The Experts below are selected from a list of 105 Experts worldwide ranked by ideXlab platform

Liu Hongyu - One of the best experts on this subject based on the ideXlab platform.

  • Recovering piecewise constant refractive indices by a single far-field pattern
    'IOP Publishing', 2020
    Co-Authors: Blåsten Emilia, Liu Hongyu
    Abstract:

    We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a perturbation to the refractive index on the corners of its support. These assumptions are satisfied, for example, in the low acoustic frequency regime. As a consequence if the perturbation is piecewise constant with either a Polyhedral nest geometry or a known Polyhedral Cell geometry, such as a pixel or voxel array, we establish the injectivity of the perturbation to far-field map given a fixed incident wave. This is the first unique determinancy result of its type in the literature, and all of the existing results essentially make use of infinitely many measurements.Peer reviewe

  • Recovering piecewise constant refractive indices by a single far-field pattern
    2020
    Co-Authors: Blåsten Emilia, Liu Hongyu
    Abstract:

    We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a perturbation to the refractive index on the corners of its support. These assumptions are satisfied for example in the low acoustic frequency regime. As a consequence if the perturbation is piecewise constant with either a Polyhedral nest geometry or a known Polyhedral Cell geometry, such as a pixel or voxel array, we establish the injectivity of the perturbation to far-field map given a fixed incident wave. This is the first unique determinancy result of its type in the literature, and all of the existing results essentially make use of infinitely many measurements.Comment: 15 pages, 1 figur

Peter Williams - One of the best experts on this subject based on the ideXlab platform.

  • Fast Polyhedral Cell Sorting for Interactive Rendering of Unstructured Grids
    Computer Graphics Forum, 1999
    Co-Authors: João L. D. Comba, James T. Klosowsk, Nelson Max, Joseph S. B. Mitchell, Cláudio T. Silva, Peter Williams
    Abstract:

    Direct volume rendering based on projective methods works by projecting, in visibility order, the Polyhedral Cells of a mesh onto the image plane, and incrementally compositing the Cell’s color and opacity into the final image. Crucial to this method is the computation of a visibility ordering of the Cells. If the mesh is “well-behaved” (acyclic and convex), then the MPVO method of Williams provides a very fast sorting algorithm; however, this method only computes an approximate ordering in general datasets, resulting in visual artifacts when rendered. A recent method of Silva et al. removed the assumption that the mesh is convex, by means of a sweep algorithm used in conjunction with the MPVO method; their algorithm is substantially faster than previous exact methods for general meshes. In this paper we propose a new technique, which we call BSP-XMPVO, which is based on a fast and simple way of using binary space partitions on the boundary elements of the mesh to augment the ordering produced by MPVO. Our results are shown to be orders of magnitude better than previous exact methods of sorting Cells.

  • an exact interactive time visibility ordering algorithm for Polyhedral Cell complexes
    Symposium on Volume Visualization, 1998
    Co-Authors: Cláudio T. Silva, Joseph S. B. Mitchell, Peter Williams
    Abstract:

    A visibility ordering of a set of objects, from a given viewpoint, is a total order on the objects such that if object a obstructs object b, then b precedes a in the ordering. Such orderings are extremely useful for rendering volumetric data. The authors present an algorithm that generates a visibility ordering of the Cells of an unstructured mesh, provided that the Cells are convex polyhedra and nonintersecting, and that the visibility ordering graph does not contain cycles. The overall mesh may be nonconvex and it may have disconnected components. The technique employs the sweep paradigm to determine an ordering between pairs of exterior (mesh boundary) Cells which can obstruct one another. It then builds on Williams' (1992) MPVO algorithm which exploits the ordering implied by adjacencies within the mesh. The partial ordering of the exterior Cells found by sweeping is used to augment the DAG created in Phase II of the MPVO algorithm. The method thus removes the assumption of the MPVO algorithm that the mesh be convex and connected, and thereby allows one to extend the MPVO algorithm, without using the heuristics that were originally suggested by Williams (and are sometimes problematic). The resulting XMPVO algorithm has been analyzed, and a variation of it has been implemented for unstructured tetrahedral meshes; they provide experimental evidence that it performs very well in practice.

