Browsing Computational Mathematics (CM) by Title
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Energynormbased and goaloriented automatic hp adaptivity for electromagnetics: Application to waveguide Discontinuities
(IEEE Transactions on Microwave Theory and Techniques, 20081231)The finiteelement method (FEM) enables the use of adapted meshes. The simultaneous combination of h (local variations in element size) and p (local variations in the polynomial order of approximation) refinements, i.e., ... 
Enhanced variational image dehazing
(SIAM Journal on Imaging Sciences, 20151231)Images obtained under adverse weather conditions, such as haze or fog, typically exhibit low contrast and faded colors, which may severely limit the visibility within the scene. Unveiling the image structure under the haze ... 
Existence of secondary bifurcations or isolas for PDEs
(Nonlinear Analysis, Theory, Methods and Applications, 20111231)In this paper, we introduce a method to conclude about the existence of secondary bifurcations or isolas of steady state solutions for parameter dependent nonlinear partial differential equations. The technique combines ... 
ExplicitinTime GoalOriented Adaptivity
(Computer Methods in Applied Mechanics and Engineering, 20190415)Goaloriented adaptivity is a powerful tool to accurately approximate physically relevant solution features for partial differential equations. In time dependent problems, we seek to represent the error in the quantity of ... 
Exponential decay of highorder spurious prolate spheroidal modes induced by a local approximate dtn exterior boundary condition
(Progress In Electromagnetics Research B, 20121231)We investigate analytically the asymptotic behavior of highorder spurious prolate spheroidal modes induced by a secondorder local approximate DtN absorbing boundary condition (DtN2) when employed for solving highfrequency ... 
Fast 2.5D Finite Element Simulations of Borehole Resistivity Measurements
(Computational Geosciences, 20180529)We develop a rapid 2.5dimensional (2.5D) finite element method for simulation of borehole resistivity measurements in transversely isotropic (TI) media. The method combines arbitrary highorder $H^1$  and $H$ (curl)conforming ... 
Fast Onedimensional Finite Element Approximation of Geophysical Measurements
(2018)There exist a wide variety of geophysical prospection methods. In this work, we focus on resistivity methods. We categorize these resistivity prospection methods according to their acquisition location as (a) on the surface, ... 
Fast simulation of throughcasing resistivity measurements using semianalytical asymptotic models. Part 1: Accuracy study
(EAGE Workshop on High Performance Computing for Upstream 2014, 20141231)When trying to obtain a better characterization of the Earth's subsurface, it is common to use borehole throughcasing resistivity measurements. It is also common for the wells to be surrounded by a metal casing to protect ... 
A FEniCSHPC framework for multicompartment BlochTorrey models
(Proceesings of ECCOMAS Congress 2016 VII European Congress on Computational Methods in Applied Sciences and Engineering, 20161130)In diffusion nuclear magnetic resonance (NMR) and diffusion magnetic resonance imaging (MRI), the multicompartment BlochTorrey equation plays an important role in probing the diffusion characteristics from a nanometer ... 
FEniCSHPC: Automated predictive highperformance finite element computing with applications in aerodynamics
(Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 20160101)Developing multiphysics finite element methods (FEM) and scalable HPC implementations can be very challenging in terms of software complexity and performance, even more so with the addition of goaloriented adaptive mesh ... 
Finite Element Simulations of LoggingWhileDrilling and ExtraDeep Azimuthal Resistivity Measurements using NonFitting Grids
(Computational Geosciences, 20180427)We propose a discretization technique using nonfitting grids to simulate magnetic fieldbased resistivity logging measurements. Nonfitting grids are convenient because they are simpler to generate and handle than fitting ... 
Finite Element Simulations of Twophase Flow and Floating Bodies Using FEniCSHPC
(13th World Congress in Computational Mechanics WCCM, New York, USA, 201807)We present a variational multiscale stabilized finite element method to solve the variable density incompressible NavierStokes equations for the simulation of twophase flow. We introduce a levelset method based on the ... 
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 ...