Monday, June 12, 2017 (special seminar)
11:00-11:50 am, Room SH203
Li-Lian
Wang
(Nanyang Technological University)
Generalized Jacobi functions of fractional degree and optimal polynomial approximations in fractional Sobolev-type spaces. See abstract here.
Thursday, April 27, 2017
11:00-11:50 am, Room SH306
Yue Yu
(Lehigh University)
Multiscale and multiphysics coupling methods with application in vascular blood flow simulations
Abstract (see PDF here): In this work, we consider the partitioned approach for fluid-structure interactions, and we develop new stabilized algorithms. There are two approaches in formulating the discrete systems in simulating fluid-structure interaction (FSI) problems: the monolithic approach, and the partitioned approach. The former is efficient for small problems but does not scale up to realistic sizes, whereas the latter suffers from numerical stability issues. In particular, in vascular blood flow simulations where the mass ratio between the structure and the fluid is relatively small, the partitioned approach gives rise to the so-called added-mass effect which renders the simulation unstable. I will present a new numerical method to handle this added-mass effect, by relaxing the exact no-slip boundary condition and introducing proper penalty terms on the fluid-structure interface, which enables the possibility of stable explicit coupling procedure. The optimal parameters are obtained via theoretical analysis, and we numerically verify that stability can be achieved irrespective of the fluid-structure mass ratio. To demonstrate the effectiveness of the proposed techniques in practical computations, I will also discuss two vascular blood flow applications in three-dimensional large scale simulations. The first application is obtained for patient-specific cerebral aneurysms. The 3D fractional-order PDEs (FPDEs) are investigated which better describe the viscoelastic behavior of cerebral arterial walls. In the second application, we apply the stabilized FSI method to heart valves, and simulate the coupling of the bioprosthetic heart valve and the surrounding blood flow under physiological conditions. Lastly, I will present the progress of our ongoing project on the multiscale coupling of the peridynamic and the classical elastic theories, with an application on simulating the material damage in arterial simulations, say, the aneurysm rupture or the heart valve failure problems.
Thursday, April 13, 2017
11:00-11:50 am, Room SH306
Guosheng
Fu (Brown University)
New Bernstein-Bezier bases for the finite element exact sequence on tetrahedra
Abstract: We present a set of new Bernstein-Bezier bases, with a local exact sequence property, for the finite element exact sequence on tetrahedra.
Thursday, April 06, 2017
11:00-11:50 am, Room SH306
Scott
Field (UMASS Dartmouth)
Fast recovery of far-field time-domain signals from near-field data
Abstract: Time-domain simulation of linear hyperbolic partial differential equations on a finite computational domain requires the introduction of a fictitious outer boundary. A long-standing challenge in the computation of waves is to identify the far-field or asymptotic signal. From data recorded on a sphere defined by the radius r1 we seek to recover the far-field signal which would reach large distances r2 including infinity. Far-field signals are particularly important as they encode information about the physical system.
In this talk, I show how far-field signal recovery is handled with a time-domain convolution of the solution recorded on a sphere r1 with a kernel. A kernel which describes signal recovery for the ordinary (acoustic) wave equation can be written in closed-form. Using rational approximation techniques developed by Alpert, Greengard and Hagstrom (AGH) this kernel can be "compressed" as a compact sum-of-poles in the frequency domain. For linear hyperbolic PDEs where one does not know a closed-form kernel representation, the AGH technique continues to provide numerically generated kernels. We use this approach to compute signals generated from binary black hole systems where the analytic kernel is not known.
Thursday, March 30, 2017
11:00-11:50 am, Room SH306
Liang Wang (WPI)
Effects of Residual Stress, Axial Stretch and Circumferential Shrinkage on Coronary Plaque Stress and Strain Calculations: an IVUS-Based Modeling Study
Abstract. Accurate stress and strain calculations are important for plaque progression and vulnerability assessment. Computational plaque models often need to start from a stress-free state which is not available directly from intravascular ultrasound (IVUS) images. In vivo IVUS image data are obtained when the blood vessel is under pressure and axially stretched. The goal of this work is to use IVUS-based near-idealized geometries and introduce a three-step model construction process to include residual stress, axial shrinkage and circumferential shrinkage and investigate their impacts on stress and strain calculations. In vivo intravascular ultrasound (IVUS) data of human coronary were acquired for model construction. In vivo IVUS movie data were acquired and used to determine patient-specific material parameter values. A three-step modeling procedure was used to make our model: a) wrap the zero-stress vessel sector to obtain the residual stress; b) stretch the vessel axially to its length in vivo; c) pressurize the vessel to recover its in vivo geometry. Several models were constructed to for our investigation, and the result indicates Models without residual stress may have large over-estimation of lumen/cap stress and strain (up to 400% higher). Thursday, March 23, 2017
11:00-11:50 am, Room SH306
Darko Volkov (WPI)
An all-frequency surface integral equation for Maxwell's equations in dielectric media. Formulation and error analysis.