  • VVS - An exact interactive time visibility ordering algorithm for Polyhedral Cell complexes
    Proceedings of the 1998 IEEE symposium on Volume visualization - VVS '98, 1998
    Co-Authors: Cláudio T. Silva, Joseph S. B. Mitchell, Peter Williams
    Abstract:

    A visibility ordering of a set of objects, from a given viewpoint, is a total order on the objects such that if object a obstructs object b, then b precedes a in the ordering. Such orderings are extremely useful for rendering volumetric data. The authors present an algorithm that generates a visibility ordering of the Cells of an unstructured mesh, provided that the Cells are convex polyhedra and nonintersecting, and that the visibility ordering graph does not contain cycles. The overall mesh may be nonconvex and it may have disconnected components. The technique employs the sweep paradigm to determine an ordering between pairs of exterior (mesh boundary) Cells which can obstruct one another. It then builds on Williams' (1992) MPVO algorithm which exploits the ordering implied by adjacencies within the mesh. The partial ordering of the exterior Cells found by sweeping is used to augment the DAG created in Phase II of the MPVO algorithm. The method thus removes the assumption of the MPVO algorithm that the mesh be convex and connected, and thereby allows one to extend the MPVO algorithm, without using the heuristics that were originally suggested by Williams (and are sometimes problematic). The resulting XMPVO algorithm has been analyzed, and a variation of it has been implemented for unstructured tetrahedral meshes; they provide experimental evidence that it performs very well in practice.

Blåsten Emilia - One of the best experts on this subject based on the ideXlab platform.

  • Recovering piecewise constant refractive indices by a single far-field pattern
    'IOP Publishing', 2020
    Co-Authors: Blåsten Emilia, Liu Hongyu
    Abstract:

    We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a perturbation to the refractive index on the corners of its support. These assumptions are satisfied, for example, in the low acoustic frequency regime. As a consequence if the perturbation is piecewise constant with either a Polyhedral nest geometry or a known Polyhedral Cell geometry, such as a pixel or voxel array, we establish the injectivity of the perturbation to far-field map given a fixed incident wave. This is the first unique determinancy result of its type in the literature, and all of the existing results essentially make use of infinitely many measurements.Peer reviewe

  • Recovering piecewise constant refractive indices by a single far-field pattern
    2020
    Co-Authors: Blåsten Emilia, Liu Hongyu
    Abstract:

    We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a perturbation to the refractive index on the corners of its support. These assumptions are satisfied for example in the low acoustic frequency regime. As a consequence if the perturbation is piecewise constant with either a Polyhedral nest geometry or a known Polyhedral Cell geometry, such as a pixel or voxel array, we establish the injectivity of the perturbation to far-field map given a fixed incident wave. This is the first unique determinancy result of its type in the literature, and all of the existing results essentially make use of infinitely many measurements.Comment: 15 pages, 1 figur

Olav Møyner - One of the best experts on this subject based on the ideXlab platform.

  • A fully implicit WENO scheme on stratigraphic and unstructured Polyhedral grids
    Computational Geosciences, 2020
    Co-Authors: Knut-andreas Lie, Trine S. Mykkeltvedt, Olav Møyner
    Abstract:

    Many authors have used higher-order spatial discretizations to reduce numerical diffusion, which can be particularly pronounced when simulating EOR processes involving active chemical substances that are transported by linear or weakly nonlinear waves. Most high-resolution methods reported in the literature are based on explicit temporal discretizations. This imposes severe time-step restrictions when applied to the type of grids seen in industry-standard simulation models of real assets, which usually have orders-of-magnitude variations in porosities and Darcy velocities that necessitate the use of implicit discretization. Herein, we propose a second-order WENO discretization suitable for complex grids with Polyhedral Cell geometries, unstructured topologies, large aspect ratios, and large variations in interface areas. The WENO scheme is developed as part of a standard, fully implicit formulation that solves for pressure and transported quantities simultaneously. We investigate the accuracy and utility of the WENO scheme for a series of test cases that involve corner-point and 2D/3D Voronoi grids and black-oil and compositional flow models.

Møyner Olav - One of the best experts on this subject based on the ideXlab platform.

  • A fully implicit WENO scheme on stratigraphic and unstructured Polyhedral grids
    'Springer Science and Business Media LLC', 2019
    Co-Authors: Lie Knut-andreas, Mykkeltvedt, Trine Solberg, Møyner Olav
    Abstract:

    Many authors have used higher-order spatial discretizations to reduce numerical diffusion, which can be particularly pronounced when simulating EOR processes involving active chemical substances that are transported by linear or weakly nonlinear waves. Most high-resolution methods reported in the literature are based on explicit temporal discretizations. This imposes severe time-step restrictions when applied to the type of grids seen in industry-standard simulation models of real assets, which usually have orders-of-magnitude variations in porosities and Darcy velocities that necessitate the use of implicit discretization. Herein, we propose a second-order WENO discretization suitable for complex grids with Polyhedral Cell geometries, unstructured topologies, large aspect ratios, and large variations in interface areas. The WENO scheme is developed as part of a standard, fully implicit formulation that solves for pressure and transported quantities simultaneously. We investigate the accuracy and utility of the WENO scheme for a series of test cases that involve corner-point and 2D/3D Voronoi grids and black-oil and compositional flow models.acceptedVersio