Program

All events are held in Smith Memorial Student Union, Room 238. This will be a paperless meeting: No program copies will be handed out. Participants are encouraged to use laptops or smartphones as all information is online here. The conference will not be providing any meals except coffee breaks. For lunch, we suggest that the participants take advantage of the Portland Farmers Market downstairs or nearby restaurants, bars and food carts.

 

 PROGRAM SUMMARY

 

08:30: Name tags, Coffee & Welcome


18:30: No-host dinner at Southpark Seafood Restaurant , 901 SW Salmon St.

 

A large table has been reserved at this restaurant based on the number of participants who indicated dinner attendance during registration. You can reach this restaurant from the conference hall by a 15 minute walk north through the park blocks.

 

 

ABSTRACTS LISTED BY SPEAKER ORDER


Some Algorithmic Aspects of Adaptive Finite Elements
 We will discuss our on-going investigation of adaptive strategies for finite element equations. We will examine a posteriori error estimates based on superconvergent derivative recovery. We then survey and compare h, p, r, and hp adaptive approaches. Some numerical examples will be provided.

Numerical approximation of Laplace eigenvalues with mixed boundary data
 Eigenfunctions of the Laplace operator with mixed Dirichet-Neumann boundary conditions may possess singularities, especially if the Dirichlet-Neumann junction occurs at angles ≥ π/2. This suggests the use of boundary integral strategies to solve such eigenproblems. As with boundary value problems, integral-equation methods allow for a reduction of dimension, and the resolution of singular behaviour which may otherwise present challenges to volumetric methods. In this talk, we present a novel integral-equation algorithm for mixed Dirichlet-Neumann eigenproblems. This is based on joint work with Oscar Bruno and Eldar Akhmetgaliyev (Caltech). For domains with smooth boundary, the singular behaviour of the eigenfunctions at Dirichlet-Neumann junctions is incorporated as part of the discretization strategy for the integral operator. The discretization we use is based on the high-order Fourier Continuation method (FC). For non-smooth (Lipschitz) domains an alternative high-order discretization is presented which achieves high-order accuracy on the basis of graded meshes. In either case (smooth or Lipschitz boundary), eigenvalues are evaluated by examining the minimal singular values of a suitably stabilized discrete system. This is in the spirit of the modification proposed by Trefethen and Betcke in the modified method of particular solutions. The method is conceptually simple, and allows for highly accurate and efficient computation of eigenvalues and eigenfunctions, even in challenging geometries.

Element based algebraic coarse spaces with application to numerical upscaling and multilevel Monte Carlo simulations
 We first provide an overview of the element agglomeration based algebraic multigrid (or AMGe) methodology for generating hierarchy of coarse spaces that form exact de Rham sequences on all coarse levels. The coarse hierarchy can be made as accurate as needed by incorporating enough degrees of freedom into the coarse spaces, by either fitting piecewise polynomials or by using degrees of freedom obtained by the spectral version of the AMGe method. The latter has been recently extended to discretization problems obtained by the mixed finite element method. The constructed coarse spaces can be used for building very robust (but with somewhat expensive setup) multilevel solvers, but more importantly, they can be used as discretization tools for deriving accurate coarse (upscaled) models for the entire de Rham sequence with applications to PDEs such as Darcy (H(div)), Maxwell (H(curl)), and elliptic (scalar or systems posed in H^1). Another application of our AMGe-based coarse spaces is in the numerical simulations of multiscale multiphysics phenomena with uncertain input data within a Multilevel Monte Carlo (MLMC) framework. Multilevel Monte Carlo techniques typically rely on geometric hierarchies of computational spaces associated with meshes obtained by successive refinement. With our approach, we can apply MLMC to unstructured meshes by using our constructed hierarchies of coarse spaces since they possess required stability and approximation properties for broad classes of PDEs. An application to subsurface flow simulations in primal and mixed finite element discretization of the SPE10 benchmark illustrates our approach.

High-performance tensor computations in quantum chemistry
 Quantum chemistry is the domain of computational science devoted to the approximate solution of the Schrödinger equation for the behavior of electrons in molecules. The most common approximations of quantum chemistry transform a complicated many-body partial differential equation into a set of linear algebra problems, many of which involve tensors. This talk will describe the state-of-the-art in tensor computations as required by one common approximation of quantum chemistry: the coupled-cluster method. We will describe the algorithms and software implementation of the two state-of-the-art tensor contraction libraries for supercomputers and the resulting scientific applications. Numerical aspects related to single-, double- and mixed-precision will also be included.

