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AuthorAmato, Nancy M. (9)Rauchwerger, Lawrence (5)Efendiev, Yalchin R. (4)Lazarov, Raytcho (4)Denny, Jory (3)View MoreJournalLecture Notes in Computer Science (13)Languages and Compilers for Parallel Computing (5)Lecture Notes in Computational Science and Engineering (4)IFIP Advances in Information and Communication Technology (3)Scale Space and Variational Methods in Computer Vision (3)View MoreKAUST Grant NumberKUS-C1-016-04 (32)UK-C0020 (6)KUK-C1-013-04 (5)KUK-I1-007-43 (5)KUK-C1-014-12 (2)View MorePublisherSpringer Nature (75)Elsevier BV (3)Oxford University Press (OUP) (1)Society for Industrial & Applied Mathematics (SIAM) (1)Springer Science + Business Media (1)View MoreSubjectaccess summary (1)adaptive (1)Algebraic methods (1)anisotropic (1)Asymptotic analysis (1)View MoreType

Book Chapter (82)

Year (Issue Date)2017 (6)2016 (3)2015 (7)2014 (7)2013 (23)View MoreItem AvailabilityMetadata Only (82)

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Computation of Value Functions in Nonlinear Differential Games with State Constraints

Botkin, Nikolai; Hoffmann, Karl-Heinz; Mayer, Natalie; Turova, Varvara (IFIP Advances in Information and Communication Technology, Springer Nature, 2013) [Book Chapter]

Finite-difference schemes for the computation of value functions of nonlinear differential games with non-terminal payoff functional and state constraints are proposed. The solution method is based on the fact that the value function is a generalized viscosity solution of the corresponding Hamilton-Jacobi-Bellman-Isaacs equation. Such a viscosity solution is defined as a function satisfying differential inequalities introduced by M. G. Crandall and P. L. Lions. The difference with the classical case is that these inequalities hold on an unknown in advance subset of the state space. The convergence rate of the numerical schemes is given. Numerical solution to a non-trivial three-dimensional example is presented. © 2013 IFIP International Federation for Information Processing.

Morphoelasticity: A theory of elastic growth

Goriely, Alain; Moulton, Derek (New Trends in the Physics and Mechanics of Biological Systems, Oxford University Press (OUP), 2011-10-11) [Book Chapter]

This chapter is concerned with the modelling of growth processes in the framework of continuum mechanics and nonlinear elasticity. It begins by considering growth and deformation in a one-dimensional setting, illustrating the key relationship between growth, the elastic response of the material, and the generation of residual stresses. The general three-dimensional theory of morphoelasticity is then developed from conservation of mass and momentum balance equations. In the formulation, the multiplicative decomposition of the deformation tensor, the standard approach in morphoelasticity, is derived in a new way. A discussion of continuous growth is also included. The chapter concludes by working through a sample problem of a growing cylindrical tube. A stability analysis is formulated, and the effect of growth on mucosal folding, a commonly seen instability in biological tubes, is demonstrated.

Monotonicity Conditions for Multirate and Partitioned Explicit Runge-Kutta Schemes

Hundsdorfer, Willem; Mozartova, Anna; Savcenco, Valeriu (Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws, Springer Nature, 2013) [Book Chapter]

Multirate schemes for conservation laws or convection-dominated problems seem to come in two flavors: schemes that are locally inconsistent, and schemes that lack mass-conservation. In this paper these two defects are discussed for one-dimensional conservation laws. Particular attention will be given to monotonicity properties of the multirate schemes, such as maximum principles and the total variation diminishing (TVD) property. The study of these properties will be done within the framework of partitioned Runge-Kutta methods. It will also be seen that the incompatibility of consistency and mass-conservation holds for ‘genuine’ multirate schemes, but not for general partitioned methods.

A Diffuse Interface Model for Incompressible Two-Phase Flow with Large Density Ratios

Xie, Yu; Wodo, Olga; Ganapathysubramanian, Baskar (Advances in Computational Fluid-Structure Interaction and Flow Simulation, Springer Nature, 2016-10-04) [Book Chapter]

In this chapter, we explore numerical simulations of incompressible and immiscible two-phase flows. The description of the fluid–fluid interface is introduced via a diffuse interface approach. The two-phase fluid system is represented by a coupled Cahn–Hilliard Navier–Stokes set of equations. We discuss challenges and approaches to solving this coupled set of equations using a stabilized finite element formulation, especially in the case of a large density ratio between the two fluids. Specific features that enabled efficient solution of the equations include: (i) a conservative form of the convective term in the Cahn–Hilliard equation which ensures mass conservation of both fluid components; (ii) a continuous formula to compute the interfacial surface tension which results in lower requirement on the spatial resolution of the interface; and (iii) a four-step fractional scheme to decouple pressure from velocity in the Navier–Stokes equation. These are integrated with standard streamline-upwind Petrov–Galerkin stabilization to avoid spurious oscillations. We perform numerical tests to determine the minimal resolution of spatial discretization. Finally, we illustrate the accuracy of the framework using the analytical results of Prosperetti for a damped oscillating interface between two fluids with a density contrast.

