u _ h$. (See Cohen et al.)

Adaptive Petrov-Galerkin Methods

Adaptive Petrov-Galerkin Methods for First Order Transport Equations: The 18th iterate of the adaptive solver and corresponding grid of model problem (6.1) with Algorithm 5.3 with $X _ h = P _ {1,T _ h}, Z _ h = P _ {3,T _ {h/8}}$ and $K = 9$ (See Dahmen et al.).

Project Highlights

Digitizing Optical Sound Tracks

The University of South Carolina Moving Image Research Collections (MIRC) is collaborating with research faculty from the University’s Interdisciplinary Mathematics Institute (IMI) to develop an open-source software application to directly reproduce the optical sound tracks of motion picture films from digital scans producing, as a result, a synchronized sound film file. For more information and to download the open-source software, please visit the project's website.

News Highlights

Special Announcements

DeVore receives Honorary Doctorate of Science from USC

During the August 2015 commencement ceremony, the university conferred an Honorary Doctorate of Science to Ronald A. DeVore, a faculty member in the Mathematics Department. Professor DeVore is currently the Robert L. Sumwalt Distinguished Professor Emeritus of Mathematics and former director of the IMI. Please visit this special announcement for more details.

USC Research CyberInfrastructure Program

Qi Wang was appointed by the Provost as the Chair of the Faculty Advisory Committee for the 2014-2015 USC Research CyberInfrastrucure Program. The RCI Program, directed by Phil Moore, is charged with providing High Performance Computing to the university. The Faculty Advisory Committee members serve as points of contact for the RCI program. Faculty and staff are encouraged to contact any Faculty Advisory Committee member for help with questions about where to turn for access to USC's research computing resources. They may also contact the RCI team directly by email:
For more information, please visit:

CAS Research Computing Center

The College of Arts and Sciences (CAS) Research Computing Center (RCC) provides high performance computing and visualization resources (including assistance with the Computational Graphics Lab of the IMI), access to software, workshops, one-on-one consulting with domain experts, and complete data management strategies to researchers across all departments and divisions within the College. For more information, please contact the Head of Research Computing, Jun Zhou ( ) or visit:

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