Now showing items 68-87 of 197

• A FEniCS-HPC framework for multi-compartment Bloch-Torrey models ﻿

(Proceesings of ECCOMAS Congress 2016 VII European Congress on Computational Methods in Applied Sciences and Engineering, 2016-11-30)
In diffusion nuclear magnetic resonance (NMR) and diffusion magnetic resonance imaging (MRI), the multi-compartment Bloch-Torrey equation plays an important role in probing the diffusion characteristics from a nanometer ...
• FEniCS-HPC: Automated predictive high-performance finite element computing with applications in aerodynamics ﻿

(Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2016-01-01)
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 goal-oriented adaptive mesh ...
• Finite element approximation of electromagnetic fields using nonfitting meshes for Geophysics ﻿

(SIAM Journal on Numerical Analysis, 2018-07)
We analyze the use of nonfitting meshes for simulating the propagation of electromagnetic waves inside the earth with applications to borehole logging. We avoid the use of parameter homogenization and employ standard edge ...
• Finite Element Simulations of Logging-While-Drilling and Extra-Deep Azimuthal Resistivity Measurements using Non-Fitting Grids ﻿

(Computational Geosciences, 2018-04-27)
We propose a discretization technique using non-fitting grids to simulate magnetic field-based resistivity logging measurements. Non-fitting grids are convenient because they are simpler to generate and handle than fitting ...
• Finite Element Simulations of Two-phase Flow and Floating Bodies Using FEniCS-HPC ﻿

(13th World Congress in Computational Mechanics WCCM, New York, USA, 2018-07)
We present a variational multiscale stabilized finite element method to solve the variable density incompressible Navier-Stokes equations for the simulation of two-phase flow. We introduce a level-set method based on the ...

(International Journal for Numerical Methods in Engineering, 2019-03)
In goal-oriented adaptive algorithms for partial differential equations, we adapt the finite element mesh in order to reduce the error of the solution in some quantity of interest. In time-dependent problems, this adaptive ...
• Fourier finite element modeling of light emission in waveguides: 2.5-dimensional FEM approach ﻿

(Optics Express, 2015-12-31)
We present a Fourier finite element modeling of light emission of dipolar emitters coupled to infinitely long waveguides. Due to the translational symmetry, the three-dimensional (3D) coupled waveguide-emitter system can ...
• Fractional Laguerre spectral methods and their applications to fractional differential equations on unbounded domain ﻿

(International Journal of Computer Mathematics, 2015-12-31)
In this article, we first introduce a singular fractional Sturm-Liouville problem (SFSLP) on unbounded domain. The associated fractional differential operator is both Weyl and Caputo type. The properties of spectral data ...
• Framework for adaptive fluid-structure interaction with industrial applications ﻿

(International Journal of Materials Engineering Innovation, 2013-12-31)
We present developments in the Unicorn-HPC framework for unified continuum mechanics, enabling adaptive finite element computation of fluid-structure interaction, and an overview of the larger FEniCS-HPC framework for ...
• FREE-FORM TOOLS DESIGN AND FABRICATION FOR FLANK SUPER ABRASIVE MACHINING (FSAM) NON DEVELOPABLE SURFACES ﻿

(MM Science Journal, 2019)
Manufacturing improvements are becoming a real need in industry. In order to satisfy these industrial requirements, they should be targeted in two different directions: new manufacturing processes and surface optimization ...
• Fusion-based variational image dehazing ﻿

(IEEE Signal Processing Letters, 2017-02-01)
We propose a novel image-dehazing technique based on the minimization of two energy functionals and a fusion scheme to combine the output of both optimizations. The proposed fusion-based variational image-dehazing (FVID) ...
• Gauss-Galerkin quadrature rules for quadratic and cubic spline spaces and their application to isogeometric analysis ﻿

(Computer-Aided Design, 2016-07-01)
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 Clough-Tocher macro-triangles ﻿

(Journal of Computational and Applied Mathematics, 2018-10-31)
A numerical integration rule for multivariate cubic polynomials over n-dimensional 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, 2017-03-22)
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, 2018-10-13)
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, 2011-12-31)
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 ...
• Goal-Oriented Adaptivity using Unconventional Error Representations ﻿

(2017-09)
In Goal-Oriented 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 ...
• Goal-oriented adaptivity using unconventional error representations for the 1D Helmholtz equation ﻿

(Computers and Mathematics with Applications, 2015-12-31)
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 ...
• Goal-oriented adaptivity using unconventional error representations for the multi-dimensional Helmholtz equation ﻿

(International Journal for Numerical Methods in Engineering, 2017-06-27)
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 ...
• Goal-Oriented p-Adaptivity using Unconventional Error Representations for a 1D Steady State Convection-Diffusion Problem ﻿

(Procedia Computer Science, 2017)
This work proposes the use of an alternative error representation for Goal-Oriented Adaptivity (GOA) in context of steady state convection dominated diffusion problems. It introduces an arbitrary operator for the computation ...