Correlation Between Pyrolysis Atmosphere and Carbon Molecular Sieve Membrane Performance Properties

Kiyono, Mayumi; Koros, William J.; Williams, Paul J. (Inorganic Polymeric and Composite Membranes - Structure, Function and Other Correlations, Elsevier BV, 2011) [Book Chapter]

Carbon molecular sieve (CMS) membranes have attractive separation performance properties, greatly exceeding an "upper bound" trade-off curve of polymeric membrane performance. CMS membranes are prepared by pyrolyzing polymers, well above their glass transition temperatures. Multiple factors, such as polymer precursor and pyrolysis protocol, are known to affect the separation performance. In this study, a correlation observed between pyrolysis atmosphere and CMS separation performance properties is discussed. Specifically, oxygen exposure during the pyrolysis process is the focus. The theory and details of the oxygen exposure and development of a new CMS preparation method using oxygen as a "dopant" will be described with a strong correlation observed with separation performance for CMS membranes prepared with various polymer precursors. In addition, study of possible mass transfer limitations on the oxygen "doping" process will be described to clarify the basis for the equilibrium-based interpretation of doping data. The method is also explored by changing the pyrolysis temperature. © 2011 Elsevier B.V.

Convex Relaxations for a Generalized Chan-Vese Model

Bae, Egil; Lellmann, Jan; Tai, Xue-Cheng (Energy Minimization Methods in Computer Vision and Pattern Recognition, Springer Nature, 2013) [Book Chapter]

We revisit the Chan-Vese model of image segmentation with a focus on the encoding with several integer-valued labeling functions. We relate several representations with varying amount of complexity and demonstrate the connection to recent relaxations for product sets and to dual maxflow-based formulations. For some special cases, it can be shown that it is possible to guarantee binary minimizers. While this is not true in general, we show how to derive a convex approximation of the combinatorial problem for more than 4 phases. We also provide a method to avoid overcounting of boundaries in the original Chan-Vese model without departing from the efficient product-set representation. Finally, we derive an algorithm to solve the associated discretized problem, and demonstrate that it allows to obtain good approximations for the segmentation problem with various number of regions. © 2013 Springer-Verlag.

From Quantification to Visualization: A Taxonomy of Uncertainty Visualization Approaches

Potter, Kristin; Rosen, Paul; Johnson, Chris R. (IFIP Advances in Information and Communication Technology, Springer Nature, 2012) [Book Chapter]

Galerkin FEM for Fractional Order Parabolic Equations with Initial Data in H − s , 0 ≤ s ≤ 1

Jin, Bangti; Lazarov, Raytcho; Pasciak, Joseph; Zhou, Zhi (Numerical Analysis and Its Applications, Springer Nature, 2013) [Book Chapter]

We investigate semi-discrete numerical schemes based on the standard Galerkin and lumped mass Galerkin finite element methods for an initial-boundary value problem for homogeneous fractional diffusion problems with non-smooth initial data. We assume that Ω ⊂ ℝd , d = 1,2,3 is a convex polygonal (polyhedral) domain. We theoretically justify optimal order error estimates in L2- and H1-norms for initial data in H-s (Ω), 0 ≤ s ≤ 1. We confirm our theoretical findings with a number of numerical tests that include initial data v being a Dirac δ-function supported on a (d-1)-dimensional manifold. © 2013 Springer-Verlag.

Electronic Transport as a Driver for Self-Interaction-Corrected Methods

Pertsova, Anna; Canali, Carlo Maria; Pederson, Mark R.; Rungger, Ivan; Sanvito, Stefano (Advances In Atomic, Molecular, and Optical Physics, Elsevier BV, 2015) [Book Chapter]

© 2015 Elsevier Inc. While spintronics often investigates striking collective spin effects in large systems, a very important research direction deals with spin-dependent phenomena in nanostructures, reaching the extreme of a single spin confined in a quantum dot, in a molecule, or localized on an impurity or dopant. The issue considered in this chapter involves taking this extreme to the nanoscale and the quest to use first-principles methods to predict and control the behavior of a few "spins" (down to 1 spin) when they are placed in an interesting environment. Particular interest is on environments for which addressing these systems with external fields and/or electric or spin currents is possible. The realization of such systems, including those that consist of a core of a few transition-metal (TM) atoms carrying a spin, connected and exchanged-coupled through bridging oxo-ligands has been due to work by many experimental researchers at the interface of atomic, molecular and condensed matter physics. This chapter addresses computational problems associated with understanding the behaviors of nano- and molecular-scale spin systems and reports on how the computational complexity increases when such systems are used for elements of electron transport devices. Especially for cases where these elements are attached to substrates with electronegativities that are very different than the molecule, or for coulomb blockade systems, or for cases where the spin-ordering within the molecules is weakly antiferromagnetic, the delocalization error in DFT is particularly problematic and one which requires solutions, such as self-interaction corrections, to move forward. We highlight the intersecting fields of spin-ordered nanoscale molecular magnets, electron transport, and coulomb blockade and highlight cases where self-interaction corrected methodologies can improve our predictive power in this emerging field.

Anisotropic Third-Order Regularization for Sparse Digital Elevation Models

Lellmann, Jan; Morel, Jean-Michel; Schönlieb, Carola-Bibiane (Scale Space and Variational Methods in Computer Vision, Springer Nature, 2013) [Book Chapter]

We consider the problem of interpolating a surface based on sparse data such as individual points or level lines. We derive interpolators satisfying a list of desirable properties with an emphasis on preserving the geometry and characteristic features of the contours while ensuring smoothness across level lines. We propose an anisotropic third-order model and an efficient method to adaptively estimate both the surface and the anisotropy. Our experiments show that the approach outperforms AMLE and higher-order total variation methods qualitatively and quantitatively on real-world digital elevation data. © 2013 Springer-Verlag.

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