262,805 research outputs found

    Efficient algorithms for the optical multi-trees (OMULT) architecture.

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    In this thesis, we have reported our investigations on efficiently implementing algorithms on the recently proposed Optical Multi-Trees (OMULT) multi-processors interconnection architecture that uses both electronic and optical links among processors. We have investigated algorithms for matrix multiplication of two matrices of size n2 x n2 and two matrices of arbitrary size, the prefix-sum of a series and some fundamental computational geometry problems. We show that some common algorithms for computational geometry---finding the convex hull, the smallest enclosing box, the empirical cumulative distribution function and the all-nearest neighbor problems of n data points can be computed on the OMULT network in O(log n) time, compared to O(√n) algorithms on the Optical Transpose Interconnection System (OTIS) mesh for each of these problems. Finally we have implemented our algorithm for matrix multiplication using the SimJava simulation tool and feel that this is a convenient environment for testing such parallel algorithms.Dept. of Computer Science. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .I85. Source: Masters Abstracts International, Volume: 43-05, page: 1751. Adviser: Subir Bandyopadhyay. Thesis (M.Sc.)--University of Windsor (Canada), 2004

    A Moving Boundary Flux Stabilization Method for Cartesian Cut-Cell Grids using Directional Operator Splitting

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    An explicit moving boundary method for the numerical solution of time-dependent hyperbolic conservation laws on grids produced by the intersection of complex geometries with a regular Cartesian grid is presented. As it employs directional operator splitting, implementation of the scheme is rather straightforward. Extending the method for static walls from Klein et al., Phil. Trans. Roy. Soc., A367, no. 1907, 4559-4575 (2009), the scheme calculates fluxes needed for a conservative update of the near-wall cut-cells as linear combinations of standard fluxes from a one-dimensional extended stencil. Here the standard fluxes are those obtained without regard to the small sub-cell problem, and the linear combination weights involve detailed information regarding the cut-cell geometry. This linear combination of standard fluxes stabilizes the updates such that the time-step yielding marginal stability for arbitrarily small cut-cells is of the same order as that for regular cells. Moreover, it renders the approach compatible with a wide range of existing numerical flux-approximation methods. The scheme is extended here to time dependent rigid boundaries by reformulating the linear combination weights of the stabilizing flux stencil to account for the time dependence of cut-cell volume and interface area fractions. The two-dimensional tests discussed include advection in a channel oriented at an oblique angle to the Cartesian computational mesh, cylinders with circular and triangular cross-section passing through a stationary shock wave, a piston moving through an open-ended shock tube, and the flow around an oscillating NACA 0012 aerofoil profile.Comment: 30 pages, 27 figures, 3 table

    MGOS: A library for molecular geometry and its operating system

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    The geometry of atomic arrangement underpins the structural understanding of molecules in many fields. However, no general framework of mathematical/computational theory for the geometry of atomic arrangement exists. Here we present "Molecular Geometry (MG)'' as a theoretical framework accompanied by "MG Operating System (MGOS)'' which consists of callable functions implementing the MG theory. MG allows researchers to model complicated molecular structure problems in terms of elementary yet standard notions of volume, area, etc. and MGOS frees them from the hard and tedious task of developing/implementing geometric algorithms so that they can focus more on their primary research issues. MG facilitates simpler modeling of molecular structure problems; MGOS functions can be conveniently embedded in application programs for the efficient and accurate solution of geometric queries involving atomic arrangements. The use of MGOS in problems involving spherical entities is akin to the use of math libraries in general purpose programming languages in science and engineering. (C) 2019 The Author(s). Published by Elsevier B.V

    An orifice shape-based reduced order model of patient-specific mitral valve regurgitation

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    Mitral valve regurgitation (MR) is one of the most prevalent valvular heart diseases. Its quantitative assessment is challenging but crucial for treatment decisions. Using computational fluid dynamics (CFD), we developed a reduced order model (ROM) describing the relationship between MR flow rates, transvalvular pressure differences, and the size and shape of the regurgitant valve orifice. Due to its low computational cost, this ROM could easily be implemented into clinical workflows to support the assessment of MR. We reconstructed mitral valves of 43 patients from 3D transesophageal echocardiographic images and estimated the 3D anatomic regurgitant orifice areas using a shrink-wrap algorithm. The orifice shapes were quantified with three dimensionless shape parameters. Steady-state CFD simulations in the reconstructed mitral valves were performed to analyse the relationship between the regurgitant orifice geometry and the regurgitant hemodynamics. Based on the results, three ROMs with increasing complexity were defined, all of which revealed very good agreement with CFD results with a mean bias below 3% for the MR flow rate. Classifying orifices into two shape groups and assigning group-specific flow coefficients in the ROM reduced the limit of agreement predicting regurgitant volumes from 9.0 ml to 5.7 ml at a mean regurgitant volume of 57 ml

