Search results for "Approx"
showing 10 items of 922 documents
Variable-Radius Offset Surface Approximation on the GPU
2020
Variable-radius offset surfaces find applications in various fields, such as variable brush strokes in 2D and 3D sketching and geometric modeling tools. In forensic facial reconstruction the skin surface can be inferred from a given skull by computing a variable-radius offset surface of the skull surface. Thereby, the skull is represented as a two-manifold triangle mesh and the facial soft tissue thickness is specified for each vertex of the mesh. We present a method to interactively visualize the wanted skin surface by rendering the variable-radius offset surfaces of all triangles of the skull mesh. We have also developed a special shader program which is able to generate a discretized vol…
A Second Order Accurate Kinetic Relaxation Scheme for Inviscid Compressible Flows
2013
In this paper we present a kinetic relaxation scheme for the Euler equations of gas dynamics in one space dimension. The method is easily applicable to solve any complex system of conservation laws. The numerical scheme is based on a relaxation approximation for conservation laws viewed as a discrete velocity model of the Boltzmann equation of kinetic theory. The discrete kinetic equation is solved by a splitting method consisting of a convection phase and a collision phase. The convection phase involves only the solution of linear transport equations and the collision phase instantaneously relaxes the distribution function to an equilibrium distribution. We prove that the first order accur…
Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis (II) HFBTHO v2.00d: a new v…
2012
We describe the new version 2.00d of the code HFBTHO that solves the nuclear Skyrme Hartree-Fock (HF) or Skyrme Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic-oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (E…
Quantitative approximation of certain stochastic integrals
2002
We approximate certain stochastic integrals, typically appearing in Stochastic Finance, by stochastic integrals over integrands, which are path-wise constant within deterministic, but not necessarily equidistant, time intervals. We ask for rates of convergence if the approximation error is considered in L 2 . In particular, we show that by using non-equidistant time nets, in contrast to equidistant time nets, approximation rates can be improved considerably.
Complex singularities and PDEs
2015
In this paper we give a review on the computational methods used to capture and characterize the complex singularities developed by some relevant PDEs. We begin by reviewing the classical singularity tracking method and give an example of application using the Burgers equation as a case study. This method is based on the analysis of the Fourier spectrum of the solution and it allows to determine and characterize the complex singularity closest to the real domain. We then introduce other methods generally used to detect the hidden singularities. In particular we show some applications of the Padé approximation, of the Kida method, and of Borel-Polya method. We apply these techniques to the s…
Impact of internal curvature gradient on the power and accommodation of the crystalline lens
2017
Human crystalline lens has a layered, shell-like structure with the refractive index increasing from cortex to nucleus (gradient index or GRIN structure). Moreover, every iso-indicial layer has a certain curvature which also varies from cortex to nucleus, with a gradient of curvature (G). In the present manuscript, the role of G on the lens power is investigated along with its implications regarding the lens paradox (change of lens power with age) and intra-capsular accommodation mechanism (larger than expected changes of lens power during accommodation compared to a homogenous lens). To this end, a simplified formulation of paraxial lens power based on thin lens approximation is developed …
Influence of pixel size on quantification of airway wall thickness in computed tomography.
2009
Objectives: The purpose of this study was to determine the point where a further decrease in voxel size does not result in better automatic quantification of the bronchial wall thickness by using 2 different assessment techniques. Materials and Methods: The results from the commonly used full-width-at-half-maximum (FWHM) principle and a new technique (integral-based method [IBM]) were compared for thin-section multidetector computed tomography (MDCT) data sets from an airway phantom containing 10 different tubular airway phantoms and in a human subsegmental bronchus in vivo. Correlation with the actual wall thickness and comparison of the wall thicknesses assessed for different voxel sizes …
Ultrafast diffraction of tightly focused waves with spatiotemporal stabilization
2008
Experimental studies of ultrafast beam shaping have come about from the need to compensate diffraction-induced dispersive effects in femtosecond laser beams. From a theoretical point of view, chromatic matching of diffracted spherical waves in the vicinity of the geometrical focus is attained by applying conveniently dispersive boundary conditions in the far-field zone, a subject thoroughly analyzed in the paraxial regime. For applications demanding high spatial resolution, however, high-numerical-aperture microscope objectives may be employed instead and would lead to nonparaxiality of the focal wavefields. These circumstances have motivated our investigation. Concretely we report on prere…
A reliable incremental method of computing the limit load in deformation plasticity based on compliance : Continuous and discrete setting
2016
The aim of this paper is to introduce an enhanced incremental procedure that can be used for the numerical evaluation and reliable estimation of the limit load. A conventional incremental method of limit analysis is based on parametrization of the respective variational formulation by the loading parameter ? ? ( 0 , ? l i m ) , where ? l i m is generally unknown. The enhanced incremental procedure is operated in terms of an inverse mapping ? : α ? ? where the parameter α belongs to ( 0 , + ∞ ) and its physical meaning is work of applied forces at the equilibrium state. The function ? is continuous, nondecreasing and its values tend to ? l i m as α ? + ∞ . Reduction of the problem to a finit…
Finite element approximation of vector fields given by curl and divergence
1981
In this paper a finite element approximation scheme for the system curl is considered. The use of pointwise approximation of the boundary condition leads to a nonconforming method. The error estimate is proved and numerically tested.