From the category archives:

Algorithms, Multiscale and High Performance Computing

To be able to understand disease states tracing back to the smallest scales – ranging from the studies of molecular mechanics to that of the cell membranes – fundamental advancements in multiscale and high performance computing are necessary. While atomistic methods are appropriate for investigations at the smallest scales, continuum models are more realistic at the larger scales. Efficient computational approaches at the atomistic scales as well as novel coarse graining technology are of interest in this thrust. Medical visualization is also an important field that supports MSI.

Example Projects- Algorithms, Multiscale and High Performance Computing, and Medical Visualization


This project aims at developing efficient crystal plasticity solvers including single yield function approaches for modeling crystalline materials. The CPFEM techniques have been coupled to both DFT and Jacobian free meltiscale methods.

Multigrid computational strategies are being developed to accelerate solution speed. Of special interest are schemes that perform robustly for changing Dirichlet boundary conditions without reforming the sparse matrix structures at multiple levels. Techniques are being developed to represent real time changes in mesh topology at the finest scale with both structured and unstructured hierarchies.

The IFEM method is a computational approach to solve and analyze complicated fluid-structure interactions. The method is twp-way coupling that is particularly useful in handling interactions between fluid and deformable solid. It captures realistic representation of the fluid and its immersed solid materials.

This is a technique to simulated the response of continua undergoing large nonlinear deformations using radial basis function neural networks which have been exhaustively trained on “response surfaces” in pre-computational steps performed on full finite element models. Computations are highly scalable as the number of neurons in the network may be dynamically chosen to control computational speed,  without the need  to remesh. Higher order polynomial reproducing neural networks have been developed to improve prediction accuracy.


This is a meshfree computational environment based on the moving least squares approximation functions, compactly supported on spherical subdomains, used in a point collocation residual minimization technique. Advantages over traditional finite elements include not having to perform numerical integration, constant Jacobians which preclude distortions and smooth solutions.This is a meshfree computational environment based on the moving least squares approximation functions, compactly supported on spherical subdomains, used in a point collocation residual minimization technique. Advantages over traditional finite elements include not having to perform numerical integration, constant Jacobians which preclude distortions and smooth solutions.

A software framework is being developed for interactive simulations. This is highly modular and extensible and is intended to reduce the development time for interactive simulations by providing necessary functionalities for visualization, collision detection and response, physical modeling and networking.

Jacobian-free global-local computational approaches are being developed for coupling disparate length scales. Explicit Jacobian-free multiscale methods are suitable for solving high strain rate problems. Implicit methods are more challenging where we have proposed the use of Newton-Krylov processes across scales. However, efficient block precoditioners must be developed without prior knowledge of the current Jacobian.

Inverse problems play an important role in medicine and biology. They provide the values and distributions of material, shape and boundary parameters that are critical in developing biomedical models. We have developed an efficient, nonlinear optimization-based strategy for solving this class of problems. This strategy relies on the use of adjoint equations, novel continuation methods and efficient preconditioners to solve such problems efficiently.

Research on the development of massively parallel simulation methods for reliable simulation using adaptive model and discretization control.

The goal of reduced order modeling is to replace a computational model with a much lower order model with reasonably high accuracy over an operating range, with a significantly lower computational cost. Linear model order reduction methods have been developed for linear viscoelastic materials based on truncated  balanced realization, Hankel optimal norm method  and modal truncation for the PAFF technique. Current research is to develop nonlinear model order reduction methods.