    High Order Cell-Centered Lagrangian-Type Finite Volume Schemes with Time-Accurate Local Time Stepping on Unstructured Triangular Meshes

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    We present a novel cell-centered direct Arbitrary-Lagrangian-Eulerian (ALE) finite volume scheme on unstructured triangular meshes that is high order accurate in space and time and that also allows for time-accurate local time stepping (LTS). The new scheme uses the following basic ingredients: a high order WENO reconstruction in space on unstructured meshes, an element-local high-order accurate space-time Galerkin predictor that performs the time evolution of the reconstructed polynomials within each element, the computation of numerical ALE fluxes at the moving element interfaces through approximate Riemann solvers, and a one-step finite volume scheme for the time update which is directly based on the integral form of the conservation equations in space-time. The inclusion of the LTS algorithm requires a number of crucial extensions, such as a proper scheduling criterion for the time update of each element and for each node; a virtual projection of the elements contained in the reconstruction stencils of the element that has to perform the WENO reconstruction; and the proper computation of the fluxes through the space-time boundary surfaces that will inevitably contain hanging nodes in time due to the LTS algorithm. We have validated our new unstructured Lagrangian LTS approach over a wide sample of test cases solving the Euler equations of compressible gasdynamics in two space dimensions, including shock tube problems, cylindrical explosion problems, as well as specific tests typically adopted in Lagrangian calculations, such as the Kidder and the Saltzman problem. When compared to the traditional global time stepping (GTS) method, the newly proposed LTS algorithm allows to reduce the number of element updates in a given simulation by a factor that may depend on the complexity of the dynamics, but which can be as large as 4.7.Comment: 31 pages, 13 figure

    Arbitrary-Lagrangian-Eulerian discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes

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    We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may also include parabolic terms in order to model dissipative transport processes. High order piecewise polynomials are adopted to represent the discrete solution at each time level and within each spatial control volume of the computational grid, while high order of accuracy in time is achieved by the ADER approach. In our algorithm the spatial mesh configuration can be defined in two different ways: either by an isoparametric approach that generates curved control volumes, or by a piecewise linear decomposition of each spatial control volume into simplex sub-elements. Our numerical method belongs to the category of direct Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation formulation of the governing PDE system is considered and which already takes into account the new grid geometry directly during the computation of the numerical fluxes. Our new Lagrangian-type DG scheme adopts the novel a posteriori sub-cell finite volume limiter method, in which the validity of the candidate solution produced in each cell by an unlimited ADER-DG scheme is verified against a set of physical and numerical detection criteria. Those cells which do not satisfy all of the above criteria are flagged as troubled cells and are recomputed with a second order TVD finite volume scheme. The numerical convergence rates of the new ALE ADER-DG schemes are studied up to fourth order in space and time and several test problems are simulated. Finally, an application inspired by Inertial Confinement Fusion (ICF) type flows is considered by solving the Euler equations and the PDE of viscous and resistive magnetohydrodynamics (VRMHD).Comment: 39 pages, 21 figure

    Airflow in a Multiscale Subject-Specific Breathing Human Lung Model

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    The airflow in a subject-specific breathing human lung is simulated with a multiscale computational fluid dynamics (CFD) lung model. The three-dimensional (3D) airway geometry beginning from the mouth to about 7 generations of airways is reconstructed from the multi-detector row computed tomography (MDCT) image at the total lung capacity (TLC). Along with the segmented lobe surfaces, we can build an anatomically-consistent one-dimensional (1D) airway tree spanning over more than 20 generations down to the terminal bronchioles, which is specific to the CT resolved airways and lobes (J Biomech 43(11): 2159-2163, 2010). We then register two lung images at TLC and the functional residual capacity (FRC) to specify subject-specific CFD flow boundary conditions and deform the airway surface mesh for a breathing lung simulation (J Comput Phys 244:168-192, 2013). The 1D airway tree bridges the 3D CT-resolved airways and the registration-derived regional ventilation in the lung parenchyma, thus a multiscale model. Large eddy simulation (LES) is applied to simulate airflow in a breathing lung (Phys Fluids 21:101901, 2009). In this fluid dynamics video, we present the distributions of velocity, pressure, vortical structure, and wall shear stress in a breathing lung model of a normal human subject with a tidal volume of 500 ml and a period of 4.8 s. On exhalation, air streams from child branches merge in the parent branch, inducing oscillatory jets and elongated vortical tubes. On inhalation, the glottal constriction induces turbulent laryngeal jet. The sites where high wall shear stress tends to occur on the airway surface are identified for future investigation of mechanotransduction.Comment: This submission is part of the APS DFD Gallery of Fluid Motio
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