Abstract: In this talk we will discuss a new surface integral equation (SIE) formulation whose solution pertains to numerical simulations of propagating time-harmonic electromagnetic waves in three dimensional dielectric media. We developed and analyzed this SIE which is governed by an operator that is of the classical identity plus compact form. A novel feature of that second-kind SIE is that, when augmented with two stabilization equations, the corresponding reformulation does not suffer from spurious resonances or low-frequency breakdown. This SIE formulation provides a tool for developing a new class of efficient and high-order algorithms (with numerical analysis) for simulation of the three dimensional dielectric media model from low- to high-frequencies. We will outline the proof of spectral numerical convergence; there are special challenges in that proof due to the use of specific quadrature rules. In particular, the typical two-dimensional case proof of convergence method (found, for example, in a textbook by Colton and Kress), is not applicable in our case. This is joint work with M. Ganesh (Colorado School of Mines).
Thursday, Feb 23, 2017
11:00-11:50 am, Room SH306
Jiahua Jiang (UMASS Dartmouth)
A Goal-Oriented Reduced Basis Methods-Accelerated Generalized Polynomial Chaos Algorithm
Abstract: The nonintrusive generalized polynomial chaos (gPC) method is a popular computational approach for solving partial differential equations with random inputs. The main hurdle preventing its efficient direct application for high-dimensional input parameters is that the size of many parametric sampling meshes grows exponentially in the number of inputs (the "curse of dimensionality"). In this talk, we design a weighted version of the reduced basis method (RBM) for use in the nonintrusive gPC framework. We construct an RBM surrogate that can rigorously achieve a user-prescribed error tolerance and ultimately is used to more efficiently compute a gPC approximation nonintrusively. The algorithm is capable of speeding up traditional nonintrusive gPC methods by orders of magnitude without degrading accuracy, assuming that the solution manifold has low Kolmogorov width. Numerical experiments on our test problems show that the relative efficiency improves as the parametric dimension increases, demonstrating the potential of the method in delaying the curse of dimensionality. Theoretical results as well as numerical evidence justify these findings.
Thursday, Feb 09, 2017 (This talk was cancelled due to
inclement weather and rescheduled to March 30, 2017)
11:00-11:50 am, Room SH306
Liang Wang (WPI)
Effects of Residual Stress, Axial Stretch and Circumferential Shrinkage on Coronary Plaque Stress and Strain Calculations: an IVUS-Based Modeling Study
Friday, Dec 09, 2016 (Rescheduled to Feb 09, 2017)
12-1pm, Room SH202
Liang Wang (WPI)
Effects of Residual Stress, Axial Stretch and Circumferential Shrinkage on Coronary Plaque Stress and Strain Calculations: an IVUS-Based Modeling Study
Friday, Dec 02, 2016
12-1pm, Room SH202
F. Patricia Medina
(WPI)
Mathematical treatment and simulation of Methane Hydrates
Abstract. The computational simulation of Methane Hydrates (MH), an ice-like substance abundant in permafrost regions and in subsea sediments, is useful for the understanding of their impact on climate change as well as a possible energy source. We consider a simplified model of MH evolution which is a scalar nonlinear parabolic PDE with two unknowns, solubility, and saturation, bound by an inequality constraint. This constraint comes from thermodynamics and expresses maximum solubility of methane component in the liquid phase; when the amount of methane exceeds this solubility, methane hydrate forms. The problem can be seen as a free boundary problem somewhat similar to the Stefan model of ice-water phase transition. Mathematically, the solubility constraint is modeled by a nonlinear complementarity constraint and we extend the theory of monotone operators to the present case of a spatially variable constraint. In our fully implicit finite element discretization, we apply recently analyzed semismooth Newton method and show that it converges superlinearly, also for other interesting test cases unrelated to MH but covered by the theory. As concerns error estimates and convergence order, we show that they are essentialy of first or half-order, depending on the norm (L2 or L1), or the variable (the smooth solubility variable or the non-smooth saturation). These results are similar to those known for the temperature and enthalpy, respectively, for Stefan problem. Part of our posterior work extended the computational model and analysis to include more variables such as salinity, pressure, temperature, and gas phase saturation, as well as in considering realistic scenarios such as those that may occur in ocean observatories along Hydrate Ridge and Cascadia Margin. However, we will focus on the initial simplified model.Friday, Nov 18, 2016
12-1pm, Room SH202
Mallikarjunaiah Muddamallappa (WPI)
On an Adaptive Finite Element Formulation of Static Mode-III Brittle Fracture With Surface Tension Excess Property
