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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 (22)View MoreItem AvailabilityMetadata Only (82)

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Domain Decomposition Solvers for Frequency-Domain Finite Element Equations

Copeland, Dylan; Kolmbauer, Michael; Langer, Ulrich (Domain Decomposition Methods in Science and Engineering XIX, Springer Nature, 2010-10-05) [Book Chapter]

The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method. © 2011 Springer-Verlag Berlin Heidelberg.

Efficient Parallel Algorithms for Unsteady Incompressible Flows

Guermond, Jean-Luc; Minev, Peter D. (Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications, Springer Nature, 2013) [Book Chapter]

The objective of this paper is to give an overview of recent developments on splitting schemes for solving the time-dependent incompressible Navier–Stokes equations and to discuss possible extensions to the variable density/viscosity case. A particular attention is given to algorithms that can be implemented efficiently on large parallel clusters.

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.

Turing’s Theory of Morphogenesis: Where We Started, Where We Are and Where We Want to Go

Woolley, Thomas E.; Baker, Ruth E.; Maini, Philip K. (Theory and Applications of Computability, Springer Nature, 2017-05-05) [Book Chapter]

Over 60 years have passed since Alan Turing first postulated a mechanism for biological pattern formation. Although Turing did not have the chance to extend his theories before his unfortunate death two years later, his work has not gone unnoticed. Indeed, many researchers have since taken up the gauntlet and extended his revolutionary and counter-intuitive ideas. Here, we reproduce the basics of his theory as well as review some of the recent generalisations and applications that have led our mathematical models to be closer representations of the biology than ever before. Finally, we take a look to the future and discuss open questions that not only show that there is still much life in the theory, but also that the best may be yet to come.

Modified Pressure-Correction Projection Methods: Open Boundary and Variable Time Stepping

Bonito, Andrea; Guermond, Jean-Luc; Lee, Sanghyun (Numerical Mathematics and Advanced Applications - ENUMATH 2013, Springer Nature, 2014-10-31) [Book Chapter]

© Springer International Publishing Switzerland 2015. In this paper, we design and study two modifications of the first order standard pressure increment projection scheme for the Stokes system. The first scheme improves the existing schemes in the case of open boundary condition by modifying the pressure increment boundary condition, thereby minimizing the pressure boundary layer and recovering the optimal first order decay. The second scheme allows for variable time stepping. It turns out that the straightforward modification to variable time stepping leads to unstable schemes. The proposed scheme is not only stable but also exhibits the optimal first order decay. Numerical computations illustrating the theoretical estimates are provided for both new schemes.

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.

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