Mathematical Modeling and Analysis

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AMR - Research Highlights

2007

• The Analysis of Self-diffusion and Migration of Spheres in Nonlinear Shear Flow Using a Traction-corrected Boundary Element Method
• Scalable Solvers for 3D Extended Mageneto Hydrodynamics
• High-order Mimetic Finite Difference Methods on Arbitrary Meshes
• The Mechanism of Surfactant Effects on Drop Coalescence
• Disjoining pressure for non-uniform thin films
• Modeling Lubrication Forces from First Principles
• Predicting the Small Scales of Alpha Models for Turbulence
• Multi-Material Interface Reconstruction from Moment Data
• Order-Independent Multi-Material Interface Reconstruction
• Understanding the Small Scales in Rotating Stratified Flow
• New Monotone Schemes for Diffusion Problems on Unstructured Meshes

2006

• A Novel Investigation of Rotating and Stratified Flows
• Linear and Nonlinear Front Instabilities in Bistable Systems

2005

• Hybrid Multiscale Method for Coupling Atomistic and Continuum Models
• Node Reconnection Algorithm for Mimetic Finite Difference Discretization of Elliptic Equations
• Numerical Study of the Two-Dimensional Navier-Stokes-Alpha Model of Turbulence
• Multilevel Upscaling of Heterogeneous Media
• New Discretization Methodology on Polyhedral Meshes
• An Efficient Linearity and Bound Preserving Remapping) for Meshes with Changing Connectivity
• The Force/Work Differencing of Exceptional Points in Lagrangian Hydrodynamics
• Rare Events in Turbulence Might not be so Rare
• The Repair Paradigm: New Algorithms and Applications to Compressible Flow
• Competing Physical Processes in Turbulent Fluid Dynamics
• Interface Reconstruction in Multi-fluid Flow Simulations
• A Family of Mimetic Finite Difference Methods on Polygonal and Polyhedral Meshes

2004

• Convergence of Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes
• A Mortar Mimetic Finite Difference Method on Non-Matching Grids
• A Subcell Remapping Method on Staggered Polygonal Grids for Arbitrary-Lagrangian-Eulerian Methods
• Bloch-Front Turbulence in a Periodically Forced Belousov-Zhabotinsky Reaction
• Differential Equations on a Network
• Rezoning of Triangular Meshes in ALE Simulations by Node Reconnection
• Inelastic Collisions between Solitons in Optical Fibers
• Numerical Methods for Simulation of Heating through Electromagnetic Induction
• Multilevel Accelerated Grid Optimization
• Superconvergence of Velocity in Mimetic Finite Difference Methods on Quadrilaterals
• Universally Embedded Spherical Symmetry in Turbulent Flows
• Parallel, Scalable, and Robust Multigrid on Structured Grids
• Error Minimization Based Rezone Strategy for ALE Methods
• Mimetic Discretizations of Diffusion Equation on Polygonal Meshes
• Computer Arithmetic for Probability Distribution Variables
• An Arbitrary-Lagrangian- Eulerian Code for General Polygonal Mesh: ALE INC.

2003

• Light Propagation through Biological Tissue
• Predictive Modeling - Coping with Uncertainty
• Curvature Estimation for Unstructured Triangulations of Surfaces
• Multiphase Patterns in Forced Reaction-Diffusion Systems
• Parameter Estimation via Risk-Based Optimization
• Quality Improvement of 3D Meshes in ALE simulation of Gas Dynamics
• Quality Improvement of Surface Meshes using Local Parameterization