Abstract. In this talk, we discuss a nonlocal, adaptive, finite element formulation of static, mode-III brittle fracture in a homogeneous, linear elastic body. The modified continuum-mechanics model incorporates a curvature dependent surface tension on the crack surface that gives rise to a linearized jump momentum balance (JMB) crack-face boundary condition containing higher order tangential derivatives. For a numerically stable finite element implementation, we propose a nonlocal boundary regularization of the JMB using a boundary Green's function and Hilbert's transform (as a Dirichlet to Neumann map) resulting in a Fredholm second kind integral equation for the crack-edge Neumann data. The obtained numerical results indicate that the crack-tip strains (and hence the stresses) are bounded with a cusp-shaped crack-surface opening profile.Friday, Nov 04, 2016
12-1pm, Room SH202
Burt Tilley (WPI)
Frequency-dependent thermal resistance of vertical u-tube geothermal heat exchangers
Abstract. Geothermal ground-source heat pumps have been used for nearly 30 years as an environmentally friendly alternative to fossil-fuel systems. The limitations on a wider range of acceptance of the technology depends on the cost of installation of a piping network through which energy is transferred between the soil and the heat transfer fluid. The cost is proportional to the piping length. The most common of these exchangers is a U-tube system, which involves a single flexible tube that is put in a vertical borehole so that both ends remain at the ground surface. The tube radius is typically much smaller than the depth of the borehole, and this presents the opportunity to simplify the modeling through asymptotic techniques. We consider a simple Cartesian model that consists of two finite-length parallel channels carrying heat transfer fluid embedded in a soil. One channel carries fluid from the surface to the bottom of the borehole, while the other carries the fluid from the bottom of the borehole to the surface. Heat transfer is driven in the fluid by advection and conduction, while only conduction is found in the soil regions, and we assume that the temperature in the fluid is quasi-steady on the soil conduction time scale. Applying asymptotic techniques, we find a separable boundary-value problem for the Laplace transforms of temperature difference in the channels and the average temperature of the fluid temperatures at a particular depth. By using the basis functions found computationally from this boundary-value problem, we construct solutions for heat transfer fluids entering the system at constant temperature and for time-harmonic entering temperature. From these results, optimal system performance depends on the frequency of the input temperature and the separation between the channels, with the exchanger performance depending on the thermal capacity of the internal soil layer.Friday, Oct 07, 2016
1-2pm, Room SH304
Marcus Sarkis (WPI)
Finite Elements Methods for Interface Problems
Abstract. We discuss two new finite element methods for elliptic problems with discontinuous diffusion coefficients where the domain mesh is not aligned with the interface. The first method is based on Immersed Interface Methods while the second one on CutFEM. We discuss error estimates totally independent of jump of the diffusion coefficients across the interface and also independent on how the interface crosses the mesh. If time permits, I will start a new discussion on my on going work about how to obtain optimal methods where the only condition is that the RHS be in L2, no regularity at all is assumed.Friday, Sept 30, 2016
1-2pm, Room SH304
Zhen Li (Brown University)
Computation of memory effects in coarse-grained modeling through the Mori-Zwanzig formulation
Abstract. Elimination of degrees of freedom from complex dynamics often introduces non-negligible memory effects, resulting in a non-Markovian, generalized Langevin equation (GLE) for the coarse-grained (CG) system in the context of the Mori-Zwanzig (MZ) formalism. For the conservation of momentum of the CG system, GLE can be reformulated into its pairwise version, i.e., non-Markovian dissipative particle dynamics (DPD) upon a pairwise decomposition. In this talk, I will introduce how to apply the rigorous theoretical approach of MZ to derive new governing equations for CG dynamics of polymeric fluids. I will demonstrate the coarse-graining procedure by running a molecular dynamics simulation of polymer melts and constructing the MZ-guided CG model directly from atomistic trajectories, as well as the computation of the memory kernel of dissipation in CG dynamics. Unlike ad hoc coarse-graining procedures, MZ-guided coarse-graining generates accurate and efficient CG model that reproduces the correct static and dynamic properties of its corresponding atomistic system. Moreover, I will introduce different coarse-graining strategies with GLE and non-Markovian DPD models to incorporate the memory effects in practical CG simulations.Friday, Sept 16, 2016
1-2pm, Room SH304
Zhaopeng Hao (Southeast University)
High-order schemes for spatial fractional partial differential equations
Friday, Sept 2, 2016
1-2pm, Room SH304
Handy Zhang (WPI)
Stabilized numerical schemes for SDEs with highly nonlinear coefficients
Abstract. Stabilized explicit schemes are discussed for stochastic differential equations (SDEs) with coefficients of polynomial growth. The polynomial growth of the coefficients brings some instability issues for classical explicit schemes such as the forward Euler scheme and Milstein scheme. In this talk, I will introduce techniques that can stabilize these schemes and obtain high-order schemes of desire.