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1,319
Efficient Implementation of Weighted ENO Schemes
, 1995
"... In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially nonoscillatory) finite difference schemes of Liu, Osher and Chan [9]. It was shown by Liu et al. that WENO schemes constructed from the r th order (in L¹ norm) ENO schemes are (r +1) th order accur ..."
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Cited by 412 (38 self)
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th order WENO scheme is as fast as the 4 th order WENO scheme of Liu et al. and, both schemes are about twice as fast as the 4th order ENO schemes on vector supercomputers and as fast on serial and parallel computers. For Euler systems of gas dynamics, we suggest to compute the weights from pressure
Comprehensible Rendering of 3D Shapes
, 1990
"... We propose a new rendering technique that produces 3D images with enhanced visual comprehensibility. Shape features can be readily understood if certain geometric properties are enhanced. To achieve this, we develop drawing algorithms for discontinuities, edges, contour lines, and curved hatchin ..."
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Cited by 293 (0 self)
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We propose a new rendering technique that produces 3D images with enhanced visual comprehensibility. Shape features can be readily understood if certain geometric properties are enhanced. To achieve this, we develop drawing algorithms for discontinuities, edges, contour lines, and curved
Color TV: Total Variation Methods for Restoration of Vector Valued Images
 IEEE Trans. Image Processing
, 1996
"... We propose a new definition of the total variation norm for vector valued functions which can be applied to restore color and other vector valued images. The new TV norm has the desirable properties of (i) not penalizing discontinuities (edges) in the image, (ii) rotationally invariant in the image ..."
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Cited by 158 (13 self)
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We propose a new definition of the total variation norm for vector valued functions which can be applied to restore color and other vector valued images. The new TV norm has the desirable properties of (i) not penalizing discontinuities (edges) in the image, (ii) rotationally invariant in the image
Γconvergence for beginners
 of Oxford Lecture Series in Mathematics and its Applications
, 2002
"... The object of convergence is the description of the asymptotic behaviour of families of minimum problems, usually depending on some parameters whose nature may be geometric or constitutive, deriving from a discretization argument, an approximation procedure, etc. Since its introduction by De Giorgi ..."
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Cited by 178 (37 self)
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Giorgi in the early 1970s convergence has gained an undiscussed role as the most
exible and natural notion of convergence for variational problems, and is now been widely used also outside the eld of the Calculus of Variations and of Partial Dierential Equations. Its
exibility is due to its being
Adaptive Discontinuous Galerkin Finite Element Methods for Compressible Fluid Flows
 SIAM J. Sci. Comput
"... this paper is to discuss the a posteriori error analysis and adaptive mesh design for discontinuous Galerkin finite element approximations to systems of conservation laws. In Section 2, we introduce the model problem and formulate its discontinuous Galerkin finite element approximation. Section 3 is ..."
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Cited by 122 (17 self)
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vector to 0fl, B(u, n) is the negative part of B(u, n) and g is a (given) realvalued function. To formulate the discontinuous Galerkin finite element method (DGFEM, for short) for (2.1), we first introduce some notation. Let 7 = {n} be an admissible subdivision of fl into open element domains n; here h
The Index of Discontinuous Vector Fields
 Journal of Mathematics
, 1995
"... . The concept of the index of a vector field is one of the oldest in Algebraic Topology. First stated by Poincare and then perfected by Heinz Hopf and S. Lefschetz and Marston Morse, it is developed as the sum of local indices of the zeros of the vector field, using the idea of degree of a map and i ..."
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Cited by 15 (3 self)
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. The concept of the index of a vector field is one of the oldest in Algebraic Topology. First stated by Poincare and then perfected by Heinz Hopf and S. Lefschetz and Marston Morse, it is developed as the sum of local indices of the zeros of the vector field, using the idea of degree of a map
Modelling frontal discontinuities in wind fields
, 1999
"... Submitted to Nonparametric Statistics A Bayesian procedure for the retrieval of wind vectors over the ocean using satellite borne scatterometers requires realistic prior nearsurface wind eld models over the oceans. We have implemented carefully chosen vector Gaussian Process models; however in so ..."
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Cited by 7 (0 self)
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Submitted to Nonparametric Statistics A Bayesian procedure for the retrieval of wind vectors over the ocean using satellite borne scatterometers requires realistic prior nearsurface wind eld models over the oceans. We have implemented carefully chosen vector Gaussian Process models; however
MAXIMIZING VISIBILITY IN NONCONVEX POLYGONS: NONSMOOTH ANALYSIS AND GRADIENT ALGORITHM DESIGN
"... Abstract. This paper presents a motion control algorithm for a planar mobile observer such as, e.g., a mobile robot equipped with an omnidirectional camera. We propose a nonsmooth gradient algorithm for the problem of maximizing the area of the region visible to the observer in a simple nonconvex p ..."
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polygon. First, we show that the visible area is almost everywhere a locally Lipschitz function of the observer location. Second, we provide a novel version of LaSalle Invariance Principle for discontinuous vector elds and Lyapunov functions with a nite number of discontinuities. Finally, we establish
Texture Synthesis over Arbitrary Manifold Surfaces
, 2001
"... Algorithms exist for synthesizing a wide variety of textures over rectangular domains. However, it remains difficult to synthesize general textures over arbitrary manifold surfaces. In this paper, we present a solution to this problem for surfaces defined by dense polygon meshes. Our solution extend ..."
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Cited by 161 (9 self)
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, and search a sample texture for similar neighborhoods. Our algorithm requires as input only a sample texture and a target model. Notably, it does not require specification of a global tangent vector field; it computes one as it goes  either randomly or via a relaxation process. Despite this, the synthesized
Results 1  10
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