Browsing Computational Mathematics (CM) by Title
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Fourier finite element modeling of light emission in waveguides: 2.5dimensional FEM approach
(Optics Express, 20151231)We present a Fourier finite element modeling of light emission of dipolar emitters coupled to infinitely long waveguides. Due to the translational symmetry, the threedimensional (3D) coupled waveguideemitter system can ... 
Fractional Laguerre spectral methods and their applications to fractional differential equations on unbounded domain
(International Journal of Computer Mathematics, 20151231)In this article, we first introduce a singular fractional SturmLiouville problem (SFSLP) on unbounded domain. The associated fractional differential operator is both Weyl and Caputo type. The properties of spectral data ... 
Framework for adaptive fluidstructure interaction with industrial applications
(International Journal of Materials Engineering Innovation, 20131231)We present developments in the UnicornHPC framework for unified continuum mechanics, enabling adaptive finite element computation of fluidstructure interaction, and an overview of the larger FEniCSHPC framework for ... 
Fusionbased variational image dehazing
(IEEE Signal Processing Letters, 20170201)We propose a novel imagedehazing technique based on the minimization of two energy functionals and a fusion scheme to combine the output of both optimizations. The proposed fusionbased variational imagedehazing (FVID) ... 
GaussGalerkin quadrature rules for quadratic and cubic spline spaces and their application to isogeometric analysis
(ComputerAided Design, 20160701)We introduce Gaussian quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. By definition, these spaces are of even degrees. The optimal quadrature ... 
Gaussian quadrature for $C^1$ cubic CloughTocher macrotriangles
(Journal of Computational and Applied Mathematics, 20181031)A numerical integration rule for multivariate cubic polynomials over ndimensional simplices was designed by Hammer and Stroud [14]. The quadrature rule requires n + 2 quadrature points: the barycentre of the simplex and ... 
Gaussian quadrature rules for $C^1$ quintic splines with uniform knot vectors
(Journal of Computational and Applied Mathematics, 20170322)We provide explicit quadrature rules for spaces of $C^1$ quintic splines with uniform knot sequences over finite domains. The quadrature nodes and weights are derived via an explicit recursion that avoids numerical solvers. ... 
Generalization of the Pythagorean Eigenvalue Error Theorem and its Application to Isogeometric Analysis
(Numerical Methods for PDEs, 20181013)This chapter studies the effect of the quadrature on the isogeometric analysis of the wave propagation and structural vibration problems. The dispersion error of the isogeometric elements is minimized by optimally blending ... 
Generalization of the Zlámal condition for simplicial finite elements in ℝ d
(Applications of Mathematics, 20111231)The famous Zlámal's minimum angle condition has been widely used for construction of a regular family of triangulations (containing nondegenerating triangles) as well as in convergence proofs for the finite element method ... 
GoalOriented Adaptivity using Unconventional Error Representations
(201709)In GoalOriented Adaptivity (GOA), the error in a Quantity of Interest (QoI) is represented using global error functions of the direct and adjoint problems. This error representation is subsequently bounded above by ... 
Goaloriented adaptivity using unconventional error representations for the 1D Helmholtz equation
(Computers and Mathematics with Applications, 20151231)In this work, the error of a given output functional is represented using bilinear forms that are different from those given by the adjoint problem. These representations can be employed to design novel h, p, and hp ... 
Goaloriented adaptivity using unconventional error representations for the multidimensional Helmholtz equation
(International Journal for Numerical Methods in Engineering, 20170627)In goal‐oriented adaptivity, the error in the quantity of interest is represented using the error functions of the direct and adjoint problems. This error representation is subsequently bounded above by element‐wise error ... 
GoalOriented pAdaptivity using Unconventional Error Representations for a 1D Steady State ConvectionDiffusion Problem
(Procedia Computer Science, 2017)This work proposes the use of an alternative error representation for GoalOriented Adaptivity (GOA) in context of steady state convection dominated diffusion problems. It introduces an arbitrary operator for the computation ... 
Grouplevel progressive alterations in brain connectivity patterns revealed by diffusiontensor brain networks across severity stages in Alzheimer's disease
(Frontiers in Aging Neuroscience, 20170701)Alzheimer’s disease (AD) is a chronically progressive neurodegenerative disease highly correlated to aging. Whether AD originates by targeting a localized brain area and propagates to the rest of the brain across ... 
High order discontinuous finitevolume/finiteelement method for CFD applications
(11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014, 20141231)The proposed method naturally merges the desirable conservative properties and intuitive physical formulation of the widely used finitevolume (FV) technique, with the capability of local arbitrary highorder accuracy and ... 
Highaccuracy adaptive modeling of the energy distribution of a meniscusshaped cell culture in a Petri dish
(Journal of Computational Science, 20151231)Cylindrical Petri dishes embedded in a rectangular waveguide and exposed to a polarized electromagnetic wave are often used to grow cell cultures. To guarantee the success of these cultures, it is necessary to enforce that ... 
Highfrequency analysis of the efficiency of a local approximate DtN2 boundary condition for prolate spheroidalshaped boundaries
(Wave Motion, 20101231)The performance of the secondorder local approximate DtN boundary condition suggested in [4] is investigated analytically when employed for solving highfrequency exterior Helmholtz problems with elongated scatterers. ... 
Highorder mixed weighted compact and noncompact scheme for shock and small length scale interaction
(International Journal of Computer Mathematics, 20131231)It is critical for a numerical scheme to obtain numerical results as accurate as possible with limited computational resources. Turbulent processes are very sensitive to numerical dissipation, which may dissipate the small ... 
Highlyaccurate 5axis flank CNC machining with conical tools
(The International Journal of Advanced Manufacturing Technology, 201804)A new method for $5$axis flank computer numerically controlled (CNC) machining using a predefined set of tappered ballendmill tools (aka conical) cutters is proposed. The space of lines that admit tangential motion of ... 
$hp$Adaptive Simulation and Inversion of Magnetotelluric Measurements
(20151218)The magnetotelluric (MT) method is a passive exploration technique that aims at esti mating the resistivity distribution of the Earth’s subsurface, and therefore at providing an image of it. This process is divided into ...