AWM at SIAM CSE 2015 Abstracts

Sunday, March 15, 2015, 9:10 AM – 10:50 AM, Room: 251 D

AWM Workshop: Research Talks by Recent Ph.D.s: Mathematical Modeling and High Performance Computing for Multi-physics and Multi-scale Problems. Part I of II

Efficient High-Order Algorithms for Solving Drift-Diffusion Systems

Authors: Ying He, University of California, Davis, USA, yinghe@math.ucdavis.edu

Abstract. I will discuss about recent developments of spectral element method (SEM) for solving drift-diffusion equations, with applications in semi- conductor device simulation, biological ion channels problems, etc. The drift-diffusion system is a non-linear system, involving the coupling of two transport equations for the carrier concentrations with the Poisson equa- tion for the electric potential. I will present our SEM algorithms, focusing on stable, efficient, and accurate time-splitting schemes, properly designed for the high-order spectral element discretizations. I will demonstrate the computational results for the study of potassium channel in a biological membrane, provided with the validation.

Estimating Residual Stresses in Arteries by an Inverse Spectral Technique

Authors: Sunnie Joshi, Temple University, USA, sjoshi@temple.edu

Abstract. A mathematical model is studied to estimate residual stresses in the arterial wall using intravascular ultrasound (IVUS) techniques. A BVP is formulated for the nonlinear, slightly compressible elastic wall, the boundary of which is subjected to a quasi-static blood pressure, and then an idealized model for IVUS is constructed by superimposing small amplitude time harmonic vibrations on large deformations. Using the classical theory of inverse Sturm-Liouville problems and opimization techniques, an inverse spectral algorithm is developed to approximate the residual stresses, given the first few eigenfrequencies of several induced pressures.

Force-based Blended Atomistic-to-continuum Coupling Method for Crystals: Theory and Computations

Authors: Xingjie Li, Brown University, U.S., xli47@uncc.edu

Abstract. We formulate a multiscale method based on blending atomistic and continuum forces. We present a comprehensive error analysis which is valid in two and three dimensions, for finite many-body interactions, and in the presence of defects. Based on a precise choice of blending mechanism, the error estimates are considered in terms of degrees of freedom. The numerical experiments confirm and extend the theoretical predictions, and demonstrate a superior accuracy of our method over other schemes.

Sunday, March 15, 2015, 1:30 PM – 3:10 PM, Room: 251 D

AWM Workshop: Research Talks by Recent Ph.D.s: Mathematical Modeling and High Performance Computing for Multi-physics and Multi-scale Problems. Part II of II

A Study of the Entanglement in Polymer Melts

Authors: Eleni Panagiotou, University of California, Santa Barbara, USA, lnpanagiotou@yahoo.com

Abstract. Polymer melts are dense systems of macromolecules. In such dense systems the conformational freedom and motion of a chain is significantly affected by entanglement with other chains which generates obstacles of topological origin to its movement. In this talk we will discuss methods by which one may quantify and extract entanglement information from a polymer melt configuration using tools from knot theory. A classical measure of entanglement is the Gauss linking integral which is an integer topological invariant in the case of pairs of disjoint oriented closed chains in 3-space. For pairs of open chains, we will see that the Gauss linking integral can be applied to calculate an average linking number. In order to measure the entanglement between two oriented closed or open chains in a system with three-dimensional periodic boundary conditions (PBC) we use the Gauss linking number to define the periodic linking number. Using this measure of linking to assess the extend of entanglement in a polymer melt we study the effect of CReTA (Contour Reduction Topological Analysis) algorithm on the entanglement of polyethylene chains. Our results show that the new linking measure is consistent for the original and reduced systems.

A Fast Explicit Operator Splitting Method for a Multi-scale Underground Oil Recovery Model

Authors: Ying Wang, University of Oklahoma, USA, wang@ou.edu

Abstract. In this talk, we propose a fast splitting method to solve a Multi-scale underground oil recovery model which includes a third order mixed derivatives term resulting from the dynamic effects in the pressure difference between the two phases. The method splits the original equation into two equations, one with flux term and one with diffusion term so that the classical numerical methods can be applied immediately. Two different spatial discretizations, second- order Godunov-type central-upwind scheme and WENO5 scheme, are used to demonstrate that higher order method provides more accurate approximation of solutions. The various numerical examples in both one and two dimensions show that the solutions may have many different saturation profiles depending on the initial conditions, diffusion parameter, and the third-order mixed derivatives parameter. The results are consistent with the study of traveling wave solutions and their bifurcation diagram. This is joint work with C.-Y. Kao, A. Kurganov, Z.-L. Qu.

Computational Study of Dynamics and Transport in Vortex-Dipole Flows

Authors: Ling Xu, Georgia State University, USA, xulingsue@gmail.com

Abstract. A finite number of dipole interactions in free space are studied numerically in order to see how they give rise to a collective fluid flow pattern that is widely seen in ocean currents and clouds. The classical Lamb Dipole is used as our vortex unit. The computation is validated by comparing results with analytic solutions of a free-translating Lamb Dipole. The results have two ingredients. First, the intra- and inner-dipole kinematic pressure fields show distinct features and they relate the phenomenon of no mass exchange in dipoles interactions. Second, a general ’rule’ of the ultimate vortical flow pattern is observed based on dipoles interactions in three setups : head on collision, head-end marching, parallel marching.

A Stabilized Explicit Scheme for Coupling Fluid-structure Interactions

Authors: Yue Yu, Lehigh University, USA, yuy214@lehigh.edu

Abstract. We develop a new stabilized explicit coupling partitioned scheme for the fluid-structure interaction problem, where the pressure and velocity are decoupled. Proper penalty terms are applied to control the variations at the interface. Using energy stability analysis, we show that the scheme is stable independent of the fluid-structure density ratio. Numerical examples are provided to show that although the penalty terms degrade the time accuracy, optimal accuracy is recovered by performing defect-correction subiterations.