Computational modeling of biofilms
 Biofilms are complex communities of microorganisms attached to surfaces or associated with interfaces. The recent explosion in biofilm research is motivated by their ubiquitous presence in environment as well as the development of new technologies such as microbial induced calcite precipitation for crack cementation, remediation for radionuclides, construction, and stabilisation of soils, and medicine. Computational models of biofilm growth and biofilm morphology are formulated at multiple scales and combine nonlinear coupled systems of reactive transport equations in evolving geometries. The main difficulty is in handling interfaces between the biofilm produced protective envelope called EPS (extracellular polymeric substance) and the bulk fluids which (may) also contain biomass. In the talk we present our new model of biofilm evolution using variational inequalities which is coupled to Navier-Stokes equations describing the bulk fluid. The model is applied at porescale where we pursue analyses and comparison with biofilm imaging (work joint with Dorthe Wildenschild). We also extend it further to biocementation models in collaboration with OSU and DOE-NETL scientists. Furthermore, we discuss upscaling from pore to corescale. This is joint work with A. Trykozko (University of Warsaw), OSU scientists: D. Wildenschild, G. Iltis, S. Schlueter, M. Torres, I. Alleau, R. Colwell, D. Koley, A. Thurber, and DOE-NETL scientist C. Verba.

Modeling debris-flows and landslides. Case study of the Oso (Washington) disaster of 2014
 Debris flows are rushing torrents of rock-sediment-water mixtures that can travel many kilometers through mountainous terrain and inundate expansive portions of the valley floors below. These and closely related hazardous flows (mudflows, landslides, lahars, etc.) are intermediate to sediment-laden flash floods and rock avalanches, and owe much of their destructive capacity to the complex interactions between solid and fluid phases. They are composed of roughly equal parts solid and liquid and they exhibit surprising mobility due to liquefaction of the solid phase, occurring because of the high fluid pressures sustained by granular motion. Predicting debris flows is difficult due to a sensitive dependence on initial soil properties, which can lead to highly destructive debris flows, or alternatively, to slow, slumping masses that quickly stabilize. We have developed a quasi two-phase depth-averaged model for simulating debris flows from initiation to deposition. In deriving the model, we employed concepts from quasi-static soil mechanics and grain mechanics in an attempt to model the full transition from stability to mobility. The resulting mathematical model is a nonconservative, hyperbolic system with a source term for the depth, momentum, volume fractions and pore-fluid pressure. The system is similar to the shallow-water equations and presents many of the same difficulties when applied to flows moving through topography. Additional challenges arise due to the sensitive dependence on initial conditions, the interacting phases, and the evolving rheology of these flows. I will describe this model and survey some of the numerical issues that arise for modeling debris flows and related phenomenon. D-Claw is a software package that we have developed for simulating debris flows in general topography. D-Claw belongs to the GeoClaw and Clawpack suite of tools. I will present D-Claw simulations of the Oso, Washington, disaster that occurred in the spring of 2014, and discuss the implications.

The Level Set Method: New approaches to combating mass loss and curvature instability
 The level set method is a powerful tool to track moving interfaces, undergoing large deformations, without the need for remeshing as with marker-particle methods or interface smearing as with diffuse-interface methods. It does, of course, come with it's own shortfalls. In particular, the method experiences somewhat severe mass loss if care isn't taken to control numerical dissipation. Additionally, the ability to reliably compute the curvature of the interface depends on how the level set is constructed. This is an issue if the evolution of the interface is curvature dependent, as it is with bending resistant interfaces. Thus, standard approaches have been developed to address both of these issues, including the use of WENO schemes and augmented reinitialization. New approaches will be presented that address mass loss and curvature computation in a more compact or straightforward way.

 

Difference Potentials Method for Interface/Composite Domain Problems
 In this talk, we will first give an introduction to the Difference Potentials Method (DPM). DPM is a framework for developing efficient, high-order accurate numerical methods for the solution of interior or exterior boundary value problems (BVPs) on arbitrary domains. DPM can be viewed as a discrete analog to the method of generalized Calderón potentials and Calderón boundary equations with projections in the theory of partial differential equations Designing numerical methods with high-order accuracy for problems with interfaces (for example, models for composite materials or fluids, etc), as well as models in irregular domains is crucial to many physical and biological applications. We will discuss recently developed efficient numerical schemes based on the idea of the Difference Potentials for elliptic and parabolic interface/composite domain problems. Numerical experiments to illustrate the accuracy and the robustness of the developed methods will be presented as well.