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.).

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.)

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.).

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.).

Pencho Petrushev

Welcome

Welcome to the Interdisciplinary Mathematics Institute (IMI)


The Institute is a mathematics research center residing within the College of Arts & Sciences at the University of South Carolina. The IMI serves to foster advanced interdisciplinary mathematical research with the potential for meaningful application and to facilitate its transfer to the academic, government and industrial sectors.

One of the great challenges of the 21st century is the development of efficient and accurate numerical models for complex physical, chemical, biological and social processes arising in various areas of science, medicine, engineering and technology. This task is additionally complicated by the enormous amounts of data gathered or produced continuously at ever accelerating rates in this age of Big Data.

The primary objective of the IMI is to increase our fundamental understanding of these processes and to develop novel mathematics and numerical algorithms for resolving them. These mathematical and algorithmic advances will inject fundamentally new ideas into areas ranging from cosmology to electron microscopy, from atmospheric sciences and oceanography to image processing, from biomathematics to tissue fabrication.

Another important purpose of the IMI is to support and expand the new PhD track in mathematics with concentration in Applied and Computational Mathematics in the Department of Mathematics at USC. It is critical for us to create better teaching environments and opportunities for educating students in the IMI thrust areas.

Our third objective is to develop and support meaningful collaborations of the IMI and its members with units and individuals within the College of Arts and Sciences, from other colleges at USC, from the US and all over the world.

Our goals are ambitious but we are ready to face the challenges they offer us.


Pencho Petrushev,
Director

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